Methodology, Investigation, Validation, Flore-Anne Martin

Krystel Ludivine Dion

Nyangoh Timoh

Pierre François Dupré

Henri Azaïs

Sofiane Bendifallah

Cyril Touboul

Yohann Dabi

Olivier Graesslin

Editing, Ludivine Dion Investigation

Validation, Supervision Krystel Nyangoh

Validation, Supervision, Timoh Methodology

Pierre François

Validation, Supervision, Henri Dupré Investigation

Supervision, Sofiane Azaïs Conceptualization

Investigation, Supervision, Cyril Touboul Investigation, Supervision, Yohan Bendifallah Conceptualization

Supervision, Olivier Dabi Conceptualization

Graesslin Investigation

Emilie Raimond Supervision

Supervision, Hélène Costaz Investigation, Supervision, Writing-Review Editing Conceptualization

Yohan Kerbage Investigation

Cyrille Supervision

Huchon Investigation

Camille Mimoun Supervision

Investigation

Martin Supervision

Koskas Investigation

Cherif Supervision

Akladios

Krystel Nyangog Timoh

Emilie Raimond

Hélène Costaz

Yohan Kerbage

Cyrille Huchon

Camille Mimoun

Martin Koskas

Cherif Akladios

Lise Lecointre

Geoffroy Canlorbe

Pauline Chauvet

Lobna Ouldamer

Jean Levêque

Vincent Lavoué
email: vincent.lavoue@chu-rennes.fr.

Vincent Pr

Lavoue

Endometrial cancer of the very elderly: Management and survival in the Francogyn population

Keywords: Investigation, Supervision, Lise Lecointre Conceptualization, Supervision, Geoffroy Canlorbe Investigation, Supervision, Pauline Chauvet Investigation, Supervision, Lobna Ouldamer Conceptualization, Methodology, Supervision, Jean Levêque Conceptualization, Supervision, Vincent Lavoué Conceptualization, Methodology, surgical oncology -endometrial cancer -elderly -adjuvant treatment -survival

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Endometrial cancer (EC) is the most common pelvic gynecologic malignancy in Europe [START_REF] Globocan | Graph production: global Cancer observatory[END_REF], with 8224 new cases per year in France in 2018 [START_REF] Defossez | Estimations nationales de l'incidence et de la mortalité par cancer en France métropolitaine entre 1990 et[END_REF]. It is the fifth deadliest cancer in women (3) with a 76% five-year survival chance in Europe in 2000-2007 [START_REF] Rauh-Hain | Management for Elderly Women With Advanced-Stage, High-Grade Endometrial Cancer[END_REF]. Age is a main risk factor for this disease (3) which explains the increase in incidence observed over the last decades as the population is aging in developed countries [START_REF] Sant | Survival of women with cancers of breast and genital organs in Europe 1999-2007: Results of the EUROCARE-5 study[END_REF]. This progression is expected to continue during the coming years, making EC a major public health concern.

Endometrial cancer in older patients gives rise to several challenges. These patients seem to be at a higher risk of aggressive histologic types [START_REF] Lachance | The effect of age on clinical/pathologic features, surgical morbidity, and outcome in patients with endometrial cancer[END_REF], and are more likely to present with an advanced stage due to late diagnosis [START_REF] Ouldamer | Impact de la prise en charge thérapeutique sur la survie chez les femmes très âgées avec cancer de l'endomètre[END_REF]. Geriatric oncologic care has its own specific issues in terms of global patient evaluation and treatment strategies, taking comorbidities into account, as well as specific nutritional, social, and psychiatric needs. This might lead to disparities in access to appropriate treatment in elderly patients with EC. For example, surgical staging is not always performed when indicated in patients of 80 years or older [START_REF] Uccella | Laparoscopic vs. open treatment of endometrial cancer in the elderly and very elderly: An age-stratified multicenter study on 1606 women[END_REF][START_REF] Bishop | Pathologic and Treatment Outcomes Among a Geriatric Population of Endometrial Cancer Patients: An NRG Oncology/Gynecologic Oncology Group Ancillary Data Analysis of LAP2[END_REF], and this has been shown to negatively influence survival in a British cohort [START_REF] Truong | The effects of age and comorbidity on treatment and outcomes in women with endometrial cancer[END_REF]. Similarly, previous studies have reported that elderly patients receive less aggressive treatment than their younger counterparts for a similar histologic stage [START_REF] Torgeson | Disparities in care for elderly women with endometrial cancer adversely effects survival[END_REF], especially concerning adjuvant treatment such as radiotherapy [START_REF] Uccella | Laparoscopic vs. open treatment of endometrial cancer in the elderly and very elderly: An age-stratified multicenter study on 1606 women[END_REF][START_REF] Truong | The effects of age and comorbidity on treatment and outcomes in women with endometrial cancer[END_REF][START_REF] Ramesh | Implications of aging in surgical oncology[END_REF] or chemotherapy when indicated. Moreover, these treatments are not significantly associated with an increase in cancer-specific complications when performed [START_REF] De Boer | Adjuvant chemoradiotherapy versus radiotherapy alone for women with high-risk endometrial cancer (PORTEC-3): final results of an international, open-label, multicentre, randomised, phase 3 trial[END_REF], and there is a known benefit for patients with high-risk tumors which are overrepresented in elderly populations [START_REF] Rousselin | Patterns of care and the survival of elderly patients with high-risk endometrial cancer: A case-control study from the FRANCOGYN group[END_REF].

Overall, despite the increase in the proportion of very elderly patients with EC, there are still no specific guidelines on diagnosis and treatment strategies. The few studies involving this population suggest that they lack access to staging and treatment options compared to standard care guidelines, resulting in a poorer outcome [START_REF] Lachance | The effect of age on clinical/pathologic features, surgical morbidity, and outcome in patients with endometrial cancer[END_REF][START_REF] Ballester | Detection rate and diagnostic accuracy of sentinel-node biopsy in early stage endometrial cancer: a prospective multicentre study (SENTI-ENDO)[END_REF]. Therefore, the objective of this study was to describe treatment management and survival in patients with EC aged 80 years and older in a large French cohort to identify risk factors of poor prognosis.

J o u r n a l P r e -p r o o f

Methods

○ Study population

We retrospectively analyzed data collected from a database of patients with EC who received primary surgical treatment between 1999 and 2019. The data were obtained from 10 institutions in France who maintain EC databases (Tours, Tenon, Dijon, Rennes, Lille, Reims, Creteil, Poissy, Bondy, and Clermont Ferrand Tertiary Hospitals) and from the SENTI-ENDO trial [START_REF] Pecorelli | Revised FIGO staging for carcinoma of the vulva, cervix, and endometrium[END_REF]. Each of these institutions have high gynecologic oncologic caseloads and perform more than 70 gynecologic oncologic surgical procedures per year. The research protocol was approved by the Institutional Review Board of the National College of French Obstetricians and Gynecologists (CNGOF) in 2014 (CEROG 2014-GYN-020). For this study, patients 80 years of age and older were selected.

○ Collected data

All the patients had undergone a preoperative endometrial biopsy and abdominopelvic magnetic resonance imaging unless contraindicated, in which case a computed tomography scan was performed.

The demographic and clinical data collected included: age, body mass index (BMI, calculated as weight in kilograms divided by the square of height in meters), and comorbidities (hypertension, diabetes, menopausal hormone therapy, history of breast cancer). Surgical data (surgical approach, nodal staging), histologic data (subtype, grade and stage based on the International Federation of Gynaecology and Obstetrics (FIGO 2009)) [START_REF] Concin | ESGO/ESTRO/ESP guidelines for the management of patients with endometrial carcinoma[END_REF], risk group based on the European Society for Medical Oncology (ESMO), European SocieTy for Radiotherapy & Oncology (ESTRO) and European Society of Gynaecological Oncology (ESGO) classification [START_REF] Querleu | Clinical practice guidelines for the management of patients with endometrial cancer in France: recommendations of the Institut National du Cancer and the Société Française d'Oncologie Gynécologique[END_REF], and adjuvant therapy were also collected.

J o u r n a l P r e -p r o o f

Lymph nodes were considered positive when macro-or micrometastases were present. A tumor was considered to have lympho-vascular space invasion (LVSI) when tumor emboli were found within a space clearly lined by endothelial cells on a hematoxylin and eosin-stained section.

The women underwent primary surgical treatment including at least total hysterectomy with bilateral salpingo-oophorectomy, with or without nodal staging (pelvic and paraaortic lymphadenectomy) according to the guidelines in place at the time of diagnosis and at the surgeon's discretion. The European guidelines recommend pelvic and paraaortic lymph node surgical staging for high-risk groups. Adjuvant therapy included vaginal brachytherapy (VBT), and/or external beam radiotherapy (EBRT), and/or chemotherapy (CT), and clinical follow-up.

Adjuvant therapy was administered on an individual basis at the discretion of a multidisciplinary committee based on the European guidelines [START_REF] Querleu | Clinical practice guidelines for the management of patients with endometrial cancer in France: recommendations of the Institut National du Cancer and the Société Française d'Oncologie Gynécologique[END_REF]. Missing data about the ESMO/ESGO/ESTRO risk groups was imputed as follows when the information was available: low risk (stage 1A grade 1 or 2 histologic type 1 tumors LVSI negative or focal), intermediate risk (stage 1A grade 3 histologic type 1 tumors LVSI negative or focal, or stage 1B grade 1 or 2 histologic type 1 tumors LVSI negative or focal, and stage 1A histologic type 2 tumors without myometrial invasion), highintermediate risk (HIR) (stage 1 endometrioid type 1 tumors with substantial and not focal positive LVSI, or stage 1B grade 3 tumors, and stage 2 tumors), high risk (stage 3 and 4a tumors without residual disease, and type 2 tumors with myometrial invasion), and advanced (stage 4b tumors, or stage 3 and 4a tumors with residual disease) [START_REF] Querleu | Clinical practice guidelines for the management of patients with endometrial cancer in France: recommendations of the Institut National du Cancer and the Société Française d'Oncologie Gynécologique[END_REF]. Clinical follow-up consisted of physical examinations and the use of imaging techniques according to the findings.

The main outcome measures were overall survival (OS) (calculated from the date of surgery to death, whether related or unrelated to cancer) or date of last follow-up for surviving patients, and disease-free survival (DFS) (calculated as time from the date of surgery to cancer recurrence).

Biopsy or imaging studies were used to diagnose recurrence which was defined as local or distant relapse.

J o u r n a l P r e -p r o o f ○ Statistical analyses

Descriptive quantitative continuous variables are expressed as the mean (± Standard Deviation [SD]) and median [range] when indicated. Descriptive qualitative variables are presented as frequencies and percentages. Women who were alive and without recurrence were censored at the date of last follow-up in the DFS analyses. Median survival time as well as survival distribution was calculated using the Kaplan-Meier survival method, and a log-rank test was used for survival comparison. We confirmed proportionality of hazards was for all variables studied thanks to log minus log plot representation. Effects were expressed as hazard ratios (HRs) with 95% confidence intervals (95%CIs). HR was considered statistically significant when the 95%CI was not 1. Data were managed in an Excel database (Microsoft, Redmond, WA, USA) and analyzed using software R © (version 3.5.0), which is available online.

J o u r n a l P r e -p r o o f

Results

○ Study population

Of the 1647 women with EC who received primary surgical treatment during the study period, 184 (11.2%) were ≥ 80 years old and comprised the study population. The mean age of the studied population was 84 years old (± 3.34). Eighty-six of these women had a BMI ≥ 25 kg/m 2 (58.9 %) and 90 had had two pregnancies or more (61.2 %). Ninety-eight had a medical history of hypertension (63.2 %), 39 of diabetes (22.7%), and 14 of breast cancer (10.4 %). Twelve of them had previously taken hormone replacement therapy (9.4%). The demographic and clinical characteristics of our population are reported in Table 1.

○ Histologic characteristics

The tumor characteristics are reported in Tables 2 and3. Thirty-six patients (20.2%) had a nonendometrioid tumor histology. Fifty-eight (38.2%) patients were in the ESMO/ESTRO/ESGO high-risk group. LVSI was present in 55 tumors LVSI (36.7%) and myometrial invasion in 91 (58%). Out of the 184 patients, 61 (50.8%) did not undergo lymphadenectomy. Of the 59 patients (86.8%) who underwent pelvic lymphadenectomy, six (10.2%) and had pelvic lymph node metastasis. Of the five patients (9.1%) who underwent paraaortic lymphadenectomy, one (20%) had paraaortic lymph node metastasis.

○ Surgical characteristics and adjuvant treatment

The surgical procedures and adjuvant treatments are reported in Table 4. Most surgeries were minimally invasive (N = 100, 57.8%), either robotic or laparoscopic. Of the 95 patients who had a formal or relative indication, 83 (45.1%) received adjuvant therapy. Overall, 69.1% patients were treated according to the standard care guidelines for EC. Fifty-three (91.4%) patients were undertreated with regards to chemotherapy. Nineteen of the 95 patients (30.2%) with a formal or relative indication of either VBRT or EBR, were undertreated.

J o u r n a l P r e -p r o o f o Survival analyses

The univariate analyses of survival (OS, DFS) are reported in Tables 1 to 4 and illustrated in Figure 1.

Five patients were excluded from OS analyses and 43 from DFS analyses because of lack of data on vital status or relapse at the time of last follow-up. Forty-nine patients were lost to follow-up (27.37 %). Thirty-three patients (25.4%) died during the follow-up period and 26 patients relapsed (18.4%).

The median follow-up of the study population was 15.27 months (range 4.85-28.79). The median OS and DFS was 16.43 months (range 6.27-24.86) and 13.55 months (range 4.49-26.6), respectively. One-year OS was 90.2 % (+/-3.2%), and 5-year OS was 49.6 % (+/-7.8%). The DFS rate at 1 year was 89 % (3.2%) and 67.7% (+/-6%) at 5 years. ). The 5-year DFS rate was 88.9 % (+/-7.4%) when the indication for chemotherapy was respected versus 53.8 % (+/-10.6%) (p = 0.00044). There was no statistically significant association between DFS and medical history or surgical route.

The comparative analyses results did not change and remained statistically significant when using the ESMO/ESGO/ESTRO recommendations from 2016 (3) (see supplementary material).

J o u r n a l P r e -p r o o f

Discussion

In this study, we observed that underuse of chemotherapy in spite of recommendation is associated with lower OS and DFS in the very elderly (aged 80 and over) with EC. Moreover, in this population we observed that lower OS and DFS are significantly associated with high-risk EC as defined by ESMO/ESTRO/ESGO, as well as a grade 3 histologic type and LVSI. Myometrial invasion was also significantly associated with a lower OS.

Our results show that very elderly patients with EC are less likely to receive chemotherapy and that this is associated with poorer OS and DFS rates. This inappropriate use of adjuvant chemotherapy is probably due to the presence of comorbidities in this group. Furthermore, elderly patients tend to be diagnosed with more advanced disease for which chemotherapy is indicated. However, we found that recommendation for chemotherapy was a risk factor for early recurrence whereas the actual use of chemotherapy was not. This might suggest that patients who actually receive chemotherapy when needed undergo a thorough selection process which introduces a bias in our survival results: we might indirectly be assessing the association of survival with performance status and not the treatment itself [START_REF] Ramesh | Implications of aging in surgical oncology[END_REF]. Recent literature is rather clear about the fact that advanced age itself is not an independent factor for poor prognosis in EC [START_REF] Fleming | Is older age a poor prognostic factor in stage I and II endometrioid endometrial adenocarcinoma?[END_REF], and neither is toxicity of radio-and chemotherapy [START_REF] Fiorentino | Do comorbidity influences acute toxicity and outcome in elderly patients with endometrial cancer treated by adjuvant radiotherapy plus brachytherapy?[END_REF]. Nonetheless, Bishop et al observed that the use of radiation as an adjuvant treatment dropped significantly after 80 years of age (9). Clark et al showed that only 50 % of their patients aged 70 and over received the adjuvant treatment when recommended, and they found that only 30 % of them are eligible in trials due to excluding comorbidities [START_REF] Clark | Adjuvant Treatment and Clinical Trials in Elderly Patients With Endometrial Cancer: A Time for Change[END_REF]. Conversely, Driver et al showed that frailty was more predictive of survival than comorbidities [START_REF] Driver | Frailty measure is more predictive of outcomes after curative therapy for endometrial cancer than traditional risk factors in women 60 and older[END_REF]. According to Eggeman et al, these two parameters were the main reason why elderly patients were undertreated in EC management [START_REF] Eggemann | Management of elderly women with endometrial cancer[END_REF].

The rate of robotic surgery in our study was quite low compared to the available literature, even in the very elderly [START_REF] Lavoue | Impact of robotics on the outcome of elderly patients with endometrial cancer[END_REF][START_REF] Zeng | Outcome of robotic surgery for endometrial cancer as a function of patient age[END_REF][START_REF] Lowe | Robotic surgical management of endometrial cancer in octogenarians and nonagenarians: analysis of perioperative outcomes and review of the literature[END_REF]. This can be explained by the fact that our study started when robotic surgery was just beginning and that it progressively became more widespread during the study period. Furthermore, the recent literature is not consensual on postoperative complications when using minimally invasive surgery in patients with EC aged 80 and older [START_REF] Bishop | Pathologic and Treatment Outcomes Among a Geriatric Population of Endometrial Cancer Patients: An NRG Oncology/Gynecologic Oncology Group Ancillary Data Analysis of LAP2[END_REF][START_REF] Zeng | Outcome of robotic surgery for endometrial cancer as a function of patient age[END_REF][START_REF] Bogani | Perioperative and long-term outcomes of laparoscopic, open abdominal, and vaginal surgery for endometrial cancer in patients aged 80 years or older[END_REF]. However, J o u r n a l P r e -p r o o f there do not seem to be more perioperative complications in this already very fragile population [START_REF] Bogani | Perioperative and long-term outcomes of laparoscopic, open abdominal, and vaginal surgery for endometrial cancer in patients aged 80 years or older[END_REF] compared with laparotomy or a vaginal approach. Moreover, more lymphadenectomies could be performed with minimally invasive surgery when indicated with specific techniques such as the use of indomethacin green for sentinel node detection in high and high-intermediate risk endometrial cancer [START_REF] Querleu | Clinical practice guidelines for the management of patients with endometrial cancer in France: recommendations of the Institut National du Cancer and the Société Française d'Oncologie Gynécologique[END_REF]. Thus, minimally invasive surgery would appear to be highly suitable to stage fragile patients such as the very elderly to determine optimal treatment (28), without a higher risk of conversion to laparotomy [START_REF] Eggemann | Management of elderly women with endometrial cancer[END_REF].

Finally, the latest recommendations [START_REF] Querleu | Clinical practice guidelines for the management of patients with endometrial cancer in France: recommendations of the Institut National du Cancer and the Société Française d'Oncologie Gynécologique[END_REF] introduce a more personalized approach with the use of molecular classification, which could also be particularly relevant in elderly patients with EC.

The proportion of elderly patients aged 80 and over in our population was similar to that observed in a North American study (11.17% vs. 10.4%, respectively) [START_REF] Gayar | Hysterectomy for uterine adenocarcinoma in the elderly: Tumor characteristics, and long-term outcome[END_REF]. Furthermore, we observed similar rates of diabetes mellitus and hypertension as in Lowe et al's population of patients aged 80 or more [START_REF] Bogani | Perioperative and long-term outcomes of laparoscopic, open abdominal, and vaginal surgery for endometrial cancer in patients aged 80 years or older[END_REF], similar proportions of stage I, II and III disease, and the same rate of patients undergoing pelvic lymph node dissection (89%). However, only 9% patients in our study underwent paraaortic lymph node dissection, versus 59% in the Lowe et al study. An American study also found LVSI and grade 3 tumors to be independent factors for recurrence in patients aged 75 and older [START_REF] Eggemann | Management of elderly women with endometrial cancer[END_REF].

The main strength of our study is that it is, to the best of our knowledge, the third largest sample size of women with EC aged 80 and older after Lowery et al and Wright et al with their studies on the American Surveillance, Epidemiology and End Results (SEER) population, and the biggest in France. Moreover, few European studies have focused on the very elderly patient with EC. Most studies describe patients aged 65 or 70 and older [START_REF] Driver | Frailty measure is more predictive of outcomes after curative therapy for endometrial cancer than traditional risk factors in women 60 and older[END_REF][START_REF] Bourgin | Endometrial cancer in elderly women: Which disease, which surgical management? A systematic review of the literature[END_REF][START_REF] Racin | Lymphadenectomy in elderly patients with high-intermediate-risk[END_REF]32), or only deal with specific histologic type or risk stage [START_REF] Ballester | Detection rate and diagnostic accuracy of sentinel-node biopsy in early stage endometrial cancer: a prospective multicentre study (SENTI-ENDO)[END_REF]. However, some limitations of this study deserve to be mentioned. Retrospective data inherently brings a classification bias. We do not know the participation rate and cannot rule out a selection bias. Our results are limited by the missing data, first concerning DFS. Nevertheless, OS seems to be a relevant endpoint in our population. Even with tumor recurrence, elderly patient might die J o u r n a l P r e -p r o o f from other reasons than cancer. Furthermore, elderly patient could die from treatment complications or autonomy loss due to inappropriate treatment or cancer. Lastly, the elderly patients have less good clinical follow up with potential missed tumor recurrence.

Other unmeasured variables such as cancer-specific survival, geriatric assessment, quality of life and reasons for lack of treatment could yield interesting information to fine-tune our results. Indeed, frailty and geriatric assessment seem to be associated with respect towards adjuvant treatment indication: therapeutic decision changed in 21% of patients after geriatric evaluation in a previous French study (33), and up to a third of cases in an American study [START_REF] Eggemann | Management of elderly women with endometrial cancer[END_REF]. Specific scores, such as the Geriatric Vulnerability Score (GVS), which can be used for global assessment, optimization and feasibility of chemotherapy in ovarian cancer (34), could improve treatment management. Moreover, we do not know whether chemotherapy was not performed because it was not suggested by the healthcare professionals or refused by the patients. Details on chemotherapy such as number of cycles, type and specific complications were not available in our study, which would also have been informative to look into. Finally, as European guidelines changed several times during the study period [START_REF] Colombo | ESMO-ESGO-ESTRO Consensus Conference on Endometrial Cancer: diagnosis, treatment and follow-up †[END_REF][START_REF] Concin | ESGO/ESTRO/ESP guidelines for the management of patients with endometrial carcinoma[END_REF] and since [START_REF] Querleu | Clinical practice guidelines for the management of patients with endometrial cancer in France: recommendations of the Institut National du Cancer and the Société Française d'Oncologie Gynécologique[END_REF], we can expect a chronological bias which calls for cautious interpretation of our results, despite the recent setting. We minimized this bias by performing supplementary analyses using the recommendations from ESMO/ESGO/ESTRO 2016 conference (3), which did not change our results. The latest recommendations from ESMO/ESTRO/ESGO now add tumor molecular classification (POLE or polymerase epsilon catalytic subunit gene, MSS/MSI or microsatellite instability and p53) as an indication criterion for adjuvant treatment and risk of recurrence. This would be an interesting variable to add to our study to analyze the management of EC in this population.

J o u r n a l P r e -p r o o f

Conclusion

Our study adds to the available literature on the management of EC in very elderly patients. Our results on OS and DFS in this French population confirm the risk factors stated by ESMO/ESTRO/ESGO. We found that very elderly patients might be at higher risk of early death or recurrence when the indication for chemotherapy is not respected. This reinforces the recent guidelines stating that age and comorbidities should not solely define treatment strategies as this population of patients often presents high risk and aggressive tumors, which require active and global treatment. Medical staff can further support their patients by informing them that adjuvant chemotherapy can improve survival rates even after 80 years old. Other studies including tumor molecular classification, frailty, and comprehensive geriatric assessment in this specific increasing portion of older patients should take place to evaluate these findings furthermore. 3. Postoperative tumor and lymph node characteristics in FRANCOGYN patients with endometrial cancer aged 80 or older (N=184) and their association with overall survival (OS) and disease-free survival (DFS) according to the Kaplan-Meier method and log-rank test (effect expressed as hazard ratio and its 95% confidence interval). NA: Not available

J o u r n a l P r e -p r o o f

  The median OS was significantly lower for patients in the ESMO/ESTRO/ESGO high-risk group (HR = 3.78, 95%CI[1.28-11.36]) compared with the low-risk group, as well as in the histologic grade 3 group (HR = 2.6, 95%CI [1.07-6.3]) compared with the grade 1 group. Myometrial invasion and LVSI were significantly associated with a lower median OS (respectively, HR = 2.24, 95%CI [1.04-4.84] and HR = 3.35, 95%CI[1.44-7.79]). Inappropriate or underuse of chemotherapy was significantly associated with a lower median OS of 12.6 months[3.73-24] versus 17.3 months[7.93-41.77] when used appropriately (HR = 4.14, 95%CI [1.62-10.56]). The 5-year OS rate was 66.4 % (+/-11.5%) when the indication for chemotherapy was respected versus 27.6 % (+/-12%) (p = 0.0013). There was no statistically significant association between OS and medical history, surgical route, or respect of an indication for another adjuvant treatment in our population.The median DFS was significantly lower in patients in the ESMO/ESTRO/ESGO high-risk group compared with the low-risk group (HR = 12.8, 95%CI [1.69-97.06]), as well as in the histologic grade 3 group compared with the grade 1 group (HR = 3.33, 95%CI[1.25-8.88]). LVSI was significantly associated with a lower median DFS (HR = 5.56, 95%CI[2.17-14.25]). In the study population, use of chemotherapy and EBR as adjuvant treatments tended to be associated with a J o u r n a l P r e -p r o o f lower median DFS (respectively HR = 4.15, 95%CI [0.94-81.34] and HR = 2.83, 95%CI [0.99-7.99]), although not statistically significant. However, inappropriate or underuse of chemotherapy was significantly associated with a lower median DFS of 10.83 months[3.73-24] versus 17.3 months[7.93-28.5] when used appropriately (HR = 9.04, 95%CI[2.04-40.12]

  endometrial cancer: Time to move from personalized cancer medicine to personalized patient medicine! Eur J Surg Oncol. 2019;45(8):1388-95. 32. Vaknin Z, Ben-Ami I, Schneider D, Pansky M, Halperin R. A Comparison of Perioperative Morbidity, Perioperative Mortality, and Disease-Specific Survival in Elderly Women (≥70 Years) Versus Younger Women (<70 Years) With Endometrioid Endometrial Cancer: International Journal of Gynecological Cancer. 2009 Jul;19(5):879-83. 33. Caillet P, Canoui-Poitrine F, Vouriot J, Berle M, Reinald N, Krypciak S, et al. Comprehensive Geriatric Assessment in the Decision-Making Process in Elderly Patients With Cancer: ELCAPA Study. JCO. 2011 Sep 20;29(27):3636-42. 34. Falandry C, Savoye AM, Stefani L, Tinquaut F, Lorusso D, Herrstedt J, et al. EWOC-1: A randomized trial to evaluate the feasibility of three different first-line chemotherapy regimens for vulnerable elderly women with ovarian cancer (OC): A GCIG-ENGOT-GINECO study. JCO. 2019 May 20;37(15_suppl):5508-5508 J o u r n a l P r e -p r o o f

Figure 1 .VBT

 1 Figure 1. Survival probability graphs of FRANCOGYN patients with endometrial cancer aged 80 or older (N=184) according to the Kaplan Meier method. Time is expressed as months. a. Overall survival probability graph. b: disease-free survival probability graph. c: comparison of overall survival probability of FRANCOGYN patients with endometrial cancer aged 80 or older (N=184) according to the Kaplan Meier method and log-rank test, depending on appropriate use of chemotherapy according to the 2021 ESMO/ESTRO/ESGO guidelines. d: Comparison of disease-free survival probability of FRANCOGYN patients with endometrial cancer aged 80 or older (N=184) according to the Kaplan Meier method and logrank test, depending on appropriate use of chemotherapy according to the 2021ESMO/ESTRO/ESGO guidelines. J o u r n a l P r e -p r o o f

Table 1 .

 1 Medical history and clinical data of FRANCOGYN patients with endometrial cancer aged 80 or older (N=184) and their association to overall survival (OS) and disease-free survival (DFS) according to the Kaplan-Meier method and log-rank test (effect expressed as hazard ratio and its 95% confidence interval). NA: Not available, BMI: Body Mass Index

	Tables and figures
	Variable		Mean	Standard	OS	DFS
				Deviation
	Age (years)		84	3.3	1.07 [0.96-1.19] 0.99 [0.87-1.14]
	BMI (kg/m2)		27.25	6	0.97 [0.91-1.04] -
			N	%	OS	DFS
		< 18	8	5.5	Ref.	Ref.
		18 -25	52	35.6	-	0.3 [0.03-3.33]
		> 25	86	58.9	-	1.18 [0.15-9.14]
		NA (N)	38	-	-	-
	Parity	0	27	18.4	Ref.	Ref.
		1	30	20.4	1.66 [0.52-5.27] 0.38 [0.07-1.94]
		2 or more 90	61.2	1.03 [0.37-2.84] 0.90 [0.32-2.51]
		NA (N)	37	-	-	-
	Hormone replacement therapy No	116	90.6	Ref.	Ref.
		Yes	12	9.4	1.75 [0.38-8.03] 0.92 [0.12-7.07]
		NA	56	-	-	-
	Hypertension	No	57	36.8	Ref.	Ref.
		Yes	98	63.2	0.96 [0.46-2]	0.47 [0.21-1.09]
		NA	29	-	-	-
	Diabetes	No	133	77.3	Ref.	Ref.
		Yes	39	22.7	0.60 [0.23-1.56] 0.54 [0.16-1.82]
		NA	12	-	-	-
	History of breast cancer	No	121	89.6	Ref.	Ref.
		Yes	14	10.4	1.21 [0.46-3.16] 0.56 [0.13-2.4]
		NA	49	-	-	-

Table

Table 4. Treatment characteristics (surgical route, adjuvant treatment indication and received treatment) of FRANCOGYN patients with endometrial cancer aged 80 or older (N=184) and their association with overall survival (OS) and disease-free survival (DFS) according to the Kaplan-Meier method and log-rank test (effect expressed as hazard ratio and its 95% confidence interval


Dianlin Hu
email: dianlin@seu.edu.cn

Yikun Zhang

Guotao Quan
email: guotao.quan@unitedimaging.com

Jun Xiang
email: jun.xiang@unitedimaging.com

Gouenou Coatrieux
email: gouenou.coatrieux@telecom-bretagne.eu

Shouhua Luo
email: luoshouhua@seu.edu.cn

Jean-Louis Coatrieux

Xu Ji
email: xuji@seu.edu.cn

Hongbin Han
email: hanhongbin@bjmu.edu.cn

Yang Chen

CROSS: Cross-Domain Residual-Optimization-Based Structure Strengthening Reconstruction for Limited-Angle CT

Keywords: processing, residual-error space regularization, structure enhancement network, data consistency, limited-angle CT reconstruction

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

-RAY Computed Tomography (CT) has been widely used in medical diagnosis, industrial non-destructive detection, and security checks [START_REF] Wang | An outlook on x-ray CT research and development[END_REF]. However, CT images will encounter severe noise and artifacts in non-ideal environments. Particularly, in the practical scenarios [START_REF] Bachar | Image quality and localization accuracy in C-arm tomosynthesis-guided head and neck surgery[END_REF][START_REF] Gao | Direct filtered-backprojection-type reconstruction from a straight-line trajectory[END_REF][START_REF] Tingberg | X-ray tomosynthesis: a review of its use for breast and chest imaging[END_REF], the measurements cannot be collected from the full-angle range. For example, in radiation therapy (RT), cone-beam computed tomography (CBCT) can be used for patient setup and dose calculation [START_REF] Jaffray | Flat-panel cone-beam computed tomography for image-guided radiation therapy[END_REF]. However, CBCT takes a long time (usually 60s) to rotate one circle, which may lead to motion artifacts caused by patient or organ movements. Limited-angle scanning mode can accelerate the acquisition time and proportionally reduce the radiation dose. Consequently, the obtained limited-angle projection data will result in degraded images with severe wedge artifacts and significantly lower practical values. To tackle this problem, many advanced reconstruction methods have been proposed, which can be divided into four categories: analytical methods, iterative (IR) optimization methods, deep learning (DL)-based methods, and deep iterative methods.

Filtered Back Projection (FBP) is a classical analytical method and has been commonly employed in CT reconstruction. FBP can fast provide high-quality images when the projection data is complete and noiseless. Nevertheless, for limited-angle CT, FBP will introduce shadow artifacts and lose tissue details.

To guarantee the consistency between reconstruction images and projection data and further improve the performance of FBP, numerous IR methods have been proposed for limited-angle CT [START_REF] Van De Sompel | A systematic performance analysis of the simultaneous algebraic reconstruction technique (SART) for limited angle tomography[END_REF]. Later, various prior regularizations were introduced into CT imaging to improve the performance in artifact removal and tissue restoration [START_REF] Hu | SISTER: Spectral-Image Similarity-Based Tensor With Enhanced-Sparsity Reconstruction for Sparse-View Multi-Energy CT[END_REF][START_REF] Wu | A High-Quality Photon-Counting CT Technique Based on Weight Adaptive Total-Variation and Image-Spectral Tensor Factorization for Small Animals Imaging[END_REF]. Considering the sparse property of image gradients, Sidky et al. applied the total variation (TV) minimization to limited-angle CT and demonstrated improvements compared to the algebraic reconstruction technique (ART) [START_REF] Sidky | Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT[END_REF]. Further, noticing the isotropic in TV was unfit for limited-angle CT, Chen et

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ACCEPTED MANUSCRIPT / CLEAN COPY developed an anisotropic TV (TV) based IR method [START_REF] Chen | A limited-angle CT reconstruction method based on anisotropic TV minimization[END_REF] for better edge preservation and wedge artifact reduction. To more effectively utilize image sparsity, Wang et al. incorporated the reweighted technique into ATV (RwATV) [START_REF] Wang | Reweighted Anisotropic Total Variation Minimization for Limited-Angle CT Reconstruction[END_REF]. Experiments showed that RwATV could generate better reconstructions with clearer structures, sharper edges, and fewer artifacts. However, RwATV maybe fail to eliminate large streaks because it was scale-dependent. Therefore, the scale-space ATV was researched to reduce the streak artifacts at different scales [START_REF] Huang | Scale-Space Anisotropic Total Variation for Limited Angle Tomography[END_REF]. L0-norm was another important prior constraint in medical imaging and it can provide a more sparse solution than TV [START_REF] Wu | Low-dose spectral CT reconstruction using image gradient ℓ0-norm and tensor dictionary[END_REF].

For example, to overcome the weakness of TV in over-smoothing low-contrast structures, Sun et al. attempted to introduce L0-norm optimization into the IR method and achieved obvious promotion [START_REF] Sun | Image reconstruction from few views by ℓ0-norm optimization[END_REF]. Then, Wang et al. paid attention to punishing the wavelet coefficients based on the L0-norm and outperformed classical CT reconstruction in metal artifact suppression [START_REF] Wang | Error bounds and stability in the L0 regularized for CT reconstruction from small projections[END_REF]. To better improve the performance in feature restoration, Xu et al. combined the L0-norm and dictionary learning (L0DL) for limited-angle CT. Both simulated and preclinical datasets claimed the proposed L0DL generated high-quality images with more clear structures [START_REF] Xu | Limited-Angle X-Ray CT Reconstruction Using Image Gradient ℓ₀-Norm With Dictionary Learning[END_REF].

In addition, non-local similarity [START_REF] Wu | Block matching frame based material reconstruction for spectral CT[END_REF], low-rank [START_REF] Wu | Non-Local Low-Rank Cube-Based Tensor Factorization for Spectral CT Reconstruction[END_REF], and sparse representation [START_REF] Liu | Discriminative feature representation to improve projection data inconsistency for low dose CT imaging[END_REF][START_REF] Wang | Spectral-Image Decomposition With Energy-Fusion Sensing for Spectral CT Reconstruction[END_REF] were also commonly used as prior knowledge in IR algorithms for CT reconstruction and achieved competitive results. Although prior-regularized IR methods can improve CT images, they had several shortcomings, including high computational cost, sensitive hyper-parameter settings, and hand-crafted regularization terms.

Recently, DL-based methods have been successfully applied to the field of medical imaging [START_REF] Hu | TRANS-Net: Transformer-enhanced Residual-error AlterNative Suppression Network for MRI Reconstruction[END_REF][START_REF] Huang | DU-GAN: Generative Adversarial Networks With Dual-Domain U-Net-Based Discriminators for Low-Dose CT Denoising[END_REF][START_REF] Zhang | TIME-Net: Transformer-Integrated Multi-Encoder Network for limited-angle artifact removal in dual-energy CBCT[END_REF]. Especially, convolutional neural network (CNN)-based methods brought more promising results than traditional reconstruction images [START_REF] Zhang | CLEAR: Comprehensive Learning Enabled Adversarial Reconstruction for Subtle Structure Enhanced Low-Dose CT Imaging[END_REF][START_REF] Hu | PRIOR: Prior-Regularized Iterative Optimization Reconstruction for 4D CBCT[END_REF][START_REF] Zhang | CD-Net: Comprehensive Domain Network With Spectral Complementary for DECT Sparse-View Reconstruction[END_REF][START_REF] Zhang | DREAM-Net: Deep Residual Error Iterative Minimization Network for Sparse-View CT Reconstruction[END_REF]. Aided by the powerful feature extraction ability of the CNN model, Gu et al. directly predict the artifacts in the wavelet domain from the degraded images and performed well in artifact reduction [START_REF] Gu | Multi-Scale Wavelet Domain Residual Learning for Limited-Angle CT Reconstruction[END_REF]. Similarly, Li et al. proposed an inpainting network to restore the missing projection data for limited-angle scanning. Then, the classical FBP or IR methods were employed to reconstruct CT images from the recovered projection data. Experiments stated that serious artifacts can be effectively reduced [START_REF] Ziheng | A sinogram inpainting method based on generative adversarial network for limited-angle computed tomography[END_REF]. Unlike the above single-domain-based methods, Anirudh et al. adopted the generative adversarial network to directly map the incomplete fan-beam sinogram data into the CT images and obtained impressive results [START_REF] Anirudh | Lose the views: Limited angle CT reconstruction via implicit sinogram completion[END_REF]. Meanwhile, Würfl et al. explored an FBP-type algorithm with a novel back-projection layer for cone-beam geometry to improve the calculating efficiency. Evaluations demonstrated this scheme outperformed analytical methods [START_REF] Würfl | Deep Learning Computed Tomography: Learning Projection-Domain Weights From Image Domain in Limited Angle Problems[END_REF]. Innovatively, Huang et al. introduced a data-consistent artifact reduction (DCAR) method based on the deep learning prior, which first inpainted the missing projection data and then iteratively improve the reconstruction images [START_REF] Huang | Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior[END_REF] with IR methods. To strengthen edge preservation, Hu et al. proposed a multi-stage reconstruction framework (SPECIAL) for limited-angle CT. Simulated and real experiments suggested that the SPECIAL method outperformed existing competitive algorithms in artifact removal and detail recovery [START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF].

Further, dual-domain-based methods have attracted great attention because of their superior performance. By jointly constraining the projection data and image data, these methods outperform single-domain-based methods. For example, to make full use of complementary correlations between the image domain and projection domain, a hybrid domain network (hdNet) was developed for limited-angle CT. Experiments suggested that the hdNet works well in eliminating artifacts [START_REF] Zhang | Artifact removal using a hybrid-domain convolutional neural network for limited-angle computed tomography imaging[END_REF]. Besides, Jiao et al. developed an intelligent back-projection network (iBP-Net) for CT reconstruction and could provide visually improved results [START_REF] Jiao | A Dual-Domain CNN-Based Network for CT Reconstruction[END_REF]. And Zhou et al. employed the dual-domain method for metal artifact reduction in low-dose CT [START_REF] Zhou | DuDoUFNet: Dual-Domain Under-to-Fully-Complete Progressive Restoration Network for Simultaneous Metal Artifact Reduction and Low-Dose CT Reconstruction[END_REF]. Considering the instabilities of deep learning methods in medical imaging, Wu et al. specifically designed an Analytic compressed iterative deep (ACID) method to stabilize the deep tomography reconstruction [START_REF] Wu | Stabilizing deep tomographic reconstruction: Part A. Hybrid framework and experimental results[END_REF][START_REF] Wu | Stabilizing deep tomographic reconstruction: Part B. Convergence analysis and adversarial attacks[END_REF]. Based on ACID, Wu et al. integrated the residual-domain processing technique into the dual-domain method for sparse-view CT and works well in artifact reduction and detail preservation [START_REF] Wu | DRONE: Dual-Domain Residual-based Optimization NEtwork for Sparse-View CT Reconstruction[END_REF][START_REF] Wu | Deep Embedding-Attention-Refinement for Sparse-view CT Reconstruction[END_REF].

According to mentioned works, both IR methods and DL-based methods were effective to improve image quality. Therefore, deep iterative reconstruction algorithms, which combined IR optimization and deep learning prior, have been researched for image restoration [START_REF] Zhang | Plug-and-Play Image Restoration with Deep Denoiser Prior[END_REF][START_REF] Sun | Deep ADMM-Net for compressive sensing MRI[END_REF]. By implementing the differentiable forward-backward operator, Cheng et al. developed an unrolled method (FSR-Net) to jointly reconstruct a high-quality CT image and its corresponding full-view projection data. FSR-Net deployed the regularization both on the image domain and projection domain and outperformed existing variational and DL-based methods [START_REF] Cheng | Learned Full-Sampling Reconstruction From Incomplete Data[END_REF]. Next, to improve the regularization capacity of deep prior and enhance data consistency, Zhou et al. employed the dense spatial-attention network with a specialized data fidelity layer for limited-angle CT reconstruction. Experiments implied that [START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF] was able to generate promising results for major lesions. Based on [START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF], Sam's Net was further investigated to utilize the hybrid-domain-based method as the backbone and lead to improvements in stability and robustness [START_REF] Chen | Sam's Net: A Self-Augmented Multi-Stage Deep-Learning Network for End-to-End Reconstruction of Limited Angle CT[END_REF]. Even though [START_REF] Cheng | Learned Full-Sampling Reconstruction From Incomplete Data[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF][START_REF] Chen | Sam's Net: A Self-Augmented Multi-Stage Deep-Learning Network for End-to-End Reconstruction of Limited Angle CT[END_REF] represented state-of-the-art methods, they cannot directly be applied to cone-beam CT due to memory limitations. Hence, some deep iterative methods with an offline scheme have been proposed. To accelerate the convergence speed of IR methods, Wang et al. adopted several DL models as regularization functions to improve the intermediate reconstruction results [START_REF] Wang | ADMM-based deep reconstruction for limited-angle CT[END_REF]. As a result, [START_REF] Wang | ADMM-based deep reconstruction for limited-angle CT[END_REF] performed better in edge preservation and artifact reduction. Besides, to solve the generalization of deep priors in the iterative process, Hu et al. designed a residual-space-based CNN model embedded in the IR method and make a significant promotion in detail restoration [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF].

Nevertheless, [START_REF] Wang | ADMM-based deep reconstruction for limited-angle CT[END_REF][START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF] needed a much longer time than other competitive methods due to the complex computational iterative procedure. Consequently, this paper proposes a ACCEPTED MANUSCRIPT / CLEAN COPY

Cross-domain

Residual-Optimization based Structure Strengthening (CROSS) framework for limited-angle CT reconstruction. The proposed CROSS method consists of three steps, which alternatively perform the CNN model on the image domain and projection domain. Specifically, in the first step, the structure strengthening network (SS-Net) is adopted to remove the artifacts and preserve the textures. Next, the missing projection data can be obtained from the results in the first step according to [START_REF] Huang | Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior[END_REF]. For the purpose of data consistency improvement, a residual network (ResNet) is applied to boost restored projection data. Different from the last step in [START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF], the proposed CROSS utilizes the SS-Net on the residual error map rather than the CT images, which could improve the restoration accuracy in the areas that have the larger attenuation coefficients. Compared to deep iterative methods [START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF][START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF], the CROSS method can be applied to cone-beam CT reconstruction with less computational cost and provides competitive results simultaneously. Experiments based on the simulated and real datasets validate that the proposed CROSS method performs well in edge preservation, detail restoration, and artifact removal.

The rest of this paper is organized as follows. Section II introduces the workflow of the proposed CROSS framework and the details of the neural network used in this work. Section III gives the experimental results and analysis of the different components in CROSS. In section IV, we will discuss some related issues and make a plan for the next work.

II. METHODOLOGY

A. CROSS Framework

To reconstruct high-quality images similar to deep iterative methods [START_REF] Cheng | Learned Full-Sampling Reconstruction From Incomplete Data[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF][START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF], but with lower computational cost, a multi-step method termed CROSS is proposed. The CROSS framework consists of three steps (as shown in Fig. 1), which alternatively employ the CNN models on the image space and projection space to gradually boost the CT images.

In the first step, a novel structure-strengthening network (SS-Net) is adopted in the image domain to remove the artifacts and restore most of the tissue details. Specifically, SS-Net takes the degraded images reconstructed from limited-angle projection data 𝒚𝒚 using the FDK algorithm as input and generates high-quality images 𝑺𝑺 𝟏𝟏 . Unlike [START_REF] Gu | Multi-Scale Wavelet Domain Residual Learning for Limited-Angle CT Reconstruction[END_REF][START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF][START_REF] Zhang | A Sparse-View CT Reconstruction Method Based on Combination of DenseNet and Deconvolution[END_REF], SS-Net designs a structure-enhanced branch, which can lead to impressive results in detail restoration.

Although the 𝑺𝑺 𝟏𝟏 obtained at the first step has satisfactory visual results, but it may fail to accurately reconstruct the areas that have larger attenuation coefficients. Therefore, the data consistency operation is employed to further improve 𝑺𝑺 𝟏𝟏 . In particular, the projection data 𝒚𝒚 𝟏𝟏 reprojected from the 𝑺𝑺 𝟏𝟏 is input into a normal ResNet and produces an improved full-view projection data 𝒚𝒚 𝟐𝟐 . Next, the residual data consistency (RDC) is utilized to evaluate the difference 𝒚𝒚 𝟑𝟑 between 𝑺𝑺 𝟏𝟏 and the available projection 𝒚𝒚 . Differing from traditional data consistency [START_REF] Huang | Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF], RDC focuses on the assessment of error maps on the projection domain and can provide superior results.

In the last step, an error image 𝑺𝑺 𝟐𝟐 is first reconstructed from the error sinogram 𝒚𝒚 𝟑𝟑 . Despite the wedge artifacts, it contains high-frequency information between the 𝑺𝑺 𝟏𝟏 and the ground truth, which can be easily restored for 𝑺𝑺 𝟏𝟏 . Hence, the SS-Net is used again to correct the 𝑺𝑺 𝟐𝟐 . Then the final results 𝑺𝑺 𝟒𝟒 can be got by adding 𝑺𝑺 𝟑𝟑 and 𝑺𝑺 𝟏𝟏 .

In general, the key point of the CROSS method is to respectively promote the reconstructed result in the residual image space and projection space, which is beneficial to recover bigger organs with high Hounsfield units (HU).

ACCEPTED MANUSCRIPT / CLEAN COPY B. Structure Strengthening Network

To better reconstruct images for limited-angle CT, the SS-Net is employed in the image domain, whose architecture is shown in Fig. 2. SS-Net has three branches, which are the image restoration sub-network, structure-enhanced sub-network [START_REF] Ma | Structure-Preserving Image Super-Resolution[END_REF][START_REF] Wang | EAA-Net: A novel edge assisted attention network for single image dehazing[END_REF][START_REF] Cai | TDPN: Texture and Detail-Preserving Network for Single Image Super-Resolution[END_REF], and feature fusion sub-network, respectively. The image restoration sub-network (IRS-Net) (as shown in Fig. 2(a)) adopts the FED-INet as the backbone [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF], which employs the asymmetric convolutional module (ACM) to improve the feature extraction and has been effectively validated for tissue restoration. IRS-Net is a classical image-domain-based method that takes the FDK reconstruction images as input and generates high-quality images 𝑩𝑩 𝟏𝟏 with most structures and less artifacts. So, IRS-Net holds the low-frequency information of CT images.

Dissimilarly, the structure enhancement sub-network (SES-Net) (as illustrated in Fig. 2 (b)) attempts to preserve the texture information contained in the CT images. SES-Net also uses the FED-INet as the backbone and inputs the FDK results but outputs the structure details 𝑩𝑩 𝟐𝟐 . Consequently, the high-frequency information of the CT images is stored in the feature maps of the SES-Net.

Since IRS-Net and SES-Net separately possess the low-and high-frequency components of the CT images, they can be further improved by fusing their feature maps. As depicted in Fig. 2(c), the feature fusion module (FFM) concatenates the feature maps together, which are extracted from the IRS-Net and SES-Net respectively, and brings improvements over 𝑺𝑺 𝟏𝟏 in edge preservation.

C. ResNet

For better reconstructing high-resolution projection data, the ResNet is utilized, whose architecture is demonstrated in Fig. 3. It consists of eight ResBlocks and each ResBlock has a residual connection to avoid vanishing or exploding gradients [START_REF] He | Deep residual learning for image recognition[END_REF].

Besides, ResNet also adopts the global residual connection to accelerate convergence and stable training [START_REF] Zhang | Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising[END_REF].

D. Residual Data Consistency

Data consistency is a widely used constraint in medical imaging [START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF][START_REF] Schlemper | A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction[END_REF], which can guarantee the worst-case performance of reconstruction methods [START_REF] Gupta | CNN-Based Projected Gradient Descent for Consistent CT Image Reconstruction[END_REF]. The classical data consistency can be rewritten as follows [START_REF] Huang | Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior[END_REF].

𝑦𝑦 3 = 𝑦𝑦 ⊕ 𝑦𝑦 2 (1)
where 𝒚𝒚 is the available limited-angle projection data, 𝒚𝒚 𝟐𝟐 represents improved high-resolution projection data processed by the ResNet (as indicated in Fig. 1) and ⊕ stands for the replacement operation which copies the 𝒚𝒚 and replaces the corresponding part of 𝒚𝒚 𝟐𝟐 with 𝒚𝒚 . Then a more accurate projection data 𝒚𝒚 𝟑𝟑 can be used for subsequent operations [START_REF] Huang | Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF].

To improve tissue preservation, the RDC is investigated and its formulation is as follows.

𝑦𝑦 3 = 𝑦𝑦 ⊕ 𝑦𝑦 2 -𝑦𝑦 1 (2)
where 𝑦𝑦 1 = 𝑨𝑨𝑆𝑆 1 , 𝐴𝐴 is the projection operation. Unlike Eq. ( 1), RDC aims to evaluate the difference between the 𝑺𝑺 𝟏𝟏 and the ground truth in the projection domain, which can improve the performance of 𝑺𝑺 𝟏𝟏 in high-attenuation regions.

E. Perceptual Loss

Perceptual loss (PL) is the widely used tool to minimize the distance between two images in feature space rather than pixel-wise similarity. In the application of medical imaging, PL can generate more tissue details and a better visual appearance [START_REF] Yang | Low-Dose CT Image Denoising Using a Generative Adversarial Network With Wasserstein Distance and Perceptual Loss[END_REF]. The definition of PL is given as:

𝐿𝐿 𝑃𝑃𝑃𝑃 (𝐼𝐼, 𝑔𝑔𝑔𝑔) = ∑ ‖Ψ 𝑖𝑖 (𝐼𝐼) -Ψ 𝑖𝑖 (𝑔𝑔𝑔𝑔)‖ 𝐹𝐹 2 𝑁𝑁 𝑖𝑖=1 (3)
where 𝐼𝐼 is the reconstructed image and 𝑔𝑔𝑔𝑔 indicates the ground truth. Ψ 𝑖𝑖 represents the feature projector [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF]. In this work, the output of the 2 nd , 4 th , 6 th , 9 th , and 12 th convolutional layer of VGG-16 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] as the feature extractor Ψ 𝑖𝑖 .

F. Texture Extraction

CNN-based models tend to blur images [START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF], therefore, to enhance the CNN models in edge preservation, texture extraction (TE) is utilized in the CROSS framework. The TE can be expressed as follows.

𝐻𝐻(𝐼𝐼) = 𝐼𝐼 -𝐹𝐹(𝐼𝐼, 𝑔𝑔) (4) where 𝑔𝑔~𝑁𝑁(𝜇𝜇, 𝜎𝜎 2 ) follows the gaussian distribution with the mean value 𝜇𝜇 and standard variation 𝜎𝜎, and 𝐹𝐹 is the filtering operation. Using Eq. ( 4), the textures and details of the image 𝐼𝐼 can be obtained (as observed in 𝑩𝑩 𝟐𝟐 of Fig. 2(b)). Texture extraction was also used in [START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF][START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF], and these texture extractions directly perform on reconstructed images to explicitly enhance detail preservation. However, in our method, the texture extraction is to extract high-frequency feature maps ACCEPTED MANUSCRIPT / CLEAN COPY with an implicit approach and then feed them into the final results.

G. Loss Function

There are three neural networks Φ 1 , Φ 2 and Φ 3 for the three steps in CROSS, respectively.

In the first stage of CROSS, the cost function of Φ 1 is described as:

Φ 1 = argmin Φ 1 �Φ 1 b1 (𝐼𝐼 𝐷𝐷 ) -𝐼𝐼 𝑁𝑁𝐷𝐷 � 𝐹𝐹 2 + �Φ 1 b2 (𝐼𝐼 𝐷𝐷 ) -𝐻𝐻(𝐼𝐼 𝑁𝑁𝐷𝐷 )� 𝐹𝐹 2 +�Φ 1 b3 (𝐼𝐼 𝐷𝐷 ) -𝐼𝐼 𝑁𝑁𝐷𝐷 � 𝐹𝐹 2 + 𝜆𝜆 1 • 𝐿𝐿 𝑃𝑃𝑃𝑃 (Φ 1 b3 (𝐼𝐼 𝐷𝐷 ), 𝐼𝐼 𝑁𝑁𝐷𝐷 ) (5)
where 𝐼𝐼 𝐷𝐷 is the limited-angle reconstructed image, 𝐼𝐼 𝑁𝑁𝐷𝐷 indicates the reference image reconstructed from the full-view projection data. Φ 1 b1 , Φ 1 b2 , and Φ 1 b3 stands for the three sub-networks in Fig. 2, λ 1 represents the hyperparameter to balance different terms in Eq. ( 5).

In the second stage, the objective function of Φ 2 is:

Φ 2 = argmin Φ 2 ‖Φ 2 (𝑦𝑦 1 ) -𝑦𝑦 𝑁𝑁𝐷𝐷 ‖ 𝐹𝐹 2 (6)
where 𝑦𝑦 𝑁𝑁𝐷𝐷 is the full-view projection data.

For the Φ 3 , it has the same optimization function with Φ 1 but with different input and reference images.

Φ 3 = argmin Φ 3 �Φ 3 b1 (𝑆𝑆 2 ) -𝑅𝑅 𝑁𝑁𝐷𝐷 � 𝐹𝐹 2 + �Φ 3 b2 (𝑆𝑆 2 ) -𝐻𝐻(𝑅𝑅 𝑁𝑁𝐷𝐷 )� 𝐹𝐹 2 +�Φ 3 b3 (𝑆𝑆 2 ) -𝑅𝑅 𝑁𝑁𝐷𝐷 � 𝐹𝐹 2 + 𝜆𝜆 2 • 𝐿𝐿 𝑃𝑃𝑃𝑃 (Φ 3 b3 (𝑆𝑆 2 ), 𝑅𝑅 𝑁𝑁𝐷𝐷 ) (7)
where 𝑆𝑆 2 = 𝐹𝐹𝐹𝐹𝐹𝐹(𝑦𝑦 3 ) , 𝑅𝑅 𝑁𝑁𝐷𝐷 = 𝐼𝐼 𝑁𝑁𝐷𝐷 -𝑆𝑆 1 , and 𝜆𝜆 2 is another hyperparameter to control the trade-off in all terms. After training the Φ 1 , Φ 2 and Φ 3 , the proposed CROSS can gradually improve the images with alternative image domain and projection domain processing.

III. EXPERIMENTS

In this work, all the experiments were conducted on a PC with CPU Inter(R) Xeon E5-2683 and GPU NIVIDA GTX TITAN. The hyper-parameters 𝜆𝜆 1 and 𝜆𝜆 2 in Eqs. ( 5) and [START_REF] Hu | SISTER: Spectral-Image Similarity-Based Tensor With Enhanced-Sparsity Reconstruction for Sparse-View Multi-Energy CT[END_REF] were set to 0.001 and 0.001, respectively. All the parameters of the three networks Φ 1 , Φ 2 and Φ 3 were updated using the Adam algorithm [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF]. Noting that these three networks were dependent and needed to be trained one by one. The learning rate was initially set to 10 -3 and linearly decreased to 1e -5 within 50 epochs. To evaluate the proposed CROSS framework, five reconstruction methods were treated as comparisons, including the FDK algorithm (Ramp-filter), TV [START_REF] Biguri | TIGRE: a MATLAB-GPU toolbox for CBCT image reconstruction[END_REF], DDNet [START_REF] Zhang | A Sparse-View CT Reconstruction Method Based on Combination of DenseNet and Deconvolution[END_REF], MSWDNet [START_REF] Gu | Multi-Scale Wavelet Domain Residual Learning for Limited-Angle CT Reconstruction[END_REF], and DCAR [START_REF] Huang | Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior[END_REF]. Specifically, DDNet, MSWDNet, and DCAR were implemented in the TensorFlow framework with Python language. FDK and TV were conducted by MATLAB 2018a. Besides, we choose the peak single-to-noise ratio (PSNR), and structural similarity index (SSIM) [START_REF] Zhou | Image quality assessment: from error visibility to structural similarity[END_REF] as the quantitative evaluations.

A. Simulated Data Results

The images of simulated experiments were downloaded from The Cancer Imaging Archive (TCIA). In this work, we adopted cone-beam geometry to evaluate different reconstruction methods for limited-angle CT. The geometry parameters were as follows. The source-to-detector distance was 100 cm and the source-to-axial distance was 50 cm, respectively. The detector size was 900×400 and each element covered an area of 1.5×1.5 mm 2 . For one circle, there were 960 views were collected. The volume was reconstructed with 512×512×200 and each voxel was 0.9×0.9×0.9 mm 3 . It was worth noting that FDK will lead to cone-beam artifacts when the reconstructed slice is far away from the central slice. To overcome this issue, we only selected the middle 120 slices in the entire volume. That means each 3D volume in the following experiments only has a size of 512×512×120. Particularly, there were 9200 2D images with the size of 512×512 selected from twenty-one patients in the TCIA dataset to simulate the cone-beam geometry as described in this section to generate the training dataset. Then, another 1000 2D images of the same size from different three patients were used to generate the validation dataset. Last, 1200 2D images selected from another three patients were utilized to generate the testing dataset. Specifically, the images from training, validation, and testing datasets belonged to different patients. The FDK algorithm was used to reconstruct the reference images from the full-sampled projection data. Two scanning angular ranges [0, 90°] and [0, 110°] were performed to assess different methods. For the DL-based methods, the input and output were 2D slices extracted from the 3D volumes. During the training phase, the patch-based scheme was adopted. Each patch had a size of 128×128 extracted from the 2D slices with the stride step of 64 and the batch size was 16. In the testing phase, the image with the size of 512×512 was directly inputted into the trained model and outputted generated result.

Table I lists the average quantitative results of reconstructed images with the scanning angular ranges of [0,90°] and [0,110°]. In Table I, it can be noticed that the analytical algorithm FDK produces the worst scores, which claims that the performance of the analytical algorithm can be affected greatly in all methods when the projection data is incomplete. Aided by the image gradient minimization and iterative forward-backword correction, TV achieves better assessments than FDK but still fails to provide competitive results, which implies that traditional methods cannot reconstruct satisfactory results with incomplete measurement data. Because of the powerful feature extraction ability, DL-based methods get better evaluation scores than traditional methods in all scanning angular ranges. Compared to MSWDNet, DDNet brings at least 0.7 dB promotion in terms of PSNR, which claims that the network with a more complex architecture may improve reconstructed results. Although DCAR gets worse scores in PSNR than DDNet, it performs well in SSIM, which means the image content provided by the DCAR is closer to the reference image due to the data consistency constraint. Notably, the proposed CROSS framework gains the best evaluations of all methods, which states the effectiveness of the multi-domain-based processing.

To further evaluate the performance visually of various algorithms, Fig. 4 illustrates the reconstruction results and the corresponding regions-of-interests (ROIs) of FDK, TV, c4)). These imply that the performance of traditional methods is significantly influenced by the completeness of projection data. From Fig. 5(d1)-(g4), it can be noted that DL-based methods promote the FDK and TV in artifact removal and tissue restoration. Similar to Fig. 4, MSWDNet and DDNet successfully recover most details and reduce artifacts. Moreover, they can produce more clear tissues than DCAR (as illustrated by the yellow arrows in Fig. 5(d3)(e2)), which is opposite to the phenomena in Fig. 4. This states that DCAR relies on the projection data, and the smaller the scanning angular range, the worse the performance. In contrast to the DCAR method, the proposed CROSS is quite robust to different scanning angular ranges and still provides ACCEPTED MANUSCRIPT / CLEAN COPY high-quality images with clear edges (as implied by the red arrows in Fig. 5(g2)(g3)) and accurate features (as marked by the red circle and arrow in Fig. 5(g1)(g4)).

ACCEPTED MANUSCRIPT / CLEAN COPY

Fig. 6 illustrates the selected coronal and sagittal views from the reconstructed CT volumes of the simulated dataset to further evaluate the visual performance of different reconstruction methods. As shown in Fig. 6, all the DL-based methods can reduce most artifacts and preserve the most of tissue features. More specifically, our proposed CROSS framework works well in detail restoration (as suggested by the red arrows in Fig. 6(e1)(e2)). However, the proposed method leads to obvious horizontal artifacts at different slices (as pointed by the yellow arrow and circle in Fig. 6(e1)(e2)). This is because all the reconstructed results are 3D images but the proposed method processes them slice by slice, which ignores the relationship between adjacent slices in the z-axis direction. To solve this problem, the proposed CROSS method is extended to a 3D version (3D-CROSS) that takes the 3D images as input. As observed in Fig. 6(f1)(f2), the 3D-CROSS successfully suppresses the horizontal artifacts. More results of 3D-CROSS can be found in the supplementary material.

B. Real Dataset Results

To further investigate different reconstruction methods for limited-angle CT, real mice dataset experiments were conducted. Again, the cone-beam scanning model was adopted and its configuration is as follows. The tube was Hamamatsu L9421-02 and the detector was Dexela 1512, respectively. The tube voltage was 60 kV and the current was 130 μA. The size of the detector was 944 × 768 and each element represented 0.072×0.072 mm 2 . The distance between the source and the detector was 44 cm and the distance between the source and the object was 22 cm, respectively. 1000 projections were collected via 360° as the full-sampled measurement data. The reconstructed 3D volume was 872×872×600 and each voxel covered the area of 0.072×0.072×0.072 mm 3 . There were four mice performed for this work. Specifically, two mice (1200 images) were used as the training dataset, one mouse (600 images) was used as the validation dataset and the rest (600 images) was used as the training dataset. Similar to the previous section, we only reconstruct the central 600 slices for each mouse to alleviate the cone-beam artifacts. The FDK algorithm was adopted to reconstruct the reference images from the full-sampled projection data. One scanning angular range ACCEPTED MANUSCRIPT / CLEAN COPY [0,110°] was performed to assess various methods. Fig. 7 shows the selected reconstruction images between different algorithms. For better visual observation, all the images in Fig. 7 were cropped to the size of 448×448. All the DL-based methods can generate high-quality images with fewer artifacts than the FDK algorithm. Moreover, in comparison approaches, DDNet produces better results in edge preservation (as indicated by the yellow arrow in Fig. 7(d2)). From the red arrows in Fig. 7

C. Comparison Between CROSS and DIOR

Deep iterative reconstruction methods have been applied for limited-angle CT and achieved superior performance to traditional DL-based methods [START_REF] Cheng | Learned Full-Sampling Reconstruction From Incomplete Data[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF][START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF]. To compare the deep iterative method and the proposed method, additional experiments were conducted from the simulated dataset with the scanning angular range of 90°. The DIOR [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF] was employed as the representative deep iterative method, which adopted the CNN model as the regularization function in the residual space to improve the image quality via the iterative process.

Fig. 8 demonstrates the reconstructed results of the DIOR and CROSS methods. Both the DIOR and CROSS perform well in artifact removal and tissue restoration (as pointed out by the yellow arrows in Fig. 8(b2)(c2)). In addition, the CROSS framework can restore accurate structural features (as marked by the red circle in Fig. 8(c1)). To sum up, the proposed method can obtain competitive results with DIOR, which proves that the multi-domain-based strategy in CROSS is effective for limited-angle CT.

D. Computational Cost

Table II lists the computational cost of various methods. All the time was computed based on the simulated dataset with 200 images and a scanning angular range of 110°. MSWDNet and ACCEPTED MANUSCRIPT / CLEAN COPY DDNet are single-domain-based methods that take the least time. IR-based methods (DCAR and DIOR) consume much longer time than other algorithms. Because of three networks and one forward-backward operation, the proposed method spends more time than MSWDNet and DDNet. However, compared to DIOR, CROSS can bring similar results within an appropriate time.

E. Ablation Study

In this section, an ablation study was performed to probe the effects of different modules of the proposed CROSS framework based on the simulated data with the scanning angular range of 90°.

The FED-INet [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF] was taken as the baseline model. Then the structure enhancement module was added to the baseline to establish the first comparison model (SS-Net). Next, the data consistency (DC) with 𝑦𝑦 3 = 𝑦𝑦 ⊕ 𝑦𝑦 1 and the image-domain network (ID-Net) was introduced to the first comparison model to build the second comparison model. Moreover, unlike the second comparison, the learned data consistency (LDC) in Eq. ( 1) with ResNet was employed to create the third comparison model. Last, the residual data consistency in Eq. ( 2) and the residual-space-based network were adopted to construct the fourth comparison model, i.e., CROSS.

Table III gives the quantitative evaluations of the progressive ablation study. It can be observed that the SS-Net brings higher scores than the baseline model in terms of PSNR, and SSIM because the structure enhancement sub-network could strengthen tissue preservation. Meanwhile, with the assistance of DC and ID-Net, the third model further promotes the reconstructed results both in CT values and image features. Replacing the DC with the learned DC, the fourth model can enhance the data consistency constraint and lead to improvements in all assessments. Notably, the proposed CROSS method gains the best evaluations in all comparison models, claiming the validity of the RDC and residual-space processing.

Besides, to explore the mechanism of different components in CROSS, the reconstructed results of various comparison models are demonstrated. The baseline model can restore most tissue features and remove artifacts, which has been validated in [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF]. With the aid of the structure enhancement module, SS-Net performs better in detail restoration (as indicated by the red circle in Fig. 9(c)). However, the third model introduces some uneven artifacts into the reconstructed images (as shown by the blue arrows in Fig. 9(d)), which may be caused by the inaccuracy of DC. After applying an additional ResNet in the projection domain, the fourth model can overcome the drawback of the previous model and lead to better results in edge preservation (as pointed out by the green arrow in Fig. 9(e)). Last, CROSS generates the most impressive images, specifically for the area with larger attenuation coefficients (as demonstrated by the yellow ellipse in Fig. 9(f)).

IV. CONCLUSION AND DISCUSSION

Deep iterative reconstruction methods have shown remarkable superiority over existing methods [START_REF] Cheng | Learned Full-Sampling Reconstruction From Incomplete Data[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF][START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF]. However, these methods often encounter two issues when being applied to practical cone-beam CT imaging, which is memory limitations [START_REF] Cheng | Learned Full-Sampling Reconstruction From Incomplete Data[END_REF][START_REF] Zhou | Limited View Tomographic Reconstruction Using a Cascaded Residual Dense Spatial-Channel Attention Network With Projection Data Fidelity Layer[END_REF] and longer running time [START_REF] Hu | DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction[END_REF]. Meanwhile, hybrid-domain-based methods can also produce high-quality results [START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF][START_REF] Yin | Domain Progressive 3D Residual Convolution Network to Improve Low-Dose CT Imaging[END_REF] and be easily used for 3D imaging within an appropriate time. Therefore, based on the hybrid-domain methods, we develop a cross-domain residual-optimization-based structure strengthening reconstruction for limited-angle CT to generate similar results with deep iterative methods. Different from [START_REF] Hu | SPECIAL: Single-Shot Projection Error Correction Integrated Adversarial Learning for Limited-Angle CT[END_REF], our CROSS framework alternatively utilizes the networks to improve CT images on the image domain and projection domain. Besides, the residual-space-based processings can further improve CROSS in tissue restoration. In addition, the utilization of the structure enhancement module also results in the promotion of the reconstructed images. Both the simulated and real datasets are performed with different scanning angular ranges to validate the proposed method. Compared to existing methods, the CROSS framework performs well in artifact reduction and edge preservation.

There are some similar works to the proposed method. For instance, to overcome the instabilities of deep learning, Wu et al. proposed an ACID framework with a combination of deep learning and compressed sensing theory [START_REF] Wu | Stabilizing deep tomographic reconstruction: Part A. Hybrid framework and experimental results[END_REF][START_REF] Wu | Stabilizing deep tomographic reconstruction: Part B. Convergence analysis and adversarial attacks[END_REF]. The key idea of ACID is to employ the pre-trained network to constrain the residual image. Inspired by it, more advanced works have been developed for sparse-view CT [START_REF] Wu | DRONE: Dual-Domain Residual-based Optimization NEtwork for Sparse-View CT Reconstruction[END_REF][START_REF] Wu | Deep Embedding-Attention-Refinement for Sparse-view CT Reconstruction[END_REF]. The RDC used in the proposed method was also inspired by ACID and applied to limited-angle CT. However, to further improve edge preservation, our proposed method adopts a more effective structure-strengthening network.

ACCEPTED MANUSCRIPT / CLEAN COPY

Although the CROSS method demonstrates encouraging improvement in limited-angle CT reconstruction, some issues are still to be noticed. First, the texture extraction used in SS-Net is might not the optimal scheme. Therefore, how constructing the texture and detail map of CT images is still an opening problem. Second, the residual data consistency brings improvements for CROSS. However, it still exists some errors to evaluate the distance between reconstructed images and the ground truth in the projection domain. It remains a challenging problem to effectively ensure data consistency. Last, the noise will be enlarged in SS-Net due to the structure extraction, which may negatively affect the performance of the proposed method. So, how to avoid noise amplification in CROSS should be noticed.

Deep-learning-based methods have demonstrated superior performance than traditional reconstruction methods in the limited-angle CT problem. Nevertheless, most of these methods focus on simulated data or preclinical data, which cannot convincingly validate their practicability in real cases. Therefore, it still has a long way to apply deep learning methods to clinical limited-angle imaging.

Fig. 1 .

 1 Fig. 1. The flowchart of the CROSS framework.

Fig. 2 .

 2 Fig. 2. The proposed SS-Net architecture.

Fig. 3 .

 3 Fig. 3. The proposed ResNet architecture.

Fig. 4 .

 4 Fig. 4. Simulated dataset reconstruction results with scanning angular angle 110°. And different rows represent different slices. The display window is [-160, 240]. MSWDNet, DDNet, DCAR, and CROSS methods with the scanning angular range of 110°. From Fig. 4(b1)-(b4), it can be seen that FDK introduces severe wedge artifacts, and the tissue and lesion become hard to be recognized. Benefiting from the minimization of image gradients, TV outperforms FDK in artifact removal (as shown in Fig. 4(c1)-(c4)). Nevertheless, most diagnostic information in TV reconstructions is still missing, which exposes the defects of traditional methods when the projection data is incomplete. Assisted by a large number of pairs of training samples and deep convolutional layers, the CNN-based model could exploit the essential features contained in the CT images. Certainly, DL-based algorithms achieve superior performance over traditional methods. Specifically, the image-domain-based methods MSWDNet and DDNet can suppress wedge artifacts and restore tissues and details as demonstrated in Fig. 4(d1)-(e4). This confirms the effectiveness of image-domain-based methods for medical imaging. Further, DCAR could boost post-processing methods in tissue restoration (as pointed out by the yellow arrow in Fig.4 (f4)). Also, it can eliminate the fake structure induced by the DDNet (as indicated by the green arrow in Fig. 4(e3)). This is because that DCAR is an IR-based method and can promote reconstructed results via iterative optimization. It is worth noting that the proposed CROSS method generates more visually improved images than other competitive DL-based methods. Particularly, CROSS is able to preserve subtle details (as observed by the red arrows in Fig. 4(g1)(g3)) and clear organ boundaries (as shown by the red arrow in Fig. 4(g2)).Fig.5exhibits the reconstruction results with the scanning angular range of 90° to probe the performance of different methods with a smaller scanning angular range. Compared to Fig.4(b1)-(c4), FDK and TV lead to worse reconstruction results with the scanning angular range of 90° (as depicted in Fig.5(b1)-(c4)). These imply that the performance of traditional methods is significantly influenced by the completeness of projection data. From Fig.5(d1)-(g4), it can be noted that DL-based methods promote the FDK and TV in artifact removal and tissue restoration. Similar to Fig.4, MSWDNet and DDNet successfully recover most details and reduce artifacts. Moreover, they can produce more clear tissues than DCAR (as illustrated by the yellow arrows in Fig.5(d3)(e2)), which is opposite to the phenomena in Fig.4. This states that DCAR relies on the projection data, and the smaller the scanning angular range, the worse the performance. In contrast to the DCAR method, the proposed CROSS is quite robust to different scanning angular ranges and still provides

Fig. 5 .

 5 Fig. 5. Simulated dataset reconstruction results with scanning angular angle 90°. And different rows represent different slices. The display window is [-160, 240].

Fig. 6 .

 6 Fig. 6. Selected coronal views and sagittal from the simulated dataset with scanning angular range of 90°. (a1)-(f1) Coronal views of reference, MSWDNet, DDNet, DCAR, CROSS, and 3D-CROSS methods. (a2)-(f2) Sagittal views of reference, MSWDNet, DDNet, DCAR, CROSS, and 3D-CROSS methods. The display window is [-140, 240] HU.

Fig. 7 .

 7 Fig. 7. Real mice dataset reconstruction images with a scanning angular angle of 110°. And different rows represent different slices. The display window is [-600, 600].

Fig. 8 .

 8 Fig. 8. Reconstruction results from the simulated dataset with the scanning angular range of 90°. The display window is [-160, 240] HU.

  (f1)-(f4), the proposed CROSS framework outperforms other DL-based methods in tissue restoration and detail preservation.

Fig. 9 .

 9 Fig. 9. Simulated dataset reconstruction results of different modules with the scanning angular range of 90°. (a) Reference (b) Baseline model (c) SS-Net. (d) +DC+ID-Net. (e) +LDC+ID-Net. (f) CROSS. The display window is [-240, 160] HU.

  al.

	CROSS: Cross-domain Residual-Optimization
	Based Structure Strengthening Reconstruction
	for Limited-Angle CT
	Dianlin Hu, Yikun Zhang, Guotao Quan, Jun Xiang, Gouenou Coatrieux, Senior Member, IEEE,
	Shouhua Luo, Jean-Louis Coatrieux, Life Fellow, IEEE, Xu Ji, Hongbin Han, Yang Chen, Senior
	Member, IEEE

ACKNOWLEDGMENTS

All authors declare that they have no known conflicts of interest in terms of competing financial interests or personal relationships that could have an influence or are relevant to the work reported in this paper.

This work was supported in part by the State Key Project of Research and Development Plan under Grants 2022YFC2408500 and 2022YFC2401600, in part by the National Natural Science Foundation of China under Grant T2225025, in part by the Key Research and Development Programs in Jiangsu Province of China under Grant BE2021703 and BE2022768. (Corresponding authors: Xu Ji, Hongbin Han).

This work involved human subjects or animals in its research.