A Meslin

O Cousin

R Forni

P Anderson

O Beck

A Beyssac

S M Brown

E Clegg

Dehouck

J Lasue
email: jlasue@irap.omp.eu

P Y Meslin

A Cousin

O Forni

R Anderson

P Beck

O Beyssac

A Brown

S M Clegg

E Dehouck

J Frydenvang

P Gasda

O Gasnault

E Hausrath

S Le Mouélic

S Maurice

P Pilleri

W Rapin

R C Wiens

SUPERCAM FIRST SHOTS: DUST COMPOSITION AND VARIABILITY

HAL is

Introduction:

The NASA Perseverance rover has been exploring Jezero crater on Mars for the past two years. Since its arrival, the rover has driven about 14 km along the bottom surface of the crater, including the Máaz formation, the Artuby ridge and Séitah formation, and the different outcrops located at the foot of the delta. The formations found in the crater floor are of igneous origin with local aqueous alteration. The main upper unit is of basaltic origin while the deepest formation is probably an olivine-rich cumulate [1,2].

Instruments: SuperCam is a multi-technique remote sensing instrument able to acquire high resolution color images, passive visible/near-infrared, Laser-Induced Breakdown Spectroscopy (LIBS) and Raman spectra, and includes a microphone [3,4]. The LIBS technique was already developed to survey the surface of Mars with ChemCam (e.g. [5]).

In a typical analysis, a series of 30 powerful laser pulses at 1064 nm ablates the surface of targets at a distance of few meters, inducing a plasma spark. The elements constituting the target are excited by the laser energy and emit photons at characteristic wavelengths, which can be analyzed by spectroscopy to determine their quantification [6,7]. During such an analysis, the several spectra obtained by the first laser shots are typically contaminated by the dust deposited on the surface of every rock target on Mars (unless it was preliminary cleaned by abrasion or another technique). The first five spectra are typically removed before calculating the composition of each target [6,7].

The first spectra acquired on each target location present a very homogeneous composition, different from the one of the underlying target. The average first shot compositions have therefore been interpreted to represent an analysis of eolian dust deposited over time on the surface of Mars and previous studies have shown the compositional similarity between the dust detected at Jezero by SuperCam and at Gale by ChemCam [8,9].

In this study, we confirm the similarity in composition between the eolian dust deposited at Jezero and that previously described at Gale crater. We further assess the possible locational variability of the first shots dust signal, and its eventual thickness variation to determine the effectiveness of dust removal by the LIBS technique.

Method:

We have used all the LIBS shot-to-shot data acquired since the landing of Perseverance (643 sols). In this dataset only the data corresponding to natural undisturbed target surfaces have been selected, by removing abraded targets, drill holes, drill tailings and calibration targets from the analysis. This corresponds to ~2900 different spectra processed by denoising, background removal, wavelength calibration, and correction for instrument response.

The average spectrum obtained from these data can then be appropriately compared with the average first shot spectrum obtained by ChemCam at Gale crater, which was built over 1500 sols (~ 8500 spectra). Further statistical analysis include time series variations and depth removal analysis as described below.

Results on composition: We have verified for the first time that the average of the very first LIBS shots for all targets can be superposed, indicating strong similarities in their Major Oxides Composition (MOC) [9]. Comparing the cloud of MOC in a ternary diagram highlights the similarity between the SuperCam and ChemCam datasets as shown in Figure 1. Locational variation of dust compositions: The time series of MOC predictions can be studied to detect if any variations in first shots composition could be linked to environmental changes (dust storms) or possible local contributions. No significant variations in the composition are detected with time for most major elements, except possibly the MgO content, which shows an increase around the Séitah area, which could be linked to a local contribution of this formation with a higher rock Mg# (Figure 2).

Thickness of the dust cover:

We use a continuous piecewise linear fit to data with residual sum of squares to detect changes in slope for the MOC composition as a function of shot number at each point [11]. This allows us to assess the shot number at which the composition contaminated by dust transitions to the main rock composition (Figure 3a). Using this automated slope change detection algorithm, it is possible to assess the average change of slope for each target (selecting those natural surface targets which have a composition significantly different from the eolian dust). The distribution of slope changes thus obtained indicates that most of changes occur at or below 5 shots (median = 4.4 shots; mad = 1.5 shots). This validates the data processing defined for LIBS (removal of first 5 shots), and gives a minimum estimate of the dust cover of only a few microns, consistent with the typical Mars dust size. Conclusions: Our analysis indicates that the dust cover studied at Jezero corresponds to a thin homogeneous material similar in composition to the eolian dust studied at Gale. This result is consistent with a global mixing of the eolian dust on Mars, or possibly a single origin for the eolian dust on Mars as proposed in previous studies (e.g. [12,13]).

Figure 1 :

 1 Figure 1: Comparison of LIBS spectra first shots of ChemCam at Gale ([10] in green) and of SuperCam at Jezero (in orange).Some disparities were observed in Mg and Ca lines in the SuperCam signal, possibly due to a contribution from local rocks. The alkali do not present very strong differences. The minor elements (H, Li, Ba, Sr, Rb, Mn, S, Cl, etc.) are essentially similar for both instruments, indicating a similar level of hydration and minor-

Figure 2 :

 2 Figure 2: Time variations in the MOC predictions of the first shots for Al2O3 and MgO data with the median value indicated in red, median absolute deviation in blue and spline smoothed curve in green.

Figure 3 :

 3 Figure 3: a. Slope change detection for MgO for target Tselchee #4 b. Histogram of slope change detection indicating that most of the changes occur at or below 5 shots.

Acknowledgments:

  The engineers and scientists of the Perseverance rover are thanked for their generous contributions to this work. This work was supported by CNES in France and by the Mars Exploration Program in the US. References: [1] Farley et al. (2022) Sci. 377.6614 (2022).

[ 2 ]

 2 Wiens et al. (2022) Sci. Adv. 8.34 (2022). [3] Maurice et al. (2021) SSR, 217(3), 1-108. [4] Wiens et al. (2021) SSR, 217(1), 1-87.[5] Maurice et al. (2016) JAAS, 31(4), 863-889. [6] Clegg et al. (2017) Spectrochim. Acta B, 129, 64-85. [7] Anderson et al. (2022) Spectrochim. Acta B 188 (2022). [8] Lasue et al. (2018) GRL, 45(20), 10968-10977. [9] Lasue et al. (2021) LPSC, 53, #1758. [10] Cousin et al. (2023) LPSC, this meeting. [11] Fearnhead et al. J. Comput. Graph. Stat. 28.2 (2019): 265-275 [12] Berger et al. (2016) GRL, 43(1), 67-75. [13] Ojha et al. (2018) Nat. Comm., 9(1), 1-7.


Gaetano Agazzotti

Fabien Pierre

Frédéric Sur

Deep image prior regularized by coupled total variation for image colorization

Keywords: Image colorization, Color halos, Deep image prior, Coupled total variation

Automatic image colorization is an old problem in image processing that has regained interest in the recent years with the emergence of deep-learning approaches with dramatic results. A careful examination shows that these methods often suffer from the so-called "color halos" or "color bleeding" effect: some colors are not well localized and may cross shape edges. This phenomenon is caused by the non-alignment of edges in the luminance and chrominance maps. We address this problem by regularizing the output of an efficient image colorization method with deep image prior and coupled total variation.

Introduction

Image and video colorization is the process of adding colors to monochromatic (black-and-white or sepia) pictures and movies, for example legacy documents. This is an ill-posed problem since many solutions may match the human perception. Industrial applications require automatic methods to reduce costs. Historically, the first semi-automatic methods made use of a reference color image or of user-defined color scribbles, in particular through variational approaches. We refer the interested reader to the recent survey paper [START_REF] Pierre | Recent approaches for image colorization[END_REF]. Since large datasets made of pairs of monochromatic and color images are easy to build (by simply desaturating a color image), it is possible to train neural networks to infer a color image from a monochromatic input image. Effective colorization algorithms based on deep learning have therefore emerged in the past few years. The present contribution focuses on automatic deep-learning-based approaches without user interaction (contrary to [START_REF] Zhang | Real-time user-guided image colorization with learned deep priors[END_REF] or to the hybrid [START_REF] Huang | Unicolor: A unified framework for multi-modal colorization with transformer[END_REF] for instance).

Most deep-learning models infer at each pixel either a color component [START_REF] Iizuka | Let there be Color!: Joint end-to-end learning of global and local image priors for automatic image colorization with simultaneous classification[END_REF][START_REF] Kim | Bigcolor: Colorization using a generative color prior for natural images[END_REF][START_REF] Pan | Exploiting deep generative prior for versatile image restoration and manipulation[END_REF][START_REF] Vitoria | ChromaGAN: Adversarial picture colorization with semantic class distribution[END_REF][START_REF] Xia | Disentangled image colorization via global anchors[END_REF] or a probability distribution over the color space [START_REF] Deshpande | Learning diverse image colorization[END_REF][START_REF] Deshpande | Learning large-scale automatic image colorization[END_REF][START_REF] Larsson | Learning representations for automatic colorization[END_REF][START_REF] Zhang | Colorful image colorization[END_REF]. To limit the computing time, these models are primarily able to infer a low-resolution color image, or are based on a super-pixel representation, or on an auto-encoder. This requires upsampling in a further stage. Upsampling the low-resolution chrominance information or erroneously picking a color through the learnt probability distribution are, however, likely to give colors which are poorly localized Fig. 1. Typical color halos in three outputs of Colorful Image Colorization [START_REF] Zhang | Colorful image colorization[END_REF]. The blue halo on the lion's rump, the orange shade on the building facade or in the sky on the right of the lighthouse, the yellow spots on the jellyfish image should be eliminated from colorization results. Input monochromatic images are shown in Fig. 8. and go across shape edges, resulting in unpleasant halos (also called color bleeding in [START_REF] Kim | Deep edge-aware interactive colorization against color-bleeding effects[END_REF]) across edges in some situations. Fig. 1 shows typical outputs of a state-of-the-art method. Other examples are described in [START_REF] Salmona | DeOldify: A review and implementation of an automatic colorization method[END_REF], a careful analysis of DeOldify [START_REF] Antic | DeCrappification, DeOldification, and super resolution[END_REF] which is a recent colorization software with impressive results. DeOldify indeed renders color images at a lower resolution than the original monochromatic image, which may give in turn erroneous color halos. This halo effect is often quite subtle and cannot be seen in small-size images as shown in most papers, which mainly aim at getting images with vivid colors. A careful examination suggests, however, that color halos prevent the raw output of these models from being used in real industrial applications.

Several contributions try to circumvent this effect. For instance, the authors of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] propose to adapt the variational method of [START_REF] Pierre | Luminancechrominance model for image colorization[END_REF] in order to restore the output of a deep network [START_REF] Zhang | Colorful image colorization[END_REF] to reduce these unwanted defects. They make use of the so-called coupled total variation whose minimization tends to align luminance and chrominance edges, so that color halos are reduced. In the context of color transfer, the authors of [START_REF] Arbelot | Local texture-based color transfer and colorization[END_REF] use edge-aware texture descriptors with bilateral filtering to reduce halos. More recently, a deep-learning method based on userdefined scribbles was proposed [START_REF] Kim | Deep edge-aware interactive colorization against color-bleeding effects[END_REF]. However, these approaches do not explicitly consider the role of upsampling.

In this paper, we propose to investigate an automated restoration using deep image prior (DIP) [START_REF] Ulyanov | Deep image prior[END_REF] together with coupled total variation [START_REF] Pierre | Luminancechrominance model for image colorization[END_REF]. The goal is to obtain a colorization free from color halos, based on the hypothesized probability distribution given by [START_REF] Zhang | Colorful image colorization[END_REF]. DIP has shown good performances in solving super-resolution from a single image [START_REF] Ulyanov | Deep image prior[END_REF]. The expected benefit is thus a correct upsampling of color information to the resolution of the input monochromatic image. We think that this restoration process is of interest in most colorization methods.

Section 2 introduces deep image prior regularized by coupled total variation and its use in image colorization. Numerical experiments are presented in Section 3. We conclude with Section 4.

Deep image prior and image colorization

Deep image prior [START_REF] Ulyanov | Deep image prior[END_REF] has been recently introduced to solve ill-posed inverse problems in image processing. It is based on the observation that convolutional neural networks are good at producing images in many applications. The solution of an inverse problem is thus sought as the output of a given neural network f θ , with a fixed random input z, whose weights θ are learnt to minimise some function based on data misfits between the observation x and the output f θ (z). Minimization is performed with the standard optimization machinery based on the back-propagation of errors. DIP falls within the scope of unsupervised learning methods.

Although several neural architectures are possible, we use an encoder-decoder with skip connections all along this paper. This architecture is used in [START_REF] Ulyanov | Deep image prior[END_REF] for super-resolution and some other problems.

What information is captured by deep image prior?

Such a model encodes short and long range correlations between pixels, as illustrated by Fig. 2. This figure shows an experiment in which the preceding network is trained so that θ minimizes f θ (z) -x where x is some image, the optimum weights being denoted by θ(x). New images are then generated as f θ(x) (z ) where the input z is randomly drawn. We can see that the distribution of the colors is kept, fine textures and larger structures as well. These properties probably explain why DIP performs well as a Bayesian prior: contrary to the classic TV prior which tends to produce cartoon images, DIP is likely to produce textured images with geometrical shapes.

Deep image prior and image colorization

Of course, it is hopeless to try to solve the colorization problem by simply minimizing with respect to θ

L(f θ (z)) -y 0 2 , (1)
where L(f θ (z)) is the luminance channel of f θ (z), y 0 is the monochromatic image to colorize, and • is the quadratic norm. The resulting f θ (z) would just show random colors. Additional prior information is required. From a monochromatic image, the "colorful image colorization" (CIC) model of [START_REF] Zhang | Colorful image colorization[END_REF] gives, at each pixel of a low-resolution 64 × 64 grid G, the probability distribution over 313 samples covering the bidimensional chrominance space (see Fig. 3). In [START_REF] Zhang | Colorful image colorization[END_REF], a post-processing stage ensures a vivid output image whose resolution is the same as the input resolution. Although very good results are obtained, the probability distribution may not be able to clearly pick a consistent color, especially around the edges of the objects which are not accurately localized over the low-resolution grid. This is illustrated by Fig. 4. Besides, upsampling the chrominance channels is required to build the full-resolution output. This step is likely to produce interpolation artifacts: in the context of colorization, the high-resolution luminance is available but upsampling the chrominance independently from the luminance gives color halos around some objects of the image.

We propose to incorporate the probability distribution given by CIC over the low-resolution pixel grid in the framework of deep image prior to produce color images at the same resolution as the input monochromatic image.

From probability distributions over a low-resolution grid to the color image

While an RGB output is chosen in the original DIP [START_REF] Ulyanov | Deep image prior[END_REF], in the present paper the output of the neural network is made of the three channels of the CIE Lab color representation, which is the color space used in [START_REF] Zhang | Colorful image colorization[END_REF]. Let us denote by L and C the mappings from an Lab image to the luminance and the (a, b) chrominance channels in CIE Lab, respectively. The original monochromatic image is denoted by y 0 , and the neural network of DIP is f θ . This network takes some fixed random z as input and produces an Lab image f θ (z) with the same resolution as y 0 . Here, the 313 samples in the bidimensional chrominance space are denoted by (c i ) 1≤i≤313 , and (w i (x)) 1≤i≤313 is the probability distribution over the c i 's at any pixel x of the low-resolution grid G, as given by CIC. Let d be the subsampling operator which maps images of the same resolution as y 0 and f θ (z) to the grid G.

Plugging information from the CIC model into the deep image prior of Eq. ( 1) can be achieved by minimizing with respect to θ the following quantity:

x∈G 313 i=1 w i (x) C d(f θ (z))(x) -c i 2 + α L(f θ (z)) -y 0 2 (2)
where α > 0 is a hyperparameter.

If the neural network f θ is complex enough, the optimum is attained for f θ whose luminance channel is close to y 0 and chrominance channels are, at any pixel x of the low-resolution grid, the average of the (c i ) samples weighted by the probability distribution (w i (x)). The DIP permits thus to upsample information from the low-resolution grid G. The problem with this formulation is twofold. First, averaging chrominances gives dull colors, especially at pixels where the probability distribution is not sharp. Second, luminance and chrominance channels are coupled only through the hidden layers of f θ , which still gives color halos.

We therefore adapt Eq. ( 2) in two ways:

1. We add a regularization term which explicitly enforces the coupling between luminance and chrominance channels. To this end, we use the coupled total variation (TV) introduced in [START_REF] Pierre | Luminancechrominance model for image colorization[END_REF]. If I is a color image of domain Ω, with luminance L and chrominance channels a and b, the coupled TV writes:

TV γ (I) = Ω γ ∇L 2 + ∇a 2 + ∇b 2 (3)
where ∇ denotes the gradient and γ > 0 is a hyperparameter of the model. Minimizing the coupled TV makes the luminance and chrominance gradients to have small values at the same pixels [START_REF] Pierre | Luminancechrominance model for image colorization[END_REF]. This consequently aligns the edges in the chrominance and luminance channels, and reduces the color halo effect. 2. We allow the probability distribution (w i (x)) to vary, in the same spirit as in [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF]. Minimizing

313 i=1 w i (x) C d(f θ (z)) (x) -c i 2
with respect to the non-negative w i (x) amounts to solving a simple linear program, the constraint being 313 i=1 w i (x) = 1. The minimum is therefore obtained at a vertex of the polytope defined by the constraints: the optimum w i (x) is such that there exists i * satisfying w i * (x) = 1 and for any i = i * , w i (x) = 0. For any x, the index i * is thus simply argmin i C d(f θ (z))(x) -c i 2 . Such a sharp probability distribution has the advantage of giving vivid colors.

Input: a monochromatic image y0, and probability distributions (wi(x))i=1...313 at every pixels x of a 64 × 64 grid G over samples (ci)i=1...313 spanning the bidimensional chromatic space (from [START_REF] Zhang | Colorful image colorization[END_REF]).

Repeat until convergence:

1. Minimize the loss (Eq. ( 5)) with respect to θ.

For any

x ∈ G, i * (x) = argmin i C d(f θ (z)) (x) -ci and wi(x) = 1 if i = i * (x),
wi(x) = 0 otherwise.

Output: the RGB image obtained from the luminance channel y0 and the chrominance channels of f θ (z).

Fig. 5. Algorithm for colorization from the low-resolution probability distributions of CIC [START_REF] Zhang | Colorful image colorization[END_REF] with deep image prior and coupled total variation.

As a consequence, we seek θ and w such that ∀x ∈ G,

313 i=1 w i (x) = 1, minimizing: x∈G 313 i=1 w i (x) C d(f θ (z)) (x) -c i 2 + α L(f θ (z)) -y 0 2 + β TV γ (f θ (z)) (4)
The optimal f θ (z) is such that all three terms are small, that is, the luminance of f θ is close to y 0 , halo effects are reduced (small coupled TV), and the chrominances over the low-resolution grid are closed to ones picked from a 0-1 probability distribution.

Compared to the original DIP [START_REF] Ulyanov | Deep image prior[END_REF], it should be noted that the additional TV γ regularisation term permits to get rid of overfitting. DIP is indeed known to overfit and requires an early-stopping strategy. The gradient descent optimization must be stopped after a certain number of iterations, which may critically depend on the inverse problem to solve. A classic way to prevent overfitting in neural network learning in general and in DIP in particular is to add a regularization term in the loss function, see [START_REF] Batard | DIP-VBTV: A color image restoration model combining a deep image prior and a vector bundle total variation[END_REF][START_REF] Liu | Image restoration using total variation regularized deep image prior[END_REF] for total-variation based regularization of DIP. In the experiments of Section 3, we indeed simply minimize the loss function without any early-stopping process.

Optimization algorithm

We use block coordinate descent to minimize Eq. ( 4): we alternate minimization with respect to θ, the parameters of the DIP neural network, and to w, the probability distributions. Minimizing with respect to θ is achieved with the classical back-propagation, and minimizing with respect to w amounts to solving a linear program as explained in Section 2.3. total loss Eq. ( 4)

Fig. 6. Minimized loss (bottom right) and its components (related to coupled TV, luminance, and chrominance) against number of iteration in a typical case.

It can be noted that minimizing Eq. ( 4) with respect to θ by gradient descent is equivalent to minimizing:

x∈G C d(f θ (z)) (x) -u(x) 2 + α L(f θ (z)) -y 0 2 + β TV γ (f θ (z)) (5) with u(x) = i w i (x)c i . Indeed, with v θ (x) = C d(f θ (z)) (x), ∇ θ x∈G 313 i=1 w i (x) v θ (x) -c i 2 = 2 x∈G 313 i=1 w i (x)∇ θ v θ (x) • (v θ (x) -c i ) = 2 x∈G ∇ θ v θ (x) • v θ (x) - i w i (x)c i = ∇ θ x∈G v θ (x) -u(x) 2 (6)
where • denotes the dot product, since i w i (x) = 1 for any x ∈ G.

Our software implementation uses the equivalent Eq. ( 5) instead of Eq. ( 4) for the unsupervised learning step to reduce the computational burden of backpropagation. The resulting algorithm is given in Fig. 5. In practice, Step 2 is performed after repeating 200 gradient descent iterations of Step 1, which limits the number of Step 2 performed, this latter step being time-consuming in spite that only a few pixels are concerned by a change of their probability distribution. Fig. 7. Chrominance channels. Left: output of CIC [START_REF] Zhang | Colorful image colorization[END_REF]. Right: proposed approach (minimization of Eq. ( 5)). The proposed approach with regularized deep image prior gives a better localization of the chrominance information, which explains reduced color halos. The corresponding color images can be seen in Fig. 2. Best seen on screen.

We can see the effect of this alternating scheme in Fig. 6. The curve of the total loss is globally smooth but contains some small jumps. The function becoming asymptotically constant after 1,000 iterations, stopping after 2,000 iterations ensures the convergence of the iterative algorithm. In all the experiments of this paper, convergence curves are similar to Fig. 6. Contrary to the standard DIP approach [START_REF] Ulyanov | Deep image prior[END_REF], there is no need for early stopping.

Numerical experiments

As mentioned in the introduction, colorization is an ill-posed problem as several different solutions may be consistent with a unique monochromatic image (for instance, the color of a car cannot be determined from its black-and-white image). Consequently, this section shows qualitative results: the goal is to assess whether the proposed approach gives plausible colorizations without color halos.

Our software programs are freely available at the following URL: https://gitlab.univ-lorraine.fr/pierre26/diptv

Parameters

The parameters have been chosen experimentally once and for all. On all the tested images, the same parameters have been used: α = 1, β = 5.10 -7 , and γ = 80. The β parameter controls the regularity of the image and works together with the γ parameter. β encourages some flat areas and small variations of the image whereas γ controls the smoothness/sharpness of the contours of the chrominance channels and the coupling of these channels with the luminance one. The optimizer minimizing the loss is ADAM with a learning rate of 2.10 -2 .

The optimization of Eq. ( 4) with respect to θ takes about 162 sec for 256×256 images on a GeForce GTX 1060 GPU with 6GB memory (2, 000 iterations, as explained in the preceding section). In comparison, the computation of the initial distribution by CIC [START_REF] Zhang | Colorful image colorization[END_REF] takes less than 2 seconds.

Experiments

In Fig. 7, chrominance channels are shown by applying a constant luminance channel equal to a 50% value. This process helps to qualitatively validate the results of a colorization algorithm by neutralising the effect of luminance. Indeed, colorized images often seem to be visually satisfactory, in spite of poorly localized chrominances. This is caused by the sensitivity of the human visual system to luminance, which hides potential defects of the colorization process. We can see that contours are sharper with our method. Moreover, regularizing with coupled total variation removes some defects on flat areas (for instance the bottom part of the sky below the plane). Sharpness of the chrominance channels shows some benefits in terms of colorization results: for instance, the orange halo on the left of the butterfly (which is the result of a wrong color assignment because of a flat probability distribution given by CIC, as proven by Fig. 4) is removed by our optimization scheme.

Fig. 8 shows some comparisons between [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] and the results obtained with (4). It emphasizes the benefit of DIP with respect to a traditional variational method. It is important to note that the outputs of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] are themselves significant improvements over the output of CIC [START_REF] Zhang | Colorful image colorization[END_REF]. It can be seen in the lion image that the contours are better respected. The blue halo over the lion's skin and the orange halo in the sky seen in the output of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] are corrected by the proposed regularization step. The space between the two lions is not blue as one would monochromatic images results of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] our results

Fig. 8. Comparison with [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF]. Left: original monochromatic images. Center: results of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] (from Figs. 5, 6 and supplementary material of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF]); right: proposed approach, minimization of Eq. ( 5). From top to bottom: lion, close-up, lighthouse, close-up, jellyfish. The proposed approach shows significant improvements over [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF], which itself improves over CIC [START_REF] Zhang | Colorful image colorization[END_REF] (see Fig. 1).

expect, but it turns out that, in this area, blue has a low probability in CIC on which our approach depends. In the lighthouse image, orange halo on the facade of the right-hand side building seen in the output of [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] disappears with the proposed approach. In the jellyfish image, the bottom right halo seen in [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] has been removed. Besides, the jellyfish is colorized with [START_REF] Mouzon | Joint CNN and variational model for fullyautomatic image colorization[END_REF] through a brown blurry halo in the chrominance channels, whereas the proposed approach produces a structured colorization well-fitted to the body of the jellyfish. However, it can also be seen that the DIP approach produces a brown spot in the lower left of the image, not related to any structure of the luminance channel. It turns out that this phenomenon sometimes appears, depending on the random initialization z of DIP. It is quite rare: we show this particular output for the sake of completeness; most outputs are not affected by it.

Conclusion

This paper proposed a deep image prior approach to image colorization, based on the probability distribution given by a state-of-the-art neural network over a low resolution pixel grid. The proposed regularization scheme was able to produce full-resolution chrominance information through a deep image prior regularized by coupled total variation, which permitted to align the chrominance and luminance edges, the latter being available at full-resolution in the original monochromatic image. As a result, we have shown that the so-called color halos (or color bleeding) were reduced, which is a first step towards effective use of colorization.

Fig. 2 .

 2 Fig. 2. Experimenting with deep image prior. First column: an image x. Second, third, and fourth columns: f θ(x) (z ) with different random inputs z .

Fig. 3 .

 3 Fig. 3. The 313 color samples in (a, b) chrominance channels used in CIC [21]. Colors correspond to the luminance value L = 50.

Fig. 4 .

 4 Fig.4. From left to right: a monochromatic image, the output of "colorful image colorization"[START_REF] Zhang | Colorful image colorization[END_REF] (default parameters), and entropy of the hypothesized probability distribution at each pixel of the 64 × 64 grid G given by CIC. The larger the entropy, the less sharp the distribution. Large entropy values can be noticed, especially around edges. Color halos can be seen, for example the orange halo on the grass at the bottom left of the butterfly, or the blue halo on the right lion's rump.

Acknowledgments This research was funded, in whole or in part, by l'Agence Nationale de la Recherche (ANR), project ANR-21-0008-01. For the purpose of open access, the authors have applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.


Crater K Castro

G Arana

I Población

S M Clegg

E F Gibbons

J.-A Manrique

P Gasda

A Udry

J Aramendia

J M Madariaga

M Veneranda

R B Anderson

G López- Reyes

A Cousin

O Forni

J Lasue

C Legett

S Maurice

A M Ollila

R C Wiens

O Beyssac

A J Brown

E Clavé

E Dehouck

T Fouchet

O Gasnault

N Lanza

J Laserna

J Martinez-Frias

P Pilleri

C Royer

F Rull

PRINCIPAL COMPONENT ANALYSIS ON THE SUPERCAM-LIBS SPECTRA OF ROCK TARGETS IN THE FIRST 640 SOLS IN JEZERO

Introduction:

The Perseverance rover completed, since leaving its Octavia Butler landing site in Jezero crater, the first science campaign on sol 381. That Crater Floor Campaign comprised the analysis of outcrops, rocks and regolith targets of the Máaz and Séítah formations together with the Artuby, and Content members. After completion of the Crater Floor campaign, the rover started the Rapid Traverse campaign (sols 382-414) to the delta front. The Delta Floor campaign started on sol 415 analyzing the Máaz/ Séítah and Séítah /delta contact and the Cape NukShak stratigraphy, to build the geological context for the western delta. Since then, many bedrocks and regolith targets have been examined, ending with the first two regolith samples that were taken on sol 639. During those science campaigns, several rock samples were collected and the abraded surfaces, tailings and cuttings were analyzed.

More than 500 targets were interrogated by SuperCam, a remote-sensing instrument that combines high-resolution imaging, visible and near-infrared (VISIR) reflectance spectroscopy (0.4-0.85, 1.3-2.6 µm), remote time-resolved green-laser Raman and fluorescence spectroscopy, laser-induced breakdown spectroscopy (LIBS), and acoustic sensing [1,2].

A detailed textural, chemical, and mineralogical analysis of the Máaz formation and the Content member of the Séítah formation concluded that they are igneous (lava flows) [START_REF] Udry | JGR Planets, e2022JE[END_REF]. The Máaz formation has some of the lowest Mg# (=molar 100×MgO/MgO+FeO) of all martian igneous rocks analyzed so far, with a mineralogy dominated by Fe-rich augite to possibly ferrosilite as well as plagioclase, and minor phases such as Fe-Ti oxides and Si-rich phases, without any olivine signals at the surface of the targets.

The Séítah formation consists of an olivine cumulate series which is weakly altered and preserves its primary texture and mineralogy. Séítah rocks are dominated by millimeter-size grains of olivine with presence of augite, pigeonite pyroxenes and other primary minerals like plagioclases and Cr-Fe-Ti-oxides [START_REF] Beyssac | JGR Planets[END_REF].

Most of results are based on the derived MOC values (major-element oxide compositions in weight percent) obtained after applying the calibration functions to the LIBS data [START_REF] Anderson | [END_REF]. The LIBS spectra were collected from 1x5, 1x10 and 3x3 rasters on those bedrocks of Máaz, Séitah and Crater Floor units.

This communication focuses on the principal components analysis (PCA) of the LIBS spectra collected from outcrops and rocks as well as from the abraded surfaces, prior to coring, and from the holes and extracted crushed materials obtained during the drilling process. The aim of this analysis is to determine whether the different analyzed materials can be better differentiated using the whole LIBS spectra, rather than using derived composition values.

Differentiation and grouping using PCA: The LIBS spectra of rock Targets until sol 640 were considered together with those of the onboard calibration targets of the SuperCam (SCCT) instrument [6,7]. The median of the LIBS spectra of each raster from the rock and SCCT targets were used to perform the PCA using the Unscrambler software [START_REF] Wiens | pdf 54th Lunar and Planetary Science Conference 2023[END_REF]. Figure 1 shows the plot of the obtained scores using the two first Principal Components (PCs). Different colors are used to visualize the distribution of rocks initially assigned to the different units. The scores of the SCCT targets (black dots) are also included for comparison.

In the PCA scores plot (Figure 1), 85% of the total variance among rocks and SCCT targets is explained with only two components. The position of the SCCT targets in the PC2 vs PC1 plot helps us to visualize the reasons (variability in the LIBS spectra as a function of the elemental composition) for the observed distribution on the four quadrants of the plot.

The right side of PC1 is dominated by the felsic SCCT targets (PMIOR0507, orthoclase, and PMIAN0106, Andesine), while the left side covers the Mg-rich SCCT targets (TSERP0102, Serpentine/Talc, PMIEN0602, enstatite, and PMIFA0506, Mg-rich olivine). The upper side of PC2 is dominated by the Ferich SCCT targets (LCMB0006, chert, and PMIFS0505, ferrosilite) while the lower part covers the Ca-rich ones (TAPAG0206, apatite, and LCA530106, calcite).

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Distribution and Interpretation:

The Máaz formation (dark blue) and the Content member (light blue) are centered with regard to PC2 but in the right most side for PC1, consistent the most felsic rocks found in the Crater Floor of Jezero [START_REF] Udry | JGR Planets, e2022JE[END_REF].

The Artuby ridge, also known as Upper Máaz [3] targets (green), are centered on both PCs and also distributed together with the more basaltic of the SCCT targets (the NTE series, LBHVO20406, standard basalt, and SHERGO2, the shergottite target).

The rocks and abraded patches of Séítah (red) are centered with regard to PC2 but a little to the left in PC1, consistent with olivine and ferrosilite [START_REF] Beyssac | JGR Planets[END_REF].

The rocks and abraded patches of Delta Floor targets (fuschia) are widespread between the most Mg-rich SCCT targets and olivine/ferrosilite ones, showing common distributions with rocks from Séítah.

The use of the LIBS spectra promotes a better distribution of all the analyzed rocks than the distribution based on the MOC values [START_REF] Wiens | pdf 54th Lunar and Planetary Science Conference 2023[END_REF], because the full spectra contain considerably more information than the derived composition values (MOC values).

The PC2 vs PC1 plot shows also some targets, initially assigned to a given formation or member of the Crater Floor, fall in the area of others based on their LIBS spectra.

The initially Upper Máaz rocks and abraded targets, Manior, Lance, Estoublon, Villette, Bellegarde191a, Souche, Montdenier 195,198,and 198 and Chanoles, are distributed in the area depicted for Lower Máaz. On the contrary, the initially Lower Máaz rocks and abraded targets, Maaz, Lhikan, Naadin, Adaa Daa, Jih, Haa ii Aah, Naltsos, Kad, Cheval Blanc, Champs, Charamel, Lagne, Lattes, Nashdoi and Tely, distribute better with the Upper Máaz targets. Also, Aurent, Sagnes, Monts du Cheval Blancs, Jabron309, Callas, Gourdon and Chamia, initially from Séítah are close to Upper Máaz and Melle close to Lower Máaz. Further discussion is needed to understand and explain this issue (e.g. presence of coatings, degradations, etc).

  Fig. 1 Scores Plot of the two Principal Components (PC2 vs PC1) obtained in the PCA treatment of the LIBS spectra (median for each raster) of the rocks until sol 640 and SCCT targets. The SCCT targets are represented in black.

Acknowledgments: We are grateful to the many engineers and scientists who have supported the Perseverance mission. We acknowledge the support of Spanish Agency for Research (AEI), NASA's Mars Exploration Program, CNES, CNRS, and other supporting organizations. SuperCam data are archived in the PDS.


M Loche

S Fabre

A Cousin

A Treiman

N Lanza

P-Y Meslin

P Gasda

D Das

B Tutolo

O Gasnault

The fate of manganese

  L'archive ouverte pluridisciplinaire

THE FATE OF MANGANESE: FRACTIONATION OF MN AND FE DURING THE KINETIC

ALTERATION PROCESS. M. Loche 1 , S. Fabre 1 , A. Cousin 1 , A. Treiman 2 , N. Lanza 3 , P-Y. Meslin 1 P. Gasda 3 , D. Das 3 , B. Tutolo 4 O. Gasnault 1 , S. Maurice 1 , R. Wiens 5 . 1 Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, UPS, CNRS, CNES, 9 avenue du Colonel Roche, 31400 Toulouse, matteo.loche@irap.omp.eu, 2 LPI 3 LANL, 4 University of Calgary, 5 Purdue Introduction: Since 2012, the MSL mission has been exploring Gale Crater, Mars. The ascension of Mount Sharp by the MSL Curiosity rover has shown that sediments were deposited in a fluvio-lacustrine environment and that water-rock interactions, often accompanied by oxidation state changes in redoxsensitive elements, were occurring [1]. One such redoxsensitive element, Mn, is commonly involved in biochemical reduction-oxidation on Earth. Mn-bearing minerals are most often formed in oxidative environments and its oxidation may be catalyzed by bacterial activity [2]. Across the traverse, the ChemCam and APXS instruments have discovered localized enrichment in Mn [3,4,5]. Recently, Mn caused much interest as it was found across the Murray formation in association with P, Fe and Mg. Both reduced and oxidized Mn material are still possible to explain these enrichments and might reflect several different fluid events. Drilling was attempted on the Mn-enriched Ayton/Groken location to sample the Mn-rich material, but the Mnbearing phase or amorphous material remained unknown [6]. Even more recently, after more than 10 years of traverse, ChemCam and APXS measured high Fe, Mn, and Zn concentrations in a remarkable sedimentary feature on the Marker Band [7]. As this abstract is written, attempts to drilling the Marker band and hopefully identifying the long-awaited Mn-bearing phase(s) are still ongoing. Overall, the Gale sediments are depleted in Mn compared to the Martian crust. This depletion is most likely caused by rock leaching and linked to the localized enrichment of Mn by weathering fluids [3]. In previous works, the enrichment of Mn as oxide material was proposed to be a marker of oxidizing conditions [4,5]. It could also be linked to more reducing conditions if found as reduced phases [8]. In this work, we use a kinetic dissolution/oxidation model of the weathering process to suggest that Mn behaves like a mobile element even under oxidative conditions, hence remaining in the fluid until water removal from evaporation, freezing or hydrated phases precipitation creates late-stage brines. We also show that Fe/Mn fractionation highlighted by APXS [3] could also happen in more oxidative environment and would not be restricted to Eh-pH space where oxidized Fe and reduced Mn species coexist.

Modelling of the alteration process:

For modelling the alteration process, we used the USGS's PHREEQC batch reaction code. This computer program can perform a variety of operations such as dissolution, precipitation and more [9]. We compute the weathering process as a simultaneous kinetic dissolution of primary phases, kinetic oxidation of Fe and Mn species in the fluid by O2 and a thermodynamic (instantaneous) precipitation/re-dissolution of secondary phases based on their saturation index. For the thermodynamic parameters, we used the Thermoddem database [10], including corrected Mg/Mn phosphates from our previous work [11] as well as some LLNL database consistent phases [10]. For most of the phases, we implemented the dissolution rates parameters from [12] and for others (e.g., magnetite) from [13]. The parameters were chosen to be as best cases for Mn and Fe oxidation: the atmospheric parameters were set to a 0.5 bar CO2 atmosphere, and 0.05 bar of O2 [14]. Rate parameters for the oxidation of Fe are computed for a surface self-catalysis, and Mn oxidation is also computed as surface catalyzed by the lepidocrocite Feoxyhydroxide [15]. For the initial solid, we based our calculation on the Rocknest (RN) sample amorphousfree normalized composition, based on CheMin results. This sample could be representative of one of the sediments sources of the Gale crater [16]. From this composition, we removed the remaining secondary phases except magnetite and ilmenite. We created custom solid solutions matching those reported by CheMin, adjusting the thermodynamic and kinetic parameters accordingly. Mn was added as a minor element in the olivine composition, as well as minor amounts of fluorapatite and pyrite to provide a P and S sources. The reactive surface is representative of nonclay minerals in basaltic sediments and is based on terrestrial modeling and experimental study [17].

Results:

We observed a fractionation between Fe and Mn during the kinetic weathering process (Fig. 1). For the iron species, we observe an initial spike of Fe(II), and continuous precipitation of Fe-oxide. For Mn, the Mn(II) total first quickly increase and later stabilize in a slow increase. At t=100y, total concentration of Mn(II) is more than an order of magnitude higher than that of Fe(II).

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Discussion: As the solution is buffered by mineral dissolution, oxidation rate increases while dissolution rate lowers until the oxidation becomes faster than dissolution. The initial spike of Fe(II) is therefore resulting of the competition between the dissolution rate (mainly of olivine), and the oxidation rate of Fe. The precipitation of Fe-oxide follows the process as Fe(III) is supplied to the solution. For Mn, we observe mostly a continuous increase in dissolved Mn(II), as the dissolution rate is faster than oxidation rate. Precipitation of Mn-phosphate and Mg-clays occurs quickly but in negligible proportion. The increasing concentration of Mn(II) under a CO2 atmosphere triggers the precipitation of Mn-carbonates, shortly decreasing Mn concentration until Mg-carbonates precipitation occurs and slows the production of Mncarbonates, hence stabilizing the Mn concentration. The timescale of the model is only indicative. Many parameters such as reactive surfaces can drastically affect it. It's important to notice that timescale vary depending on the system: in this modeled atmosphere open system, the same body of water stays in equilibrium with the atmosphere and the exact same rock, which is unlikely to happen for an extended period, because of fluid renewal (run-off) and rock burial. For longer-lived, lower W/R and higher temperature scenarios, typically closed systems, removal of dissolved O2 in ground water by Fe oxidation would quickly consume the dissolved O2 limiting even more Mn oxidation, therefore increase the fractionation. In these conditions, carbonates would be naturally inhibited and other phases such as clays would precipitate [18]. Precipitation of rhodochrosite is interesting as the pH is always lower than 6.4 during the initial kinetic surface alteration process. As we did not observe Mn-carbonates in situ, it is likely that: 1) Mncarbonates could reach saturation, but at this low pH, its sluggish precipitation rates would limit its formation, both in weathering and evaporation scenarios, hence increasing the fractionation process by preventing Mncarbonate formation and 2) The weathering process never reached this advancement, hence Mn-carbonates never reached saturation because dissolved Mn concentration was too low. Low temperature, run-off, sedimentation rate, short-lived hydrological system or shielding of the primary minerals by iron-oxide and/or amorphous silica can prevent further advancement and high concentration. Overall, the Mn oxidation rate is extremely optimistic, probably overestimating the final Mn(II) [15,19]. During the runs we performed at lower pO2, we found out that when dynamically weathering and oxidizing, primary minerals dissolution mostly controls the oxidation rate trough pH variation.

Therefore, removal of Mn(II) species by oxidation remains unlikely, forming Mn-rich brines in the later stage. A recent modeling and experimental study confirmed that Mn-oxide could be formed by oxyhalogen species [19]. Another possibility would be to form Mn-phosphates or Mn-chloride during evaporation, but more modeling and experimental works remain to assess this hypothesis.

Conclusion:

During the alteration process, a fractionation between Mn and Fe is triggered by differential in oxidation rates. Oxidation rates are mostly dynamically pH controlled by the dissolving minerals, rather than controlled by O2. We showed the importance of computing kinetics of dissolution and oxidation simultaneously, as even strictly thermodynamically favored phases can be difficult to form. This restrict Mn-oxides as a proxy for oxygen levels, as they could likely not be formed even under high O2 pressures and are also likely oxidized by other agents. Fe-oxide is likely a better O2 proxy. In an article in preparation, we will develop the model outcome using a different set of parameters.

Fig. 1 -

 1 Fig. 1 -Run of the kinetic weathering and oxidation at t=3°C and W/R = 10

Acknowledgments:

The engineers and scientists who operate the Curiosity rover are thanked for their generous contributions to this work.