Camille Diou

Lionel Torres

Michel Robert

Implementation of a Wavelet Transform Architecture for Image Processing

Keywords: Image compression, integrated processor, lifting scheme, multi-resolution analysis, wavelet transform

The wavelet transform appears to be an efficient tool for image compression. Many works propose an implementation of the pyramid a1gorithm with some improvement to reduce its treatment time or to increase its performances. However, the pyramid a1gorithm remains silicon area costly, essentially because of its memory needs, and depending on the size of filters used. This paper proposes a new implementation of the wavelet transform using the lifting scheme. This method proposes many improvements such as in-place calculation, small memory needs, and easy inverse transform.

I.INTRODUCTION

Compression is a necessary step for data transnnSSlOn or storage. Whereas there are many ways of compressing still images, the JPEG method is the most widely used. On the other hand, the video compression often remains based on the MPEG. The goal of this work is to develop a generic wavelet core that can be used as an Integrated Processor in integrated systems for many applications as image/video compression, edge detection, moving objects detection. This paper shows a comparison between the Mallat's pyramid algorithm (PA) [START_REF] Mallat | A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation[END_REF] and the lifting scheme (LS), a new tool for creating wavelets [START_REF] Sweldens | The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets[END_REF][START_REF] Sweldens | The Lifting Scheme: A Construction of Second Generaton Wavelets[END_REF][START_REF] Fernandez | LIFTPACK: A Software Package for Wavelet Transforms using Lifting[END_REF].

Next, we present the pyramid algorithm's implementation based on filter banks, and our architecture based on the lifting scheme.

WAVELET TRANSFORM AND MULTI-RESOLUTION ANALYSIS

The multi-resolution analysis [START_REF] Mallat | A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation[END_REF] uses two functions to project a signal on two spaces: the wavelet function extracts the details (high frequency signal); the scaling function keeps the approximation (low frequency signal). By translating and dilating the wavelet, we can analyse the signal all over the time and at different resolution levels. Different wavelet techniques exist for image processing [START_REF] Hubbard | Ondes et Ondelettes[END_REF][START_REF] Truchetet | Ondelettes pour le signal numerique[END_REF] depending on the signal to be analysed. We concentrate our efforts on the pyramid and the lifting scheme algorithms.

Filter banks and pyramid algorithm (PA)

The relationship between the wavelet multi-resolution analysis and filter banks was first shown by Mallat [START_REF] Mallat | A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation[END_REF]. The image is filtered by both high-pass and low-pass filters along horizontal direction, giving, respectively, an approximation of the original image and its horizontal details. This scheme is re-applied on the two sub-images along the vertical direction, giving us the three horizontal, vertical and diagonal details sub-images, and the 2-D approximated sub-image (Figure 1, left). The inverse transform is obtained by inverse filtering with the corresponding filters (Figure 1, right).

The lifting scheme (LS)

The lifting scheme algorithm [START_REF] Sweldens | The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets[END_REF][START_REF] Sweldens | The Lifting Scheme: A Construction of Second Generaton Wavelets[END_REF][START_REF] Sweldens | Building your Own Wavelet at Horne[END_REF][START_REF] Fernandez | LIFTPACK: A Software Package for Wavelet Transforms using Lifting[END_REF] presents many advantages compared to the pyramid algorithm [START_REF] Sweldens | Building your Own Wavelet at Horne[END_REF]: calculations are performed in-place for an important memory saving;

the algorithm shows an inherent SIMD parallelism at all scales; inverse transform is obtained easily from the direct transforrn; 103 this scheme can be performed even when the Fourier techniques are no longer suitable (for example when the sampIes are not evenly placed, that causes problems with the filter banks because of the sub-sampling)

Transform

It is composed of the three following steps (see Figure 2 for details): split: this step separates the signal into two parts. The more correlated the sub-signals are, the better the predict; practically, the signal is divided into a set of even indexed sampIes (S), and another one of odd indexed sampIes (D); predict: the first set S is used to predict the second one D, according to a defined function; the difference between the predicted set and the original one is kept as the detail signal; update: the detail signal D is used to update the unmodified set S, in order to keep the average value of the signal. This can be resumed by the following implementation:

(oddj_peven j _ l ) := Split(s) oddj-l-= Predict(even j _ l )

even j _ l + = Update(odd j _ l ) Figure 2 gives the schemes for I-D decomposition-recomposition. For a 2-D transforrn, we simply apply the same method to each output, and process the scheme along the vertical direction.

The implemented wavelet depends on the prediction function. The higher the degree of the prediction function is, the smoother the wavelet. If the prediction is very dose to the signal, the detail coefficients (i.e. the wavelet coefficients) will be very smalI.

Let's take an example with a linear prediction: if the original signal x is split into the detail signal d and the smooth signal s, we have: Before the prediction: [START_REF] Mallat | A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation[END_REF]

d k =X 2k + 1 (2) Sk = X 2k
And after the update:

Camille DIOU, Lionel TORRES, Michel ROBERT After the linear prediction:

1 (3) d k = X2k+l--(X2k +X 2k + 2 ) 2 1 (4) Sk = X 2k + "4 (d k _1 + d k )
The equation 3 gives us the corresponding high-pass filter, and when inserting equation 3 into 4, we get the corresponding low-pass filter:

HP = l-.! LP = . .! ._.!J 2 ' 2 8'4'4'4' 8 2.2.

Inverse transform

The inverse transform scheme contains three steps (undo update, undo predict and merge) which are obtained by reversing the order of the operations and by changing the signs of the operators, as shown in Figure 2.

We resume it with: even j _ 1 -= Update(odd j _ 1 )

odd j _ 1 + = Predict(even j _ 1 ) Sj := Merge(odd j _ p even j _ 1 ) The equivalent filter is obtained by putting one detail coefficient to 1, all others to 0, and computing the inverse transform. It gives the high-pass filter. Doing the same with a smooth coefficient gives the low-pass filter.

HP = LP = l.!.•l . . !. J 8' 4'4' 4' 8
2"2 Note that the filters we obtain correspond to the wavelet defined by Cohen, Daubechies and Fauveau (CDF) [START_REF] Cohen | Bi-orthogonal bases of compactly supported wavelets[END_REF].

ARCHITECTURES

There are many works on the implementation of the WT on FPGA [START_REF] Truchetet | Implementation of still-image compressiondecompression scheme on fpga circuits[END_REF][START_REF] Guermeur | Une implantation de la transformee en ondelettes discretes a base de circuits FPGA[END_REF] or ASIC [START_REF] Limqueco | A VLSI Architecture for Separable 2-D Discrete Wavelet Transform[END_REF][START_REF] Gauthier Lafruit | An Efficient VLSI Architecture for 2-D Wavelet Image Coding with Novel Image Scan[END_REF][START_REF] Fridman | On the synthesis of regular VLSI architectures for the I-D discrete wavelet transform[END_REF][START_REF] Grzeszczak | VLSI Implementation of Discrete Wavelet Transform[END_REF][START_REF] Devices | Ultralow Cost Video Codec[END_REF]. Most of them propose improvements to the pyrarnid algorithm [START_REF] Gauthier Lafruit | An Efficient VLSI Architecture for 2-D Wavelet Image Coding with Novel Image Scan[END_REF][START_REF] Urriza | Locality Improvement of the Pyrarnid Algorithm to Compute the Discrete Wavelet Transform[END_REF], or to the implementation (systolic or sernisystolic architecture, parallel or serni-parallel design [START_REF] Limqueco | A VLSI Architecture for Separable 2-D Discrete Wavelet Transform[END_REF][START_REF] Fridman | On the synthesis of regular VLSI architectures for the I-D discrete wavelet transform[END_REF][START_REF] Grzeszczak | VLSI Implementation of Discrete Wavelet Transform[END_REF]). But these methods rely on the same algorithm to perform the WT.

In this section, we present how we can implement this wavelet transform, first using filter banks, then with the lifting scheme. Then, we compare the methods to point out the number of needed operators, the silicon area cost and the memory cost of each method.

Filter banks architecture

Figure 3 shows a basic implementation of the pyramid algorithm for a 1-D wavelet transform. The number of operators is chosen in order to correspond to the CDF wavelet (the implementation with lifting scheme is shown in Section 3.2). An implementation of the 2-D wavelet transform using the CDF wavelet is shown in [START_REF] Truchetet | Implementation of still-image compressiondecompression scheme on fpga circuits[END_REF]. We can see, in Figure 3 that the filters described above are present three times and that an important memory is necessary to perform the transform. At least the two 128x256 memories must be on-chip if we want to keep good performance during the transform. All these memories and the filters need an important silicon area. The inverse transform is not shown, but it needs a consequent memory too: 112 kB are necessary in the architecture presented in [START_REF] Truchetet | Implementation of still-image compressiondecompression scheme on fpga circuits[END_REF]. The Table 1 shows the theoretical performances for this system for 5 levels of resolutions on a 256x256 image (see [START_REF] Truchetet | Implementation of still-image compressiondecompression scheme on fpga circuits[END_REF]), taking into account the following values: 250 ns per pixel for the analysis, and 40 ns per pixel for the synthesis. This table does not show the times of the quantizationldequantization process, which are small compared to the transform.

The evaluated number of CLB for an implementation in a XC4005 family FPGA is about 340. Thus, the implementation of the wavelet transform needs around 5 kgates, without the memory.

3.1.1. Lifting scheme architecture I-D structure We saw in the section 2.2 that the implementation of the lifting scheme requires few operators. We need, for each step (prediction and update), two adders in the decomposition and two adders in the recomposition. We can see in Figure 4 that there is no need for memory during the I-D transform: the transformed coefficients overwrite the original ones during the decomposition. Thus the transform block can be seen from outside as a delay line. The transform can be performed in pseudo real-time, depending on the system dock. We get the same condusion for the reconstruction step. Unlike the I-D case, we need, in the 2-D case, some memory to perform the transform. Before starting the transform along the columns, we have to wait until the transform along the rows is achieved. There are different ways of doing this:

we wait that the first I-D decomposition is achieved, we store the image in a memory, rotate it by 90° or address the memory in a different manner, and we perform the second decomposition;

we only wait that a few rows are treated and then start the vertical decomposition on these rows. When the following rows are achieved, we continue the vertical decomposition on them. This last case is the most interesting from a memory point of view, but we also have to define the method to access the memory: we receive a few lines, and we want to transform them along the columns.

Figure 6 shows how we can start the vertical decomposition after the horizontal decomposition of the three or four first ones is achieved. We start the horizontal decomposition by computing the detail coefficients, and reuse them to compute the approximation. Once the 3 first lines are treated, we can start the vertical decomposition. When the fourth line (detail) is treated, the line of vertical detail coefficients is achieved too. Both this line and the previously treated one can then be used to compute the vertical average coefficients. While the vertical average is treated, the next vertical detail can be processed concurrently, while the horizontal average is also being calculated. Thus, in order to perform the complete 2-D transform, we only need a memory that can contain 4 lines of the image, i.e. for a 256x256 images at 8 bits per pixel, 4x256x8=1 kBytes.

Comparisons

Number of logic blocks. The lifting is very interesting for integrated systems because of liule need for logic blocks. The table below show the difference between the lifting scheme and the filter banks. We saw that the filter banks architecture needs around 340 logic cells. The lifting scheme only needs around 190 (24 adders x 8 blocks per adder).

Furthennore, to perform the multiplication, using bit shifting, the lifting scheme needs only 12 shifts whereas filter banks needs, for a 1-0 transfonn. For a 2-0 transfonn, this increases to 36 and 102 respectively.

Memory. One of the main advantages of the lifting scheme is the inplace calculation. We don't need any buffer memory to perfonn the transform: the wavelet coefficients overwrite the original ones (Figure 7). Figure 7 shows, on a real image, the Mallat and lifting scheme coefficients distribution after a 2-level decomposition. The on-chip memory needed for the filter banks design is approximately the size of an entire image whereas, for a lifting scheme implementation, this memory is reduced to a few lines. Table 3 shows the memory necessary for the filter banks method as described in [START_REF] Truchetet | Implementation of still-image compressiondecompression scheme on fpga circuits[END_REF]. 3. Memory need of the lifting scheme compare to the filter banks for a 256x256 image of 256 grey-levels Thus, the lifting scheme implementation needs two times less logic blocks and very litde memory compared to filter banks architecture. Furthennore, as the lifting scheme computes the wavelet transfonn in-place, we want to evaluate its perfonnance at video rate. We see, in the next section, a first implementation of the lifting scheme.

HARDWARE IMPLEMENTATION

Overview

We have started to validate the lifting scheme architecture in real-time with an APTIX prototyping p1atfonn [START_REF] Aptix | [END_REF]. This programmable platfonn (Figure 8) contains Altera lOk100 FPGA, used to implement the wavelet transfonn with the necessary memory. A OSP core (ST 0950) is used to perfonn the quantization and the coding of the wavelet coefficients. Figures 10 and11 show the implementation of the 2-0 lifting scheme. The input image is first decomposed horizontally. We get two sub-images at half the pixel dock frequency. Thus, we can altematively decompose them along the vertical direction, switching between detail sub-image and smoothed subimage. To keep the video rate, we have to interlace the two sub-images' lines -putting one data of the first sub-image in the memory, and then one data of the second sub-image -and compute the resulting image along vertical direction. Because of the in-place calculation, the horizontal decomposition of the image can be perfonned at the video rate. The original set of data at the frequency F is decomposed into two subsets (detail and average) at the frequency F/2. A simulation of the 1-0 horizontal lifting scheme decomposition shows that this block needs 116 Altera's Flex lOk100 logic cells, that is, 2% of the chip. Thus, there is no noticeable difficulty in implementing the first 1-0 horizontal decomposition block. Thus, wel1 point out the vertical decomposition below.

Vertical decomposition of the sub-images

There are different ways of computing the vertical decomposition: we can use FIFO memories or RAM. The FIFO seem to be more efficient because they need no memory managing, in the strict sense of the tenn. But, the logic necessary to manage the four FIFO increases considerably the complexity. We describe here the two methods.

Using FIFO memories

We consider that a first computed odd line OOn_l is present in the first FIFO Fl. A first not computed even line Sn is in the FIFO F2. A first not computed odd line On+1 is in the third FIFO F3 . When the second not computed even line Sn+2 is ready, we compute the detail coefficient line from Sn, On+1 and Sn+2' We name these coefficients OOn+I .These coefficients are used to compute the average coefficients SSn from OOn.1> Sn and OOn+l. The coefficients SSn and DOn_I are written to the output of the FIFO F2 and FI respectively. The DDn+1 replaces the DDn_1 in Fl and the Sn+2 replace the Sn in F2. Now, we have OOn+1 in Fl and Sn+2 in F2; F3 is free. When On+3 is ready, we stock it in F3 and wait for Sn+4 which is necessary for ca1culating 00n+3. Then, the scheme can be repeated from the beginning. Using RAM The method described above shows the complexity of the FIFO memories managing. We have to use numerous multiplexers and demultiplexers for choosing between the video input (the output of the 10 transform block) or the output of the FIFO. All the logic that must be developed could be used to implement a RAM controller. Thus, instead of using FIFO memories, we could use RAM and address the data in a standard way (Figure 11).

Implementation

A first evaluation of the system presented in Figure 10 shows that the system uses 554 Altera's logic cells (i.e. 25% of the Flex lOk100 chip), and 6144 memory bits, that is 25% of the total memory of the Flex lOk100. All these results are given for 8 bits bus width. With a c10ck frequency about 30 MHz, this will allow the treatment in real-time, of images with a size of 800x800 pixels in 256 grey-Ievel by increasing the size of the FIFO or the RAM. The needed memory can be implemented on the Altera's lOk100 FPGA. By using pipeline techniques, we estimate that we can obtain a c10ck frequency of 60 MHz, allowing us to process images in HDTV format.

First results of using the LS for image compression show a compression ratio of about 10 for a Peak Signal to Noise Ratio (PSNR) of 30 dB, which is the minimal admitted value for a good image quality. We are currently working on improving the compression ratio to get a value around 40, by using a well-adapted quantization and arithmetic coding [START_REF] Antonini | Image Coding Using Vector Quantization in the Wavelet Transform Domain[END_REF][START_REF] Antonini | Image Coding Using Wavelet Transform[END_REF][START_REF] Mathieu | Compression d'image par transformee en ondelette et quantification vectorielle[END_REF].

CONCLUSION

In this paper, we have shown a new way of implementing the wavelet transform. This method combines an efficient processing rate with low area cost and memory use. It can easily be adapted to perform the inverse transform. The design re-use and IP cores concept is becoming increasingly present in the top down design flow; it is changing the way electronic engineers works. The impact on time-to-market can be considerable; for this reason, we intend to develop a complete architecture for wavelet transform which can be used as a wavelet IP core for image processing applications.

lI! 1 Figure 1 .

 11 Figure 1. Wavelet transform image decomposition (left) and recomposition (right)

Figure 2 .

 2 Figure 2. Signal decomposition (Jeft) and recomposition (right) with lifting scheme

Figure 3 .

 3 Figure 3. Pyramid algorithm implementation. Left: basic filtering cello Right: whole structure

Figure 4 .Figure 5 .

 45 Figure 4. Structure of the lifting scheme blocks: transform (left) and inverse transform (right) 2-D structure For the 2-D implementation, we use the same blocks, organised in a cascade as shown in Figure 5. ...................... -_ ........ . ! Hoci'Z.OntaJ clecomposition

  " ... ' , ... : , ... , .1 . . . . . . . . ' . 1-::"=: . L..---...V .... c; ' :-.; Co: () C.: C.: ' ::' Nol ,., ..... p'lIro'h."'" o ... Itolll, ..... ponat . -. o ... Itolll, ..... puledclo\oj i o Jk;'s ..... puled._ _ Jk;'S ..... puledclo\oj l I,::, _ Ccmpulolhodd.;1 10 0 0 I Ccmpulo lho .... r.

Figure 6 .

 6 Figure 6. Memory need ofthe 2-D lifting scheme

Figure 7 .

 7 Figure 7. Distribution of the wavelet's coefficients: a: pyramid algorithm and b: lifting scheme and 2-1evels decomposition of an image. c: Mallat and d: LS coefficients distribution. e: original and I re-composed images

Figure 8 .

 8 Figure 8. APTIX prototyping platfonn 4.2. Horizontal decomposition of the input image

Figure 9 .

 9 Figure 9. Three FIFO are used to perform the vertical decomposition

Figure 10 .

 10 Figure 10. (Jeft) Implementation of the lifting scheme using FIFO Figure 11. (right) Implementation of the lifting scheme using RAM

Table 1 .

 1 Compression and decompression times of a filter banks architecture

	Line	Colurnn		Total
	31.7 ms	31.7 ms	64ms
	Data reading	Data reading	Image writing	Total
	Of first cells	Of last cells
	4.556 ms	8.857 ms	3.491 ms	17ms

Table 2 .

 2 Operators necessary for one step (transform or inverse transform)

	Lifting scheme	Filter banks
	Total (2-D)	12 adders	Total (2-D)	21 adders

Table

		Lifting scheme	Filter banks
	Decomposition	I kB	84kB
	Recomposi ti on	I kB	112 kB


Camille Diou

Lionel Torres

Michel Robert
email: robert>@linnm.fr

A WAVELET CORE FOR VIDEO PROCESSING

Keywords: Image processing, lifting scheme, multi-resolution analysis, wavelet core, wavelet transform

The wavelet transform appears to be an efficient tool for image processing. However, the pyramid algorithm remains silicon area costly, essentially because of its memory needs, and depending on the size of filters used. This paper proposes a new implementation of the wavelet transform using the lifting scheme. Using an improved method of managing the data flow and the RAM, this method proposes many improvements such as in-place calculation, small memory needs, and easy inverse transform.

INTRODUCTION

In compression applications using the wavelet transform, in many image processing systems that rely on wavelet algorithms (segmentation, edge detection), the processing time is an important feature and a high speed (or real-time) treatment cannot ever be reached with software implementations. A good solution is to implement a complete system and its memory on a chip, within the data acquisition hardware (System on Chip).

This paper shows a comparison between the MALLAT'S pyramid algorithm (PA) [l] and the lifting scheme (LS), a new method for creating wavelets [START_REF] Wim | The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets[END_REF][START_REF] Wim | The Lifting Scheme: A Construction of Second Generation Wavelets[END_REF]61. Next, we present the pyramid algorithm's implementation based on filter banks, and our architecture based on the lifting scheme. This architecture presents many advantages as a good integration, high frequency processing and low memory needs.

WAVELET TRANSFORM AND MULTI-RESOLUTION ANALYSIS

The multi-resolution analysis [ 11 uses two functions to project a signal on two spaces. The wavelet function extracts the details (high frequency signal) and the scaling function keeps the approximation (low frequency signal). By translating and dilating the wavelet, we can analyze the signal all over the time and at different resolution levels.

Filter banks and pyramid algorithm (PA)

Fig. 1. Wavelet transform image decomposition

The image is filtered by both high-pass and low-pass filters along horizontal direction, then subsampled to give two sub-images that contain, respectively, an approximation of the original image and its horizontal details. This scheme is re-applied on the two sub-images along the vertical direction, giving us the three horizontal, vertical and diagonal details sub-images, and the 2-D approximated sub-image.

Figure 1 shows the 2-D MALLAT wavelet transform.

To get a multi-resolution analysis, the approximation signal (low-pass band) is reintroduced into another filter banks set connected in a cascade way with the first one: this is the pyramid algorithm.

The lifting scheme (LS)

The lifting scheme algorithm [3,4,5, 61 presents many advantages compared to the filter banks [START_REF] Wim | Building your Own Wavelet at Home[END_REF]: 0 all calculations can be performed in-place for an im-0 the algorithm shows an inherent SIMD parallelism at 0 the inverse transform is obtained easily from the di-portant memory saving; all scales; rect transform.

Transform

The lifting scheme is composed of several elementary steps that when applied successively construct a predefined wavelet. When using the Cohen-Daubechies-Feauveau 2-2 biorthogonal wavelet [START_REF] Cohen | Bi-orthogonal bases of compactly supported wavelets[END_REF], the number of steps is reduced to the three following (see Figure 2): 395 0-7803-62~7-7/00/$10.00 0 2000 IEEE split: separates the signal into 2 parts. The more correlated the sub-signals are, the better the predict; predict: the first set is used to predict the second one, according to a defined function; the difference between the predicted set and the original one is kept as the detail signal; update: the detail signal is used to update the untouched set, in order to keep the average value of the signal.

-0 O ( 0 . 0 1

0 0 0 0 0 0 0 0 a 2.

Inverse transform

The inverse transform scheme contains the same steps (in this case: undo update, undo predict and merge) which are obtained by reversing the order of the operations and by changing the signs of the operators, as shown in Figure 2, right.

ARCHITECTURES

We have seen in the previous sections that the lifting scheme presents many advantages for the implementation of the WT.

In this sections, we will point out this advantages by presenting two architectures for the WT. The first one is a filter banks architecture which implementation isn't improved enough for performing the 2D WT. Readers can find more information on this implementation in [START_REF] Truchetet | Implementation of stillimage compression-decompression scheme on fpga circuits[END_REF]. The architecture we propose is based on the lifting scheme and allows some improvements for the 2D WT calculation.

Filter banks (FB) architecture

Fig. 3. Implementation of the PA: a: basic filtering cells, b: whole 2D structure An implementation of the 2-D wavelet transform using the CDF wavelet is shown in [7]. We see in Figure 3b that the 3 filter banks (Figure 3a) are present, and that an important memory is necessary between the filters to perform the transform. Furthermore, the size of the filters corresponds to those described in section 2.2.1, that is 5 coefficients for the fist filter (LP), and 3 coefficients for the second (HP), that implies a total of 6 adders per filter bank.

Lifting scheme architecture

1-D structure

We saw in the section 2.2 that the implementation of the lifting scheme requires few operators. We need, for each step (prediction and update), a total of four adders to perform the complete stage (Figure 4). We can see in Figure 4 that there is no need for memory during the 1-D transform: the transformed coefficients overwrite the original ones during the decomposition. Thus, the transform can be performed in real-time, at the pixel clock. We get the same conclusion for the reconstruction step. Furthermore, unlike the FB method, the subsampling is done before the computations, thus there is no lost of computational time.

Number of logic blocks

The lifting is very interesting for integrated systems because of little need for logic blocks. The table 1 shows the differ-ence between the lifting scheme and the filter banks. This table also shows the number of adders that we need to perform either the transform or the inverse transform, in the 1-D and 2-D cases.

# adders (1 D) # adders (2D) Mem. need (dec.) Mem. need (rec.)

Memory

We saw that we don't need any memory during the transform, because the calculated values replace the original ones. Using the method described in section 4.1.1, we can reduce the memory need for the 2D transform, as shown in table 1.

.

Lifting scheme Filter banks

4 6 12 18 < 1 kB 84 kB < 1 kB 112kB !.
to the next incoming value (Fig. 7-5), and once the whole line is treated, we can reload the memories c and d with the incoming lines (Fig. 7-6) and repeat the scheme from the beginning.

We can figure out which type of memory we will use.

two FIFO of sizes N and ($ + l), to keep a constant data rate at the output of the two FIFO. For memories a and b we just have to use two delay lines of size N (where N is the size of the line)

0 0 0 8 0 8
Mem. need (dec.)

3kB 84kB
Mem. need (rec.)

3kB 112kB

Max. image size

x 2048 256x256

Can process video ?

Yes no

Unknown Unknown

Fig. 6. 2D implementation of the lifting scheme

Figure 6 shows the implementation of the 2-D lifting scheme. The input image is first decomposed horizontally. Then, using some improved techniques, we will decompose it along vertical axis using only 3.5 memory lines. There is no noticeable difficulty in implementing the first 1 -D horizontal decomposition block, thus, we'll point out the vertical decomposition.

Vertical decomposition of the sub-images : the linebufer method

Figure 7 shows the different steps of the 2-D transform using lifting. We consider that the memory a contains the previous already computed detail line. memory b contains the previous approximation. When the 1-D decomposed detail lines is computed, we store it in the memory c. We can then start the vertical decomposition when the approximation coefficient comes in (Fig. 7-l). Once the detail is computed, we can re-use it with the previous detail to compute the average (Fig. 7-2). Next, we extract the previous detail and average (Fig. 7-3) and replace them respectively with the computed detail and average (Fig. 7-4). We re-apply this scheme

Implementation results

The table 2 below shows the performances of our system compared to filter banks [START_REF] Truchetet | Implementation of stillimage compression-decompression scheme on fpga circuits[END_REF] and ADV 601. Notice that the needed memory in this table is extended to the maximum size of the images that the system can treat.

ARCHITECTURE FOR THE MULTI-RESOLUTION ANALYSIS

2D multi-resolution decomposition architectures

There are two easy-to-implement multi-resolution architectures: 0 the first one consists in using a picture memory used to store the whole approximation sub-image, as the Figure 3.b shows.

0 the second solution is to reproduce as many transform blocks as necessary (i.e. one block per level).

The first solution needs too many memory for an onchip implementation (several kilobytes of memory). The second solution increases the hardware resources needed (the transform blocks and their associated memory). Thus, we have to develop a method to perform the multi-resolution 2D analysis that will re-use the same wavelet transform block, and minimize the necessary memory.

The proposed architecture

output S1R8m -Fig. 8. Architecture for the multi-resolution analysis

The architecture we propose is based on the Recursive Pyramid Algorithm. The RPA consists of re-arranging the order of the N outputs such that an output is scheduled at the earliest possible instance [9, 101. Figure 9 shows how the recursive pyramid algorithm produces a regular data flow with samples from different resolutions.

To compute the multi-level WT, we have to store the low resolutions samples in memory cells until we can compute them, and interlace them with the original samples in the input data flow. Therefore, we use some small FIFO and a multiplexer at the input of the system. A context switching procedure will allow us to store this samples in the appropriate buffers (latches or FIFO). Each time the system will switch its working context, all the corresponding data will be loaded from the memory cells, and the previous ones stored. Figure 8 shows the modified architecture to perform the WT. The WT begins with the original input data flow. The computed 2D-coefficients are stored in their corresponding input FIFO memories. As soon as two samples from next resolution are ready in this FIFO, we can switch the working context to this level. This will save the current samples in their appropriate memory cells (latches) in the horizontal 1D transform block, and read the data in the latches corresponding to the current level. Thus, all the old data are stored and the new ones are read in one clock cycle. After the computations, the result is sent to the corresponding FIFO. The vertical ID transform block works in the same manner. The total memory of the modified architecture re-mains smaller than 7Nb, where b is the size of the samples in bits, and is equivalent to others architectures [9, lo].

In order to validate this method, we are currently working on the implementation of the architecture for the multiresolution in a Flex lOkl00 FPGA.

CONCLUSION

In this paper, we have shown a new way of implementing the wavelet transform. This method combines an efficient processing rate with low area cost and memory use. It can easily be adapted to perform the inverse transform.The described architecture provides a good integration and can be easily prototyped on a FPGA (Field Programmable Gate Array), due to the small memory and the few operators needed.

The system and its memory (latches or FIFO) are designed to allow an optimal working frequency and is not hardware dependent. The inherent SIMD parallelism and the pipeline techniques used allow the system to work at very high frequency. We intend to extend the architecture to allow different wavelet to be be implemented, by using programmable coefficients and user defined lifting steps number.

Fig. 2 .

 2 Fig. 2. Signal decomposition and recomposition with lifting

detailFig. 4 .

 4 Fig. 4. Structure of the lifting scheme transform block

Fig. 5 .

 5 Fig. 5. Vertical decomposition after computation of 3 lines 3.3. Comparisons

  banks [7] I 601 [8] I I ax. oixeI rate I 66 MHz I 1 MHz I 14.75 MHz I

Table 1 .

 1 Resources needed by lifting vs. pyramid algorithm

	768x288
	Yes

Table 2 .

 2 Performances of lifting vs. PA and ADV601


Jun Yoshida

Elodie Guerin

Mélissa Arnault

Cédric Constantin

Benoit Mortemard De Boisse

Dany Carlier

Marie Guignard

Claude Delmas

NewP2 -Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 Layered Oxide as Electrode Material for Na-Ion Batteries

Sodium layered oxide, Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 , with a P2-type structure was synthesized by a co -precipitation method and characterized as positive electrode of sodium batteries. The P2-Na x Mn 0.60 Ni 0.30 Co 0.10 O 2 electrode delivered a high specific capacity of 185 mAh/g in the 1.5-4.3 V range at 1 st cycle at C/20 rate; however, rapid capacity decay is observed. In the 1.7-4.0 V range the capacity is equal to 125 mAh/g with a fading considerably reduced. The rate capability is reasonably good. According to the electrochemical profile, a potential plateau around 4.2 V vs. Na + /Na, meaning a bi-phasic domain, and several voltage drops that could be related to single phase domains in a narrow sodium content range are observed. Even if the capacity decreases when the battery is cycled above 4.0 V, there is no irreversible structural change.

Owing to abundant sodium resource and therefore the low price of sodium compounds, sodium-ion batteries are thought to be one of favorite future batteries for hybrid vehicles (HVs). Recently, a rapid expansion of the HVs market is inducing to grow lithium consumption. Therefore, to face lack of lithium resource problem, it is necessary to develop sodium-ion battery technology. Concerning positive electrode materials, Na x MO 2 layered type phase have been studied for a long time. They were first studied in the 80's by Delmas et al. [1][2][3] Layered Na x MO 2 are classified into several groups denoted such as P2 or O3. The letter indicates the site environment of sodium with oxygen (prismatic or octahedric) and the number indicates the number of MO 2 slabs within the hexagonal cell. 4 For instance in the P2 type structure, we focus on in this study, sodium ions are in trigonal prismatic sites between two MO 2 slabs with different orientations. In the 2000's many studies were performed in Dahn's group on P2-Na 2/3 Ni 1/3 Mn 2/3 O 2 phases and their cobalt substituted derivatives. [5][6][7][8] These authors characterized these materials and used them as precursors for the syntheses of new lithium phases obtained by exchange reactions. For several years, thanks to the potential interest of sodiumion batteries, a huge number of researches are carried out on layered sodium oxides and in particular on P2 type phases. [9][10][11][12] The higher ion diffusivity in trigonal prismatic environment vs. octahedral one 13 led several researchers to report that P2-type structure leads to higher capacity and cyclability than the O3 one. Yabuuchi et al. reported that P2-Na 2/3 Fe 1/2 Mn 1/2 O 2 exhibits a capacity for the first cycle of 190 mAh/g, which was higher than that of reported O3 ( 100-110 mAh/g). 14 Some of us discussed electrochemical performances between P2 and O3 structure types for Na x Mn 1-y Fe y O 2, and they deduced that those of P2-type material were better than those of O3-type one. 15 Other authors reported on different phases with P2-type structure: Na x Fe y Mn 1-y O 2 , 16 23 have been investigated in order to improve the electrochemical performances by analogy with lithium-based materials as LiMn 1/3 Ni 1/3 Co 1/3 O 2 . 24 Yuan et al. recently reported on a Na 0.67 Mn 0.65 Fe 0.20 Ni 0.15 O 2 material, which delivers a high specific capacity of 208 mAh/g in the 1.5-4.3 V range vs. Na + /Na. 25 In this work, we focus on the Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 composition obtained by a co-precipitation method. Its crystal structure and morphology are characterized using X-ray diffraction (XRD) and scanning electron microscopy (SEM); electrochemical properties were also examined in Na cells.

z E-mail: delmas@icmcb-bordeaux.cnrs.fr

Experimental

Synthesis methods.-A co-precipitation method is used to make the aimed compound. Two solutions, one made of Co(NO 3 ) 2 • 6H 2 O, Ni(NO 3 ) 2 • 6H 2 O and Mn(NO 3 ) 2 • 4H 2 O (one mole/l of the transition metal ions with the selected composition), and another one made of Na 2 CO 3 (one mole/l) , were simultaneously dropped into a beaker with 450 ml of distilled water by using a syringe pusher with a flow of 50 ml/min, with stirring at 700 rpm and keeping at 50 • C. Therefore, all along the precipitation the target material stoichiometry and the pH was maintained. The precipitate thus formed was washed with distilled water 5 times, and dried at 80 • C for two days. The dried powder was mixed with Na 2 CO 3 in a glove box filled under argon to reach the Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 composition. A 10 wt% excess of Na 2 CO 3 was added to compensate its volatility at high temperature. The mixture was calcinated at 600 • C for 6 hours, and then heated at 900 • C for 12 hours in air or in oxygen. Finally, it was quenched in air down to room temperature. Preliminary experiments have shown that there is no difference either from a structural nor an electrochemical point of view when the syntheses were realized under air or oxygen.

Characterization.-Powder XRD patterns were recorded on a powder diffractometer (D5000, Bruker or Enpyrean, Panalytical) equipped with a Cu target (Cu kα 1, 2 ). The measurement was carried out from 10 • to 80 • with steps of 0.02 • ; the total acquisition time was 14 h 30. To prevent the effect of water, all the XRD experiments were done in a homemade air-tight sample holder. The cell parameter refinement was performed with LeBail method in FullProf program. 26 Morphological images were observed on a Hitachi S4500 field emission scanning electron microscope (SEM) with an accelerating voltage of 3.0 kV. Gold coating was implemented before the observations. The electrochemical performances were evaluated in two electrodes configuration using metallic sodium as the counter electrode in Swagelok or coin type cells. The positive electrode was a mixture containing 88 wt% of the active material, 10 wt% of carbon black as electronic conductor and 2 wt% of polytetrafluoroethylene (PTFE) as binder. The electrolyte was 1 M NaPF 6 (Alfa Aesar 99%) in propylene carbonate (Sigma Aldrich anhydrous 99%) with 2 wt% of fluoroethylene carbonate (FEC) as additive. Galvanostatic performances were evaluated at the C/20 current rate at 25 • C. All cell voltages are given vs Na + /Na redox couple.

Results

Material syntheses and characterization.-A systematic study of several compositions was made to obtain P2 type phases with the Na x (Mn,Ni,Co)O 2 formula. The amount of sodium was selected equal to 0.70 that is the classical sodium amount to obtain this structural type; this leads to an average transition metal oxidation state equal (i) Mn 3+ and Ni 3+ cannot be simultaneously present as Mn 3+ + Ni 3+ gives spontaneously Mn 4+ + Ni 2+ via an internal redox reaction, (ii) Co 4+ is no longer stable in front of Ni 2+ . All tests with various compositions satisfying the previous requirements, but containing Ni 3+ were unsuccessful whatever the experimental conditions; NiO was present in all samples. Table I gives a summary of the various experiments which have been done. It clearly appears that when the theoretical amount of Ni 3+ decreases the amount of NiO experimentally found in the sample as an impurity decreases. In the literature, all P2 type materials with general formula Na x (Mn,Ni,Co)O 2 satisfy the previous requirements. They can contain Mn 3+ , Mn 4+ Co 3+ and Ni 2+ ; but never Ni 3+ . 7,8,23 Therefore, we selected compositions with no trivalent Ni 3+ with general formula: Na 0.70 Mn 0.3+x Ni x Co 0.7-x O 2 . In this case, materials with the P2 type structure were obtained as pure phases. This behavior seems to be related to the stability of the P2 structure as in the case of the lithium O3 phases, Ni 3+ and Ni 2+ can be simultaneously present (Li 1.12 Mn 0.37 Ni. 0.37 Co 0.13 O 2 for example). 27 Further studies are required to understand this behavior. Among all possible compositions we focused our study on the Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 composition which contains a small amount of expensive cobalt. This phase was obtained in air at 900 • C as described in the experimental part. Its XRD powder pattern is shown in Fig. 1. The profile was refined in the hexagonal system with the classical space group of the P2 type phase (P6 3 /mmc). All diffraction lines are indexed that shows that no impurities can be detected by XRD. The cell parameters are a hex. = 2.8842(1) Å, and c hex. = 11.089(1) Å. Images of the particles are given in Fig. 2. They illustrate that average diameter of primary and secondary particles are around 1-2 μm and 60 μm, respectively. The primary particles have hexagonal shape, which is typical in the layered materials. 3a. The specific capacity is equal to 185 mAh/g at the 1 st cycle when the battery is cycled in the 1.5-4.3 V range. A small shift is observed between the first and the second charge that may result from electrolyte oxidation in relation with the formation of the solid electrolyte interphase (SEI) involving the FEC additive. 28 The effect of the upper and lower voltage cut-off values has been also studied. As shown in Fig. 3b and3c, cycling the battery in the 1.5-4.0 V and 1.7-4.0 V voltage ranges limits significantly the capacity fading in comparison to that in the 1.5 V-4.3 V range. Fig. 4 shows the comparison of the discharge capacity evolutions along with the cycling number. It can be noticed that the capacity retention given in the 1.7-4.0 V range is approximately 94%, which is higher than those in the other voltage ranges (82% in 1.5-4.0 V, 58% in 1.5-4.3 V). In the 1.7-4.0 V range the shape of the curve is not modified at all that emphasizes the reversibility of the intercalation/deintercalation reaction in this voltage range.

The rate capability test was performed from C/20 to C during a cycling in the 1.7-4.0 V range. At each rate three cycles were done. At the end of the experiment, three cycles at C/20 were also done for comparison. As shown in Fig. 5 the capacity decreases from 120 mAh/g at C/20 to 80 mAh/g at C and return to 127 mAh/g when the rate comes back to C/20. A slight increases is even observed, which can result from an activation of the material. No material activation is observed during the C/20 cycling in the same voltage range. One can assume that at high rate, there are large concentration gradients that induce constraints within the particles. A chemical grinding of the primary particles or an increase of the porosity of the secondary particles could improve the reaction kinetics and therefore, increase the cell capacity.

The shape of the curve shows the existence on several parts separated by rapid changes in voltage. In a first step the battery was discharged to 1.5 V. This initial discharge profile, given in the inset of Fig. 3a, indicates that sodium ions can be inserted up to x = 0.90, not reaching the full occupancy for the sodium sites that is a general phenomenon occurring in layered materials. In this part of the discharge it is assumed that only the Mn 4+ /Mn 3+ redox couple is active: Mn 4+ ions are reduced to Mn 3+ to compensate Na + intercalation. Nevertheless, further experiments are required to prove that cobalt ions are not partially reduced to the divalent state as we have previously reported in the case of the P2-Na x Co 2/3 Mn 1/3 O 2 system. 19,29 During the battery charge above 2. ularly stable in a narrow sodium content range. It is assumed that these voltage drops are related to the occurrence of sodium / vacancy orderings between the MO 2 slabs. Such a behavior is generally not observed in a multication slab composition. In general, the cationic disorder within the slab prevents any sodium ordering in the interslab space. From the redox point of view it is assumed that for x < 0.7, Ni 2+ are oxidized to Ni 3+ in a first step then to Ni 4+ . Cobalt oxidation has also to be considered. In the case of P2-Na x CoO 2 system, Co 4+ ions are observed in the whole voltage range between 2.3-3.8 V range. 30 In addition, like in lithium systems, the oxidation of Mn 4+ is not expected. Furthermore, 0.35 Na + ions are deintercalated between 2.30 V and 3.75 V; this suggests that Ni 2+ to Ni 3+ oxidation is the main process in this composition range. The plateau around 4.2 V is identified with the occurrence of biphasic domain. Fig. 6 gives a comparison of the XRD patterns of the materials recovered after one charge of the cell at 4.0 V and 4.3 V, respectively. At 4.0 V the XRD pattern is characteristic of the P2 type structure, whereas the 4.3 V one is very different. Only two main lines are observed: (i) the first one is equal to the interslab distance (c hex. /n), (ii) the second one is characteristic of the classical intra-slab distance (a hex. ). Obviously, there is a change in the slab packing, but there is no enough data to identify the structural type. For intermediate sodium amounts in the 4.2 V plateau a mixture of both phases is observed on the XRD patterns. The length of the plateau continuously decreases upon cycling, while the capacity between 4.0 V and 2.0 V remains almost constant. In previous papers Lu et al. reported the possibility of the transition from P2 to O2 structure type for P2-Na 2/3 Ni 1/3 Mn 2/3 O 2 at high voltage, 31 while Yabuuchi et al. mentioned that in the P2-Na 2/3 Fe 1/2 Mn 1/2 O 2 system the phase transition to OP4 structure type occurs by gliding of slabs at the end of the charge. 14 In both cases, these structural changes result from slab gliding. In the hypothesis of the transition to O2 structure type all trigonal prismatic sites are converted to octahedral ones, whereas in the hypothesis of the transition to OP4 structure transition only 1 over 2 of those sites is alternatively transformed. In our material, it can be assumed that Na deintercalation for x < 0.35 leads to slab gliding with local formation of O2 type interslab spaces. It results in the formation of stacking faults that prevent a clear characterization of the material. Experiments are in progress to characterize the structure of the material obtained at high voltage. It is well-known that the stability of the trigonal prismatic vs octahedral environment of alkali ions in layered structures depends on the intercalation amount but also on the ionicity of the M-O bonds that is directly related to the slab composition see Fig. 3 in ref. 4.

As shown on Fig. 3, even if the capacity on the 4.2 V plateau decreases rapidly upon cycling, the structural defects formed during the charge seem to disappear in discharge, as the shape on the discharge curve below 4.0 V is not modified even after 10 cycles. In order to study the material stability the following experiment was done. In a first step, as shown in Fig. 7, 10 cycles were done in the 3.0-4.3 V voltage range where the phase transition occurs. The length of the 4.2 V plateau decreases continuously. The experiment was continued with the same battery in the 1.5-4.0 V range for 10 more cycles. The shape of the curve is preserved upon cycling, which shows that no material degradation occurs during the cycling at high voltage. An XRD pattern was recorded on material recovered after 10 cycles in the 3.0-4.3 V range. At the end of the last discharge the cell voltage was maintained at 3.0 V for 24 hours to obtain a very homogeneous material. The material composition is close to Na 0.60 Mn 0.60 Ni 0.30 Co 0.10 O 2 . Its XRD pattern (Fig. 8), typical of the P2 phase, shows that the material is well crystallized. The comparison of the cell parameters to those of the Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 starting phase (a hex. = 2.8786 (1) Å and c hex = 11.163 (1) Å for the material at 3.0 V compared to a hex. = 2.8842(1) Å and c hex. = 11.089(1) Å for the pristine material) confirms the higher average oxidation state of transition metal ions (smaller a hex ) and the smaller amount of sodium (higher c hex. ). To determine the effect of the cycling on the particle size we selected three diffraction lines with very different Miller indexes. The comparison of the shape of the (103), ( 106) and (110) diffraction lines (Fig. 9) shows that there is no broadening of the (110) line, whereas there is a small broadening of the (103) and (106) ones. These lines were selected because: (i) they do not overlap with other diffractions lines (see Fig. 1), (ii) they have different Miller indexes that allows to discriminate between in slab plane and along the c axis coherence lengths. This result shows that the coherence length is maintained in the hexagonal plane, whereas it decreases slowly along the c axis that suggests the presence of some extended defects along this axis. SEM experiments after various numbers of cycles in various voltage ranges are in progress.

A capacity fading also occurs when the battery is discharged down to low voltage. Discharging the battery down to 1.5 V implies the reduction of Mn 4+ to Mn 3+ in a larger amount than for a discharge down to 1.7 V. It is assumed that the existence of Mn 3+ ions leading to the Jahn-Teller distortion of MnO 6 octahedra, which can induce constraints and defects in the material that may increase the capacity fading.

Conclusions

P2-Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 was synthesized using the coprecipitation method. To get a pure P2 phase, it is required to avoid Ni 3+ in the targeted composition. Therefore, the composition was determined to have only Ni 2+ in the pristine material. This material delivers 185 mAh/g as maximum specific capacity. In the voltage plateau indicating bi-phase transition around 4.2 V, it can be assumed that O2 type stacking faults occurred within the P2 structure. Although the capacity retention after 20 cycles in the 1.5-4.3 V range is only 58%, it could achieve high cycle retention (94%) when the cut-off voltage is limited in 1.7-4.0 V. The reason of this capacity fade either in charge or in discharge is not clear. XRD study after 10 cycles in the high voltage range, where the fading is quite large, shows that the crystallinity on the structure is preserved. Further investigations are in progress to understand the relationships between electrochemical properties and structural changes.

  75 Mn 0.30 Ni 0.425 Co 0.275 O 2 0.375 P2 + NiO VL Na 0.80 Mn 0.30 Ni 0.425 Co 0.275 O 2 0.325 P2 + NiO L Na 0.70 Mn 0.35 Ni 0.275 Co 0.375 O 2 0.225 P2 + NiO L Na 0.75 Mn 0.35 Ni 0.275 Co 0.375 O 2 0.175 P2 + NiO M Na 0.80 Mn 0.35 Ni 0.275 Co 0.375 O 2 0.125 P2 + NiO M -S Na 0.70 Mn 0.425 Ni 0.425 Co 0.15 O 2 0.30 P2 + NiO L Na 0.90 Mn 0.425 Ni 0.425 Co 0.15 O 2 0.10 P2 + O3 + NiO S Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 0 P 2 -(VL : Very large, L : Large, M : Medium, S : Small) to 3.3. Then, the relative amount of transition metals was determined having in mind the relative stability of the various redox couples:

Figure 1 .

 1 Figure 1. XRD pattern of the Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 phase synthesized by a co-precipitation method: (black) full pattern matching pattern, (red) experimental data, (blue) difference plots.

Figure 2 .

 2 Figure 2. SEM images of P2-Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 powder.

Figure 3 .

 3 Figure 3. Galvanostatic curves of Na//P2-Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 at C/20 in various voltage ranges. The black dot indicates the initial voltage. (a) in 1.5-4.3 V. A magnification around the initial point is shown in the inset. (b) 1.5-4.0 V. (c) 1.7-4.0 V. The first discharge and the following first cycle are represented by the red line.

Figure 4 .

 4 Figure 4. Change in specific capacity upon cycling of Na//P2-Na 0.70 Mn 0.60 Ni 0.30 Co 0.10 O 2 in various voltage ranges.

Figure 5 .

 5 Figure 5. Effect of the cycling rate on the specific capacity.

Figure 6 .

 6 Figure 6. XRD patterns of the material recovered on both sides of the plateau. (a) After charge at 4.0 V; (b) After charge at 4.3 V. G: graphite.

Figure 7 .

 7 Figure 7. Effect of the cycling in the 3.0-4.3 V range on the shape of the cycling curve in the 1.5-3.0 V range.

Figure 8 .

 8 Figure 8. XRD pattern of the battery material recovered at 3.0 V after 10 cycles in the 3.0-4.3 V range: (black) full pattern matching pattern, (red) experimental data, (blue) difference plots.

Figure 9 .

 9 Figure 9. Comparison of the broadening of the (a) (110) hex , (b) (103) hex and (c) (106) hex diffraction lines of the starting material (red line) and after 10 cycles in the 3.0-4.3 V range (blue line). To allow the comparison of their FWHM, the lines have been shifted along the 2θ angle; simultaneously their maximum has been normalized.

  Na 2/3 Ni 1/3 Mn 2/3 O 25,17,18 Na 2/3 Co 2/3 Mn 1/3 O 2 19 and Na 0.70 Mn 0.11 Co 0.89 O 2+z 20 for example, which exhibit interesting electrochemical behavior. P2 type structure with three transition metals, such as Na 2/3 Co x Ni 1-x Mn 2/3 O 2 , 6,7 Na 0.45 Ni 0.22 Co 0.11 Mn 0.66 O 2 , 21 Na 0.67 Mn 0.65 Co 0.20 Ni 0.15 O 2 , 22 Na 2/3 Co 2/3 Ni 1/9 Mn 2/9 O 2

Acknowledgments

The authors thank C. Denage for technical assistance and Toyota, CNRS and Region Aquitaine for financial support.


Marie-Madeleine Bertucci
email: marie-madeleine.bertucci@u-cergy.fr

Mounia Illourmane
email: mounia.illourmane@u-cergy.fr

Marie-Madeleine Coordonnées

Bertucci

Mounia Illourmanne

Keywords: Quelles approches ? Quels usages ?, corpus audio, transcription, reconnaissance vocale, indexation, archivage, conservation du patrimoine immatériel

come     Copyright "Transcrire un corpus audio dans la perspective de la préservation du patrimoine culturel immatériel. Les obstacles rencontrés, les méthodologies retenues, les questions restées en suspens"

par les énonciateurs. Le patrimoine culturel immatériel, porté par la convention de l'UNESCO du 17 octobre 2003, et sa conservation supposent deux types de questionnements. D'une part, on l'a vu, il s'agit de concevoir différemment les politiques patrimoniales, en les envisageant du point de vue des détenteurs du patrimoine et non plus seulement du point de vue des experts, d'autre part d'élaborer des modalités de préservation des données autres que celles du patrimoine matériel, ce sur quoi va porter la communication. Cette recherche a donc pour objet de sauvegarder une expression culturelle encore vivante mais néanmoins menacée, la mémoire des Chibanis, et de mettre à la disposition de la communauté scientifique et d'un plus large public le cas échéant un ensemble de données peu accessibles matériellement et s'inscrivant dans le cadre du patrimoine culturel immatériel. Par ailleurs, ce projet s'inscrit dans le contexte de la réflexion menée actuellement en SHS sur la constitution de corpus d'archives numériques et de la pérennisation de leur accessibilité par la numérisation et l'indexation des sources. La communication se déroulera en deux temps. Dans un premier temps, Marie-Madeleine Bertucci présentera la problématique générale des modalités de conservation du patrimoine mémoriel d'une communauté minorée, les chibanis du quartier de la Goutte d'Or dans une perspective sémiotique et sociolinguistique. Dans un second temps, Mounia Illourmane abordera les questions liées à la transcription du corpus qui se sont posées au fil de l'avancée du travail. Marie-Madeleine Bertucci I. Problématique générale des modalités de conservation du patrimoine mémoriel d'une communauté minorée, les chibanis du quartier de la Goutte d'Or dans une perspective sémiotique et sociolinguistique. I.1 Position du problème. L'émergence du sujet migrant à travers le prisme de la mémoire Le patrimoine culturel immatériel désormais (PCI), porté par la convention de l'UNESCO du 17 octobre 2003, et sa conservation supposent deux types de questionnements. D'une part, il s'agit d'élaborer des modalités de préservation des données autres que celles du patrimoine matériel, d'autre part, le PCI suppose de concevoir différemment les politiques patrimoniales, en les envisageant du point de vue des détenteurs du patrimoine et non plus seulement du point de vue des experts. Pour ce faire, on soulignera d'emblée la nécessité de faire émerger une mémoire de l'immigration qui permette à la fois i de changer le regard sur les migrants et ii d'éviter l'obstacle de l'enfermement dans des récits mémoriels qui constitueraient une assignation identitaire clivante, au sujet de laquelle on fera l'hypothèse qu'elle est un frein à l'intégration. Les entretiens, qui constituent le corpus permettent de mettre en mots la mémoire de ces existences modestes et de les rendre visibles et audibles. Ils constituent un ensemble de connaissances, un savoir sur une forme d'immigration, discrète, voire invisible, alors que cette génération de migrants a été le témoin de transformations importantes et notamment de l'émergence d'une néo-traditionnalisation des moeurs, voire d'un retour du religieux chez les jeunes générations. L'un des intérêts des entretiens, et non de moindres est de mettre en évidence ces effets de contraste entre ces deux générations. Par ailleurs, les entretiens constituent un témoignage sur le quartier de la Goutte d'Or et montrent en quoi celui-ci est à un lieu à la fois privé et public auquel s'attachent les mémoires de ces migrants et qui fait l'objet de discours. Ils constituent une méthodologie pertinente pour appréhender certaines trajectoires de migrants et pour faire émerger leur degré d'insertion dans la société française contemporaine à travers les types de liens sociaux qu'ils ont noués. La recherche tentera de mettre en évidence la présence d'éléments tangibles récurrents dans les entretiens, qui prennent la valeur de traces ou de supports de mémoire, comme la valeur des lieux, les formes de vécu, le potentiel émotionnel et thématique qui s'y rapportent (Bertucci, 2006). On fera l'hypothèse que l'identité des migrants se dit à travers des lieux et thèmes (topoï) privilégiés : par exemple, le rapport à la langue et aux lieux d'origine et le rapport à la langue française, la mobilité, l'arrivée en France, l'insertion professionnelle et l'intégration, les liens avec les autres migrants, avec les français, l'hypothèse du retour au pays, la mémoire et l'oubli du passé.... On postulera donc des similitudes dans l'expérience des sujets concernés.

I.2 Les entretiens biographiques

On supposera qu'une impulsion narrative est sous-jacente aux entretiens et qu'elle fait apparaître chez les informateurs une impulsion à se représenter en se racontant (Bertucci, 2006). Les informateurs se situent parfois dans des situations de marginalité, voire de conflit ou de crise et sont confrontés à l'altérité. On peut penser que cette situation de distance peut les amener à mettre en mots et à relier des éléments isolés de leur histoire. Les entretiens biographiques rendent possible l'émergence d'un sujet qui ne peut être visible que par un détour par sa vie personnelle, laquelle en s'articulant au champ du social fait émerger une forme spécifique d'identité. Or, l'entretien biographique, donne à lire la biographie des individus. Il est un moyen d'accéder à la connaissance de l'autre parce qu'il met en place un ordre du sens (Adam, 1995) et lui donne une forme, une forme qui fait sens. En cela, il est particulièrement apte à exprimer l'altérité. Se saisissant comme objet et quasi personnage, le narrateur ou quasi narrateur (Ricoeur, 1983) se pose à la fois en sujet et en objet, donnant de ce fait au lecteur ou à l'auditeur une possibilité d'appréhender des éléments identitaires au nombre desquels figurent les lieux selon notre hypothèse. La finalité de la recherche est de mettre en lumière l'expérience qu'a le sujet et le type d'identité qui en résulte dans une démarche herméneutique (Bertucci, 2006). Le processus réflexif est au centre de la méthodologie dans la mesure où il permet la construction et la représentation de l'autre dans la confrontation avec lui dans un espace social, historicisé et contextualisé. Cette approche paraît d'autant plus pertinente lorsque la recherche porte, comme ici, sur des identités potentiellement clivées entre les langues, les cultures, les appartenances, car la dynamique réflexive de l'entretien biographique amène les informateurs à construire le sens par eux-mêmes. On admettra également que l'organisation des discours mémoriels, malgré la diversité des informateurs, n'est pas forcément aléatoire et qu'il existe un ordre narratif signifiant, résultant d'une expérience de l'espace et du temps singulière, qui est celle de la mobilité, qu'elle soit exil ou migration (Bertucci, 2009 ;2017). Enfin, on supposera que de par son caractère rétrospectif, les discours des informateurs impliquent un processus mémoriel particulier signifiant par ses souvenirs mais aussi par ses silences et qu'il y a une part de l'histoire du narrateur qui n'est pas remémorée.

I. 3 Principes méthodologiques

La démarche prendra appui de manière très souple sur les méthodes mises en oeuvre par la socio-histoire (Noiriel, 2006 a), les cultural studies (Thompson, 1963), les subaltern studies [START_REF] Merle | Les subaltern studies. Retour sur les principes fondateurs d'un projet historiographique de l'Inde coloniale[END_REF]) avec l'objectif d'aller vers une conception de l'histoire perçue comme « une histoire anthropologique qui s'intéresse surtout aux liens que tissent les individus entre eux dans le cadre de leur vie quotidienne » (Noiriel, 2006 b : 40). Elle s'appuiera également sur une forme d'observation participante et une typologie des médiations sociales. Cette démarche suppose un engagement particulier de l'observateur, une réflexivité en retour par la pratique d'une observation participante, supposant un décentrement socioculturel et ce que Lévi-Strauss appelle une « distanciation sociale » (1955 : 416). Comprendre l'autre et le connaître implique de se distancier de soi pour appréhender son expérience de l'exil, interprétée comme une expérience de rupture avec la culture d'origine. Les entretiens biographiques peuvent être interprétés comme trace de cette expérience. Une typologie des médiations sociales est également requise (Ferrarotti, 1990 : 61). On postulera donc qu'un individu reflète un ou plusieurs pôles sociaux et inversement que le système social se projette vers l'individu et ce à travers des médiations. Chaque comportement individuel est à la fois la synthèse d'une structure sociale et une individualisation de l'histoire sociale collective (Ibid. : 21). Il est la représentation, l'attestation de l'altérité, et donc il affirme ce que Bakhtine appelle la relation exotopique (1978), laquelle rend possible de poser en tant que telle l'existence de l'Autre et son aptitude à parler en son nom.

Je passe maintenant la parole à Mounia Illourmane qui va aborder dans une seconde partie les différents problèmes posés par la transcription du corpus au fil de l'avancée de son travail de thèse.

Mounia Illourmane

« La mise en mots de la mémoire des chibanis du quartier de la Goutte d'Or à Paris », un sujet qui m'a eté proposé par Marie-Madeleine Bertucci, ma directrice de these. L'ideé est de sauvegarder et de mettre en mots la meḿoire de ces vieux immigreś, en partant d'un corpus d'archives audio, de documents authentiques et d'enregistrements vocaux qui n'ont fait l'objet d'aucune manipulation au preálable. En effet, l'identification de certaines pistes de recherches est une etape qui s'avere nećessaire, suite à l'exploitation des donneés transcrites avec l'objectif de mettre au point des methodologies de recherches et des approches pour mieux apprehender le traitement et l'analyse du corpus.

Les donneés

La rećupeŕation des donneés aupres de Jean-Marc Bombeau a eu lieu en dećembre 2014 dans les locaux de la galerie de « l'Echomuseé » dans le XVIII eme arrondissement de Paris. Il s'agit de documents authentiques, sequences videós, bandes son et photos, peu accessibles mateŕiellement. Ces donneés sont brutes et repreśentent une manne de ressources et de mateŕiaux pour la constitution de notre corpus.

Mise au point d'un outil de classement, d'indexation et d'arborescence

Les donneés sont sauvegardeés sur un disque dur. Avec ma directrice de recherche, on a reálisé un pre-test sur un ećhantillon afin de trouver une methodologie d'organisation des donneés reçues. Par la suite, j'ai conçu un outil de mise en ordre des donneés en utilisant une methodologie d'inventaire qui consiste à etablir une liste exhaustive des eĺeḿents figurants dans le disque dur, en eĺaborant un inventaire physique qui correspond à un comptage manuel de chaque type de document dont les procedeś sont le regroupement, le classement, l'indexation et l'arborescence.

Le disque dur est preśenté ici comme le support de stockage des donneés à exploiter, sauvegardant ces dernieres d'une maniere hieŕarchique, en subdivision, c'est là le principe de l'arborescence, cela s'apparente à des dossiers qui peuvent en contenir à leur tour d'autres sous dossiers subdiviseś. Ce scheḿa de stockage et d'arborescence peut etre recreé autant de fois que possible. Afin de determiner avec exactitude la nature et la quantité des mateŕiaux detenus, l'arborescence permet donc de voir la hieŕarchisation du contenu, il s'agit de scheḿas qui permettent de mieux apprehender l'organisation des donneés. L'inventaire est donc composé de 132 pages format A4 avec 191 tableaux, preśenteś sous la forme suivante (colonnes de gauche à droite) :

• Document, type du document, remarque ; • Bande son, dureé, remarque ; • Sequence videó, dureé, remarque ; • Photo, remarque.

A[ l'issue de cette deḿarche on a seĺectionné les donneés à exploiter dans notre etude, ce qui a orienté notre choix sur les bandes son.

Geńeŕation d'un corpus

La recherche à partir des corpus oraux est tres reṕondue en sociolinguistique. C'est une deḿarche empirique traitant des donneés authentiques. L'étape suivante consiste à transcrire et à baliser le corpus.

Les bandes son sont transcrites en orthographe standard. La partie transcrite comporte 213 pages et repose sur des enregistrements d'archive audio, composé de 18 bandes son. La dureé totale des enregistrements est de 6 heures et 58.32 minutes. La dureé varie d'une bande son à une autre, la plus courte est de 03.58 minutes et la plus longue est de 1 heure et 2.04 minutes. Dans le corpus on distingue au total 33 « quasi personnages » (Ricoeur 1983), dont 04 intervieweurs et 29 chibanis. Toutefois, une anonymisation totale du corpus s'avere nećessaire pour la protection des donneés personnelles des chibanis. De ce fait, nous avons choisi de ne pas constituer d'archive sonore. L'exploitation des bandes son se limite seulement à la version transcrite de celles-ci, ce qui sous-entend une non utilisation de la version sonore.

Prise en main des logiciels

Il s'agit d'une transcription mot à mot, j'ai mis par ećrit exactement tout ce qui est dit à l'oral incluant des phrases incompletes, des reformulations et des intonations, on y lira aussi les remarques d'ordre geńeŕal « tu voulais que je te filme aussi », les mots reṕeteś à l'oral « avait des problemes, des problemes avec leur enfant », des arrets frequents sont nećessaires pour ajouter les eĺeḿents extralinguistiques comme les rires et les heśitation. La transcription manuelle reste donc incontournable pour notre corpus. Ce type de transcription a principalement pour but la reálisation d'une retranscription authentique, tout en respectant les enchaınements et les chevauchements de l'enregistrement oral. Les transcriptions qu'utilisent les linguistes conservent soigneusement toutes les particulariteś des productions orales : reṕetitions, heśitations, amorces de mots, retouches. (Baude 2006 : 30) C'est une technique tres utile mais coûteuse en temps. Selon les estimations courantes, un minimum de trente minutes de travail est nećessaire pour transcrire une minute d'enregistrement. (Baude 2006 : 30). Cette opeŕation nećessite l'utilisation d'un lecteur audio et d'un traitement de texte, entre lesquels il est essentiel de faire des va-et-vient successifs de Play/stops, pour les transcrire par saisie sur l'editeur de texte « Word office ». Neánmoins, j'ai eǵalement utilisé les logiciels « Express Scribe » et « E-Speaking ».

Express Scribe 1 est un logiciel professionnel de lecture audio qui permet de lire des fichiers audio au format Wav ou MP3. Ce programme ne permet pas la conversion automatique des fichiers audio en texte, mais il contient d'autres fonctionnaliteś pour rendre le processus plus facile. Tel que la transcription, un outil conçu pour faciliter la transcription des enregistrements audio au clavier dans un editeur de texte. La fonction de contrôle permet de contrôler la vitesse de lecture, qui se gere entierement à partir des touches d'acces rapides du clavier. On peut sauvegarder, lire ou revenir en arriere en utilisant les touches retour, avance rapide. Le logiciel dispose d'une option de chargement automatique des fichiers audio. Elle est accessible à partir d'un peŕipheŕique (lecteur cd ou dvd, clé USB…) ou d'un reśeau local. E-Speaking2 , est un logiciel shareware3 de contrôle et de reconnaissance vocale, disponible en teĺećhargement. Il a pour fonction la dicteé et l'exećution des tâches sur ordinateur par voix de l'utilisateur, Il assure de meilleurs reśultats en s'inteǵrant à Word Office, il contient eǵalement des commandes inteǵreés comme Voice Dictation pour la dicteé, elle consiste à reformuler sous forme intelligible et grammaticalement correcte les propos de l'utilisateur.

Pourquoi l'emploi de ces deux outils ?

Les systemes de transcription doivent etre adapteś en fonction des corpus à transcrire. (Baude 2006 : 31). Partant des diffeŕentes difficulteś techniques rencontreés lieés à la transcription du corpus, nous abordons ici certaines solutions pour y remedier. L'emploi de ces deux logiciels a permis la transcription des enregistrements des chibanis en restant le plus fidelement possible à l'original tout en tenant compte des nombreuses contraintes d'ordre syntaxique, orthographique et phonologiques reśultant du caractere oral des donneés.

Difficulteś rencontreés

La transcription des entretiens preśente des difficulteś d'ordre pratique. La premiere difficulté est lieé au caractere oral des donneés d'un point de vue syntaxique, orthographique et phonologique. Les logiciels de transcription automatique ne correspondent pas à notre corpus, il a donc fallu tirer profit des logiciels à notre disposition, cependant nous sommes obligeés de recourir à un traitement majoritairement manuel, meme si ces logiciels facilitent grandement la tâche de transcription des donneés. Afin de contrôler au mieux la transcription inteǵrale une telle deḿarche est nećessaire, le travail manuel et l'assistance des outils informatique est incontournable.

De plus, la reconnaissance vocale n'a pas pour option d'interpreter et de retranscrire d'autres voix que celle de l'utilisateur. Des lors, la seule utilisation possible est de reṕeter à voix haute devant un microphone les propos tenus par les chibanis pour que le logiciel les retranscrive en texte. El tant donné que les logiciels de reconnaissance vocale ne prennent pas en compte les diffeŕents accents des locuteurs, il est essentiel de revoir et de corriger les textes retranscrits.

Analyse et traitement des donneés recueillies

Il s'agit de reáliser une analyse de contenu des entretiens, cette etude est meneé selon une methodologie d'analyse visant à extraire les eĺeḿents pertinents qui constitueront la base du sujet. L'analyse de contenu cherche à savoir ce qui est derriere les paroles sur lesquelles elle se penche. La linguistique est une etude de la langue, l'analyse de contenu est une quete, à travers des messages, de reálité autre. (Bardin 1977 : 48).

Une fois les entretiens transcrits, je procede au dećorticage des donneés brutes, le discours des personnes intervieweés contient des informations à exploiter. Tout document parle, ećrit ou sensoriel contient potentiellement une quantité d'informations sur la personne qui en est l'auteur, sur le groupe auquel elle appartient, sur les faits et eveńements qui y sont relateś, sur les effets rechercheś par la preśentation de l'information, sur le monde ou sur le secteur du reél dont il est question. (Mucchielli 1984 : 17) A[ partir des reśultats de cette premiere deḿarche, j'ai reálisé l'etude theḿatique, ainsi, l'analyse qualitative se fonde sur les reśultats quantitatifs. L'analyse de contenu peut etre une analyse de "signifieś" (ex : l'analyse theḿatique) mais elle peut etre aussi une analyse des "signifiants" (analyse lexicale) (Bardin 1977 : 39).

Conclusion Mounia Illourmane

Pour conclure, on notera que certaines questions autours de l'exploitation de l'inventaire et de l'arborescence hieŕarchique du disque dur restent en suspens, finalement, comment peut-on exploiter au mieux cette base de donneés ? Quelle methodologie d'etude adopter ? Marie-Madeleine Bertucci L'intérêt de ce travail est qu'il permet de conserver les traces de voix minorées, celles des chibanis du point de vue du patrimoine culturel immaterial et d'analyser l'intérêt du support audio dans cette perspective. Ce type de support ne va pas pas sans poser de problèmes comme a essayé de le montrer Mounia Illourmane. La question restée en suspens est celle de l'utilisation de l'arborescence réalisée pour indexer et classer les données de départ dans la perspective de l'analyse du corpus et l'impact éventuel de ce type de description sur les modalités de conceptualisation de la thématique et le déroulement de la recherche.

Bibliographie

  Adam, J.-M. 1995. « Aspects du récit en anthropologie ». In Adam, J.-M., Borel, M.-J., Calame, C. , Kilani, M. Le discours anthropologique, description, narration, savoir. Lausanne : Payot. pp. 251-283. Bakhtine, M. 1978 [éd. fr.]. Esthétique et théorie du roman. (Olivier, D. trad.) Paris : Gallimard. Bardin, L. 2003. L'analyse de contenu. Paris : Presse universitaire de France. Baude, O. Corpus oraux : les « bonnes pratiques » des linguistes. Laboratoire Ligeŕien de Linguistique UMR 7270. pp. 1-104. Baude, O. (dir) 2006. Corpus oraux. Guide des bonnes pratiques. Paris : CNRS El ditions. Berelson, B. 1952. « Content Analysis in Communication Research » in Ghiglione, R., Matalon, B. 1978. Les Enquêtes Sociologiques. Paris : Armand Colin.

  . En effet, l'analyse de contenu s'appuie sur la cateǵorisation quantitative et qualitative. C'est une technique de recherche pour la description objective, systeḿatique et quantitative du contenu manifeste de la communication. (Berelson 1952 cité dans Ghiglione & Matalon 1978 : 155). Elle permet de concilier les deux methodes et de reáliser un tri statistique de l'ensemble des donneés recueillies. En effet, c'est un travail de synthese, afin d'etablir un inventaire des mots les plus occurrents et des themes les plus saillants, pour reáliser une analyse lexicale d'une part et une analyse theḿatique d'autre part. L'ideé d'appliquer sur le corpus la methode d'analyse lexicale est proposeé par Marie-Madeleine Bertucci et reáliseé par Mounia Illourmane.

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