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DNA exhibits remarkable potential as a data storage solution due to its impressive storage density and long-term stability, stemming from its inherent biomolecular structure. However, developing this novel medium comes with its own set of challenges, particularly in addressing errors arising from storage and biological manipulations. These challenges are further conditioned by the structural constraints of DNA sequences and cost considerations. In response to these limitations, we have pioneered a novel compression scheme and a cutting-edge Multiple Description Coding (MDC) technique utilizing neural networks for DNA data storage. Our MDC method introduces an innovative approach to encoding data into DNA, specifically designed to withstand errors effectively. Notably, our new compression scheme overperforms classic image compression methods for DNA-data storage. Furthermore, our approach exhibits superiority over conventional MDC methods reliant on auto-encoders. Its distinctive strengths lie in its ability to bypass the need for extensive model training and its enhanced adaptability for fine-tuning redundancy levels. Experimental results demonstrate that our solution competes favorably with the latest DNA data storage methods in the field, offering superior compression rates and robust noise resilience., Comment: Xavier Pic and Trung Hieu Le are both equal contributors and primary authors

Multiple Description Coding (MDC) is an error-resilient source coding method designed for transmission over noisy channels. We present a novel MDC scheme employing a neural network based on implicit neural representation. This involves overfitting the neural representation for images. Each description is transmitted along with model parameters and its respective latent spaces. Our method has advantages over traditional MDC that utilizes auto-encoders, such as eliminating the need for model training and offering high flexibility in redundancy adjustment. Experiments demonstrate that our solution is competitive with autoencoder-based MDC and classic MDC based on HEVC, delivering superior visual quality., Comment: Accepted at IEEE MMSP 2023

Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (rarely accessed data), has motivated research for alternative systems of data storage. Because of its biochemical characteristics, synthetic DNA molecules are now considered as serious candidates for this new kind of storage. This paper presents some results on lossy image compression methods based on convolutional autoencoders adapted to DNA data storage, with synthetic DNA-adapted entropic and fixed-length codes. The model architectures presented here have been designed to efficiently compress images, encode them into a quaternary code, and finally store them into synthetic DNA molecules. This work also aims at making the compression models better fit the problematics that we encounter when storing data into DNA, namely the fact that the DNA writing, storing and reading methods are error prone processes. The main take aways of this kind of compressive autoencoder are our latent space quantization and the different DNA adapted entropy coders used to encode the quantized latent space, which are an improvement over the fixed length DNA adapted coders that were previously used., Comment: arXiv admin note: substantial text overlap with arXiv:2203.09981

Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (i.e. rarely accessed), has motivated research for alternative systems of data storage. Because of its biochemical characteristics, synthetic DNA molecules are now considered as serious candidates for this new kind of storage. This paper introduces a novel arithmetic coder for DNA data storage, and presents some results on a lossy JPEG 2000 based image compression method adapted for DNA data storage that uses this novel coder. The DNA coding algorithms presented here have been designed to efficiently compress images, encode them into a quaternary code, and finally store them into synthetic DNA molecules. This work also aims at making the compression models better fit the problematic that we encounter when storing data into DNA, namely the fact that the DNA writing, storing and reading methods are error prone processes. The main take away of this work is our arithmetic coder and it's integration into a performant image codec.

Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (i.e. rarely accessed), has motivated research for alternative systems of data storage. Because of its biochemical characteristics, synthetic DNA molecules are considered as potential candidates for a new storage paradigm. Because of this trend, several coding solutions have been proposed over the past years for the storage of digital information into DNA. Despite being a promising solution, DNA storage faces two major obstacles: the large cost of synthesis and the noise introduced during sequencing. Additionally, this noise increases when biochemically defined coding constraints are not respected: avoiding homopolymers and patterns, as well as balancing the GC content. This paper describes a novel entropy coder which can be embedded to any block-based image-coding schema and aims to robustify the decoded results. Our proposed solution introduces variability in the generated quaternary streams, reduces the amount of homopolymers and repeated patterns to reduce the probability of errors occurring. In this paper, we integrate the proposed entropy coder into four existing JPEG-inspired DNA coders. We then evaluate the quality -- in terms of biochemical constraints -- of the encoded data for all the different methods.

Remote control vehicles require the transmission of large amounts of data, and video is one of the most important sources for the driver. To ensure reliable video transmission, the encoded video stream is transmitted simultaneously over multiple channels. However, this solution incurs a high transmission cost due to the wireless channel's unreliable and random bit loss characteristics. To address this issue, it is necessary to use more efficient video encoding methods that can make the video stream robust to noise. In this paper, we propose a low-complexity, low-latency 2-channel Multiple Description Coding (MDC) solution with an adaptive Instantaneous Decoder Refresh (IDR) frame period, which is compatible with the HEVC standard. This method shows better resistance to high packet loss rates with lower complexity., Comment: Accepted at IEEE ICIP 2023

In this paper, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask smoothness and coupled optimization. In order to cope with communication constraints, we propose and study an adaptive decentralized strategy where the agents employ differential randomized quantizers to compress their estimates before communicating with their neighbors. The analysis shows that, under some general conditions on the quantization noise, and for sufficiently small step-sizes $\mu$, the strategy is stable both in terms of mean-square error and average bit rate: by reducing $\mu$, it is possible to keep the estimation errors small (on the order of $\mu$) without increasing indefinitely the bit rate as $\mu\rightarrow 0$. Simulations illustrate the theoretical findings and the effectiveness of the proposed approach, revealing that decentralized learning is achievable at the expense of only a few bits.

Recently, convolutional auto-encoders (CAE) were introduced for image coding. They achieved performance improvements over the state-of-the-art JPEG2000 method. However, these performances were obtained using massive CAEs featuring a large number of parameters and whose training required heavy computational power.\\ In this paper, we address the problem of lossy image compression using a CAE with a small memory footprint and low computational power usage. In order to overcome the computational cost issue, the majority of the literature uses Lagrangian proximal regularization methods, which are time consuming themselves.\\ In this work, we propose a constrained approach and a new structured sparse learning method. We design an algorithm and test it on three constraints: the classical $\ell_1$ constraint, the $\ell_{1,\infty}$ and the new $\ell_{1,1}$ constraint. Experimental results show that the $\ell_{1,1}$ constraint provides the best structured sparsity, resulting in a high reduction of memory and computational cost, with similar rate-distortion performance as with dense networks.

Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (rarely accessed data), has motivated research for alternative systems of data storage. Because of its biochemical characteristics, synthetic DNA molecules are now considered as serious candidates for this new kind of storage. This paper presents some results on lossy image compression methods based on convolutional autoencoders adapted to DNA data storage. The model architectures presented here have been designed to efficiently compress images, encode them into a quaternary code, and finally store them into synthetic DNA molecules. This work also aims at making the compression models better fit the problematics that we encounter when storing data into DNA, namely the fact that the DNA writing, storing and reading methods are error prone processes. The main take away of this kind of compressive autoencoder is our quantization and the robustness to substitution errors thanks to the noise model that we use during training., Comment: Submitted to ICIP 2022

The exponentially increasing demand for data storage has been facing more and more challenges during the past years. The energy costs that it represents are also increasing, and the availability of the storage hardware is not able to follow the storage demand's trend. The short lifespan of conventional storage media -- 10 to 20 years - forces the duplication of the hardware and worsens the situation. The majority of this storage demand concerns "cold" data, data very rarely accessed but that has to be kept for long periods of time. The coding abilities of synthetic DNA, and its long durability (several hundred years), make it a serious candidate as an alternative storage media for "cold" data. In this paper, we propose a variable-length coding algorithm adapted to DNA data storage with improved performance. The proposed algorithm is based on a modified Shannon-Fano code that respects some biochemichal constraints imposed by the synthesis chemistry. We have inserted this code in a JPEG compression algorithm adapted to DNA image storage and we highlighted an improvement of the compression ratio ranging from 0.5 up to 2 bits per nucleotide compared to the state-of-the-art solution, without affecting the reconstruction quality., Comment: Submitted in EUSIPCO 2022

This paper introduces a novel non-Separable sPAtioteMporal filter (non-SPAM) which enables the spatiotemporal decomposition of a still-image. The construction of this filter is inspired by the model of the retina which is able to selectively transmit information to the brain. The non-SPAM filter mimics the retinal-way to extract necessary information for a dynamic encoding/decoding system. We applied the non-SPAM filter on a still image which is flashed for a long time. We prove that the non-SPAM filter decomposes the still image over a set of time-varying difference of Gaussians, which form a frame. We simulate the analysis and synthesis system based on this frame. This system results in a progressive reconstruction of the input image. Both the theoretical and numerical results show that the quality of the reconstruction improves while the time increases.

The efficient storage of digital data is becoming very challenging over the years due to the exponential increase in the generation of data which can't compete with the existing storage resources. Furthermore, the infrequently accessed data can be safely stored for no longer than 10-20 years due to the short life-span of conventional storage devices. To this end, recent studies have proven DNA to be a very promising candidate for the long-term storage of digital data. Several pioneering works have proposed different encoding methods for the specific encoding of images into a quaternary DNA representation while first compressing the image using the classical JPEG standard to reduce the high cost of DNA synthesis. However this type of compression is not optimized with respect to the quaternary DNA code and results in an open-loop workflow. In our previous works we have introduced the first closed-loop solution for generating a constrained fixed-length quaternary code which allows controlling the synthesis cost thanks to a source allocation algorithm. In this paper, we extend our studies to proposing a variable-length encoding solution which is based on the JPEG standard., Comment: Submitted to EUSIPCO 2021 conference

With huge data acquisition progresses realized in the past decades and acquisition systems now able to produce high resolution grids and point clouds, the digitization of physical terrains becomes increasingly more precise. Such extreme quantities of generated and modeled data greatly impact computational performances on many levels of high-performance computing (HPC): storage media, memory requirements, transfer capability, and finally simulation interactivity, necessary to exploit this instance of big data. Efficient representations and storage are thus becoming "enabling technologies'' in HPC experimental and simulation science. We propose HexaShrink, an original decomposition scheme for structured hexahedral volume meshes. The latter are used for instance in biomedical engineering, materials science, or geosciences. HexaShrink provides a comprehensive framework allowing efficient mesh visualization and storage. Its exactly reversible multiresolution decomposition yields a hierarchy of meshes of increasing levels of details, in terms of either geometry, continuous or categorical properties of cells. Starting with an overview of volume meshes compression techniques, our contribution blends coherently different multiresolution wavelet schemes in different dimensions. It results in a global framework preserving discontinuities (faults) across scales, implemented as a fully reversible upscaling at different resolutions. Experimental results are provided on meshes of varying size and complexity. They emphasize the consistency of the proposed representation, in terms of visualization, attribute downsampling and distribution at different resolutions. Finally, HexaShrink yields gains in storage space when combined to lossless compression techniques.

Living in the age of the digital media explosion, the amount of data that is being stored increases dramatically. However, even if existing storage systems suggest efficiency in capacity, they are lacking in durability. Hard disks, flash, tape or even optical storage have limited lifespan in the range of 5 to 20 years. Interestingly, recent studies have proven that it was possible to use synthetic DNA for the storage of digital data, introducing a strong candidate to achieve data longevity. The DNA's biological properties allows the storage of a great amount of information into an extraordinary small volume while also promising efficient storage for centuries or even longer with no loss of information. However, encoding digital data onto DNA is not obvious, because when decoding, we have to face the problem of sequencing noise robustness. Furthermore, synthesizing DNA is an expensive process and thus, controlling the compression ratio by optimizing the rate-distortion trade-off is an important challenge we have to deal with. This work proposes a coding solution for the storage of digital images onto synthetic DNA. We developed a new encoding algorithm which generates a DNA code robust to biological errors coming from the synthesis and the sequencing processes. Furthermore, thanks to an optimized allocation process the solution is able to control the compression ratio and thus the length of the synthesized DNA strand. Results show an improvement in terms of coding potential compared to previous state-of-the-art works., Comment: Submitted to EUSIPCO 2019 conference

We propose the design of an original scalable image coder/decoder that is inspired from the mammalians retina. Our coder accounts for the time-dependent and also nondeterministic behavior of the actual retina. The present work brings two main contributions: As a first step, (i) we design a deterministic image coder mimicking most of the retinal processing stages and then (ii) we introduce a retinal noise in the coding process, that we model here as a dither signal, to gain interesting perceptual features. Regarding our first contribution, our main source of inspiration will be the biologically plausible model of the retina called Virtual Retina. The main novelty of this coder is to show that the time-dependent behavior of the retina cells could ensure, in an implicit way, scalability and bit allocation. Regarding our second contribution, we reconsider the inner layers of the retina. We emit a possible interpretation for the non-determinism observed by neurophysiologists in their output. For this sake, we model the retinal noise that occurs in these layers by a dither signal. The dithering process that we propose adds several interesting features to our image coder. The dither noise whitens the reconstruction error and decorrelates it from the input stimuli. Furthermore, integrating the dither noise in our coder allows a faster recognition of the fine details of the image during the decoding process. Our present paper goal is twofold. First, we aim at mimicking as closely as possible the retina for the design of a novel image coder while keeping encouraging performances. Second, we bring a new insight concerning the non-deterministic behavior of the retina., Comment: arXiv admin note: substantial text overlap with arXiv:1104.1550

Our goal is to revisit rank order coding by proposing an original exact decoding procedure for it. Rank order coding was proposed by Simon Thorpe et al. who stated that the retina represents the visual stimulus by the order in which its cells are activated. A classical rank order coder/decoder was then designed on this basis [1]. Though, it appeared that the decoding procedure employed yields reconstruction errors that limit the model Rate/Quality performances when used as an image codec. The attempts made in the literature to overcome this issue are time consuming and alter the coding procedure, or are lacking mathematical support and feasibility for standard size images. Here we solve this problem in an original fashion by using the frames theory, where a frame of a vector space designates an extension for the notion of basis. First, we prove that the analyzing filter bank considered is a frame, and then we define the corresponding dual frame that is necessary for the exact image reconstruction. Second, to deal with the problem of memory overhead, we design a recursive out-of-core blockwise algorithm for the computation of this dual frame. Our work provides a mathematical formalism for the retinal model under study and defines a simple and exact reverse transform for it with up to 270 dB of PSNR gain compared to [1]. Furthermore, the framework presented here can be extended to several models of the visual cortical areas using redundant representations.

We present a novel bio-inspired and dynamic coding scheme for static images. Our coder aims at reproducing the main steps of the visual stimulus processing in the mammalian retina taking into account its time behavior. The main novelty of this work is to show how to exploit the time behavior of the retina cells to ensure, in a simple way, scalability and bit allocation. To do so, our main source of inspiration will be the biologically plausible retina model called Virtual Retina. Following a similar structure, our model has two stages. The first stage is an image transform which is performed by the outer layers in the retina. Here it is modelled by filtering the image with a bank of difference of Gaussians with time-delays. The second stage is a time-dependent analog-to-digital conversion which is performed by the inner layers in the retina. Thanks to its conception, our coder enables scalability and bit allocation across time. Also, our decoded images do not show annoying artefacts such as ringing and block effects. As a whole, this article shows how to capture the main properties of a biological system, here the retina, in order to design a new efficient coder., Comment: 12 pages; Advanced Concepts for Intelligent Vision Systems (ACIVS 2011)