Laurent Jacques

Laurent Jacques, Christophe De Vleeschouwer

This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be applied. The main contribution of this paper is twofold. First, we prove that if a discrete dictionary reaches a minimal density criterion, then the corresponding discrete MP (dMP) is equivalent in terms of convergence to a weakened hypothetical continuous MP. Interestingly, the corresponding weakness factor depends on a density measure of the discrete dictionary. Second, we show that the insertion of a simple geometric gradient ascent optimization on the atom dMP selection maintains the previous comparison but with a weakness factor at least two times closer to unity than without optimization. Finally, we present numerical experiments confirming our theoretical predictions for decomposition of signals and images on regular discretizations of dictionary parametrizations.

Jérome Eertmans, Enrico M. Vitucci, Vittorio Degli-Esposti et al.

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the power of the interaction order. This bottleneck limits its use in large-scale or real-time applications, forcing traditional tools to rely on heuristics to reduce the number of path candidates at the cost of potentially reduced accuracy. To overcome this limitation, we propose a comprehensive machine-learning-assisted framework that replaces exhaustive path searching with intelligent sampling via Generative Flow Networks. Applying such generative models to this domain presents significant challenges, particularly sparse rewards due to the rarity of valid paths, which can lead to convergence failures and trivial solutions when evaluating high-order interactions in complex environments. To ensure robust learning and efficient exploration, our framework incorporates three key architectural components. First, we implement an \emph{experience replay buffer} to capture and retain rare valid paths. Second, we adopt a uniform exploratory policy to improve generalization and prevent the model from overfitting to simple geometries. Third, we apply a physics-based action masking strategy that filters out physically impossible paths before the model even considers them. As demonstrated in our experimental validation, the proposed model achieves substantial speedups over exhaustive search -- up to $10\times$ faster on GPU and $1000\times$ faster on CPU -- while maintaining high coverage accuracy and successfully uncovering complex propagation paths. The complete source code, tests, and tutorial are available at https://github.com/jeertmans/sampling-paths.

Julián Tachella, Laurent Jacques

Recent advances in unsupervised learning have highlighted the possibility of learning to reconstruct signals from noisy and incomplete linear measurements alone. These methods play a key role in medical and scientific imaging and sensing, where ground truth data is often scarce or difficult to obtain. However, in practice, measurements are not only noisy and incomplete but also quantized. Here we explore the extreme case of learning from binary observations and provide necessary and sufficient conditions on the number of measurements required for identifying a set of signals from incomplete binary data. Our results are complementary to existing bounds on signal recovery from binary measurements. Furthermore, we introduce a novel self-supervised learning approach, which we name SSBM, that only requires binary data for training. We demonstrate in a series of experiments with real datasets that SSBM performs on par with supervised learning and outperforms sparse reconstruction methods with a fixed wavelet basis by a large margin.

Rémi Delogne, Vincent Schellekens, Laurent Jacques

Rank-one projections (ROP) of matrices and quadratic random sketching of signals support several data processing and machine learning methods, as well as recent imaging applications, such as phase retrieval or optical processing units. In this paper, we demonstrate how signal estimation can be operated directly through such quadratic sketches--equivalent to the ROPs of the "lifted signal" obtained as its outer product with itself--without explicitly reconstructing that signal. Our analysis relies on showing that, up to a minor debiasing trick, the ROP measurement operator satisfies a generalised sign product embedding (SPE) property. In a nutshell, the SPE shows that the scalar product of a signal sketch with the "sign" of the sketch of a given pattern approximates the square of the projection of that signal on this pattern. This thus amounts to an insertion (an "inception") of a ROP model inside a ROP sketch. The effectiveness of our approach is evaluated in several synthetic experiments.

Anatole Moureaux, Chloé Chopin, Simon de Wergifosse et al.

We present a demonstration of image classification using an echo-state network (ESN) relying on a single simulated spintronic nanostructure known as the vortex-based spin-torque oscillator (STVO) delayed in time. We employ an ultrafast data-driven simulation framework called the data-driven Thiele equation approach (DD-TEA) to simulate the STVO dynamics. This allows us to avoid the challenges associated with repeated experimental manipulation of such a nanostructured system. We showcase the versatility of our solution by successfully applying it to solve classification challenges with the MNIST, EMNIST-letters and Fashion MNIST datasets. Through our simulations, we determine that within an ESN with numerous learnable parameters the results obtained using the STVO dynamics as an activation function are comparable to the ones obtained with other conventional nonlinear activation functions like the reLU and the sigmoid. While achieving state-of-the-art accuracy levels on the MNIST dataset, our model's performance on EMNIST-letters and Fashion MNIST is lower due to the relative simplicity of the system architecture and the increased complexity of the tasks. We expect that the DD-TEA framework will enable the exploration of deeper architectures, ultimately leading to improved classification accuracy.

Julián Tachella, Mike Davies, Laurent Jacques

Recently, many self-supervised learning methods for image reconstruction have been proposed that can learn from noisy data alone, bypassing the need for ground-truth references. Most existing methods cluster around two classes: i) Stein's Unbiased Risk Estimate (SURE) and similar approaches that assume full knowledge of the noise distribution, and ii) Noise2Self and similar cross-validation methods that require very mild knowledge about the noise distribution. The first class of methods tends to be impractical, as the noise level is often unknown in real-world applications, and the second class is often suboptimal compared to supervised learning. In this paper, we provide a theoretical framework that characterizes this expressivity-robustness trade-off and propose a new approach based on SURE, but unlike the standard SURE, does not require knowledge about the noise level. Throughout a series of experiments, we show that the proposed estimator outperforms other existing self-supervised methods on various imaging inverse problems.

Victor Sechaud, Laurent Jacques, Patrice Abry et al.

In numerous inverse problems, state-of-the-art solving strategies involve training neural networks from ground truth and associated measurement datasets that, however, may be expensive or impossible to collect. Recently, self-supervised learning techniques have emerged, with the major advantage of no longer requiring ground truth data. Most theoretical and experimental results on self-supervised learning focus on linear inverse problems. The present work aims to study self-supervised learning for the non-linear inverse problem of recovering audio signals from clipped measurements. An equivariance-based selfsupervised loss is proposed and studied. Performance is assessed on simulated clipped measurements with controlled and varied levels of clipping, and further reported on standard real music signals. We show that the performance of the proposed equivariance-based self-supervised declipping strategy compares favorably to fully supervised learning while only requiring clipped measurements alone for training.

Valentin de Bassompierre, Jean-Charles Delvenne, Laurent Jacques

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design node embeddings whose dot products capture meaningful notions of node similarity induced by the graph. Graph kernels offer a principled way to define such similarities, but their direct computation is often prohibitive for large networks. Inspired by random feature methods for kernel approximation in Euclidean spaces, we introduce randomized spectral node embeddings whose dot products estimate a low-rank approximation of any specific graph kernel. We provide theoretical and empirical results showing that our embeddings achieve more accurate kernel approximations than existing methods, particularly for spectrally localized kernels. These results demonstrate the effectiveness of randomized spectral constructions for scalable and principled graph representation learning.

Victor Sechaud, Laurent Jacques, Patrice Abry et al.

Learning based methods are now ubiquitous for solving inverse problems, but their deployment in real-world applications is often hindered by the lack of ground truth references for training. Recent self-supervised learning strategies offer a promising alternative, avoiding the need for ground truth. However, most existing methods are limited to linear inverse problems. This work extends self-supervised learning to the non-linear problem of recovering audio and images from clipped measurements, by assuming that the signal distribution is approximately invariant to changes in amplitude. We provide sufficient conditions for learning to reconstruct from saturated signals alone and a self-supervised loss that can be used to train reconstruction networks. Experiments on both audio and image data show that the proposed approach is almost as effective as fully supervised approaches, despite relying solely on clipped measurements for training.

Jérome Eertmans, Enrico Maria Vitucci, Vittorio Degli-Esposti et al.

With the increasing presence of dynamic scenarios, such as Vehicle-to-Vehicle communications, radio propagation modeling tools must adapt to the rapidly changing nature of the radio channel. Recently, both Differentiable and Dynamic Ray Tracing frameworks have emerged to address these challenges. However, there is often confusion about how these approaches differ and which one should be used in specific contexts. In this paper, we provide an overview of these two techniques and a comparative analysis against two state-of-the-art tools: 3DSCAT from UniBo and Sionna from NVIDIA. To provide a more precise characterization of the scope of these methods, we introduce a novel simulation-based metric, the Multipath Lifetime Map, which enables the evaluation of spatial and temporal coherence in radio channels only based on the geometrical description of the environment. Finally, our metrics are evaluated on a classic urban street canyon scenario, yielding similar results to those obtained from measurement campaigns.

Jérome Eertmans, Nicola Di Cicco, Claude Oestges et al.

Radio propagation modeling is essential in telecommunication research, as radio channels result from complex interactions with environmental objects. Recently, Machine Learning has been attracting attention as a potential alternative to computationally demanding tools, like Ray Tracing, which can model these interactions in detail. However, existing Machine Learning approaches often attempt to learn directly specific channel characteristics, such as the coverage map, making them highly specific to the frequency and material properties and unable to fully capture the underlying propagation mechanisms. Hence, Ray Tracing, particularly the Point-to-Point variant, remains popular to accurately identify all possible paths between transmitter and receiver nodes. Still, path identification is computationally intensive because the number of paths to be tested grows exponentially while only a small fraction is valid. In this paper, we propose a Machine Learning-aided Ray Tracing approach to efficiently sample potential ray paths, significantly reducing the computational load while maintaining high accuracy. Our model dynamically learns to prioritize potentially valid paths among all possible paths and scales linearly with scene complexity. Unlike recent alternatives, our approach is invariant with translation, scaling, or rotation of the geometry, and avoids dependency on specific environment characteristics.

Victor Sechaud, Patrice Abry, Laurent Jacques et al.

In recent years, deep neural networks have emerged as a solution for inverse imaging problems. These networks are generally trained using pairs of images: one degraded and the other of high quality, the latter being called 'ground truth'. However, in medical and scientific imaging, the lack of fully sampled data limits supervised learning. Recent advances have made it possible to reconstruct images from measurement data alone, eliminating the need for references. However, these methods remain limited to linear problems, excluding non-linear problems such as phase retrieval. We propose a self-supervised method that overcomes this limitation in the case of phase retrieval by using the natural invariance of images to translations.

Théo Hanon, Nicolas Mil-Homens Cavaco, John Kiely et al.

Representing and processing data in spherical domains presents unique challenges, primarily due to the curvature of the domain, which complicates the application of classical Euclidean techniques. Implicit neural representations (INRs) have emerged as a promising alternative for high-fidelity data representation; however, to effectively handle spherical domains, these methods must be adapted to the inherent geometry of the sphere to maintain both accuracy and stability. In this context, we propose Herglotz-NET (HNET), a novel INR architecture that employs a harmonic positional encoding based on complex Herglotz mappings. This encoding yields a well-posed representation on the sphere with interpretable and robust spectral properties. Moreover, we present a unified expressivity analysis showing that any spherical-based INR satisfying a mild condition exhibits a predictable spectral expansion that scales with network depth. Our results establish HNET as a scalable and flexible framework for accurate modeling of spherical data.

Alexander Stollenwerk, Laurent Jacques

We propose a novel algorithm for distributed stochastic gradient descent (SGD) with compressed gradient communication in the parameter-server framework. Our gradient compression technique, named flattened one-bit stochastic gradient descent (FO-SGD), relies on two simple algorithmic ideas: (i) a one-bit quantization procedure leveraging the technique of dithering, and (ii) a randomized fast Walsh-Hadamard transform to flatten the stochastic gradient before quantization. As a result, the approximation of the true gradient in this scheme is biased, but it prevents commonly encountered algorithmic problems, such as exploding variance in the one-bit compression regime, deterioration of performance in the case of sparse gradients, and restrictive assumptions on the distribution of the stochastic gradients. In fact, we show SGD-like convergence guarantees under mild conditions. The compression technique can be used in both directions of worker-server communication, therefore admitting distributed optimization with full communication compression.

Sjoerd Dirksen, Martin Genzel, Laurent Jacques et al.

Neural networks with random weights appear in a variety of machine learning applications, most prominently as the initialization of many deep learning algorithms and as a computationally cheap alternative to fully learned neural networks. In the present article, we enhance the theoretical understanding of random neural networks by addressing the following data separation problem: under what conditions can a random neural network make two classes $\mathcal{X}^-, \mathcal{X}^+ \subset \mathbb{R}^d$ (with positive distance) linearly separable? We show that a sufficiently large two-layer ReLU-network with standard Gaussian weights and uniformly distributed biases can solve this problem with high probability. Crucially, the number of required neurons is explicitly linked to geometric properties of the underlying sets $\mathcal{X}^-, \mathcal{X}^+$ and their mutual arrangement. This instance-specific viewpoint allows us to overcome the usual curse of dimensionality (exponential width of the layers) in non-pathological situations where the data carries low-complexity structure. We quantify the relevant structure of the data in terms of a novel notion of mutual complexity (based on a localized version of Gaussian mean width), which leads to sound and informative separation guarantees. We connect our result with related lines of work on approximation, memorization, and generalization.

Stéphanie Guérit, Siddharth Sivankutty, John Aldo Lee et al.

The lensless endoscope (LE) is a promising device to acquire in vivo images at a cellular scale. The tiny size of the probe enables a deep exploration of the tissues. Lensless endoscopy with a multicore fiber (MCF) commonly uses a spatial light modulator (SLM) to coherently combine, at the output of the MCF, few hundreds of beamlets into a focus spot. This spot is subsequently scanned across the sample to generate a fluorescent image. We propose here a novel scanning scheme, partial speckle scanning (PSS), inspired by compressive sensing theory, that avoids the use of an SLM to perform fluorescent imaging in LE with reduced acquisition time. Such a strategy avoids photo-bleaching while keeping high reconstruction quality. We develop our approach on two key properties of the LE: (i) the ability to easily generate speckles, and (ii) the memory effect in MCF that allows to use fast scan mirrors to shift light patterns. First, we show that speckles are sub-exponential random fields. Despite their granular structure, an appropriate choice of the reconstruction parameters makes them good candidates to build efficient sensing matrices. Then, we numerically validate our approach and apply it on experimental data. The proposed sensing technique outperforms conventional raster scanning: higher reconstruction quality is achieved with far fewer observations. For a fixed reconstruction quality, our speckle scanning approach is faster than compressive sensing schemes which require to change the speckle pattern for each observation.

Vincent Schellekens, Laurent Jacques

The compressive learning framework reduces the computational cost of training on large-scale datasets. In a sketching phase, the data is first compressed to a lightweight sketch vector, obtained by mapping the data samples through a well-chosen feature map, and averaging those contributions. In a learning phase, the desired model parameters are then extracted from this sketch by solving an optimization problem, which also involves a feature map. When the feature map is identical during the sketching and learning phases, formal statistical guarantees (excess risk bounds) have been proven. However, the desirable properties of the feature map are different during sketching and learning (e.g. quantized outputs, and differentiability, respectively). We thus study the relaxation where this map is allowed to be different for each phase. First, we prove that the existing guarantees carry over to this asymmetric scheme, up to a controlled error term, provided some Limited Projected Distortion (LPD) property holds. We then instantiate this framework to the setting of quantized sketches, by proving that the LPD indeed holds for binary sketch contributions. Finally, we further validate the approach with numerical simulations, including a large-scale application in audio event classification.

Vincent Schellekens, Laurent Jacques

In compressive learning, a mixture model (a set of centroids or a Gaussian mixture) is learned from a sketch vector, that serves as a highly compressed representation of the dataset. This requires solving a non-convex optimization problem, hence in practice approximate heuristics (such as CLOMPR) are used. In this work we explore, by numerical simulations, properties of this non-convex optimization landscape and those heuristics.

Rémi Gribonval, Antoine Chatalic, Nicolas Keriven et al.

This article considers "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is first constructed by computing carefully chosen nonlinear random features (e.g., random Fourier features) and averaging them over the whole dataset. Parameters are then learned from the sketch, without access to the original dataset. This article surveys the current state-of-the-art in compressive learning, including the main concepts and algorithms, their connections with established signal-processing methods, existing theoretical guarantees -- on both information preservation and privacy preservation, and important open problems.

Vincent Schellekens, Laurent Jacques

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified to a linear inner product of the random Fourier features of those signals: random projections followed by a periodic map, the complex exponential. It is known that a simple quantization of those features (corresponding to replacing the complex exponential by a different periodic map that takes binary values, which is appealing for their transmission and storage), distorts the approximated kernel, which may be undesirable in practice. Our take-home message is that when the features of only one of the two signals are quantized, the original kernel is recovered without distortion; its practical interest appears in several cases where the kernel evaluations are asymmetric by nature, such as a client-server scheme. Concretely, we introduce the general framework of asymmetric random periodic features, where the two signals of interest are observed through random periodic features: random projections followed by a general periodic map, which is allowed to be different for both signals. We derive the influence of those periodic maps on the approximated kernel, and prove uniform probabilistic error bounds holding for all signal pairs from an infinite low-complexity set. Interestingly, our results allow the periodic maps to be discontinuous, thanks to a new mathematical tool, i.e. the mean Lipschitz smoothness. We then apply this generic framework to semi-quantized kernel machines (where only one signal has quantized features and the other has classical random Fourier features), for which we show theoretically that the approximated kernel remains unchanged (with the associated error bound), and confirm the power of the approach with numerical simulations.

Vincent Schellekens, Laurent Jacques

Generative networks implicitly approximate complex densities from their sampling with impressive accuracy. However, because of the enormous scale of modern datasets, this training process is often computationally expensive. We cast generative network training into the recent framework of compressive learning: we reduce the computational burden of large-scale datasets by first harshly compressing them in a single pass as a single sketch vector. We then propose a cost function, which approximates the Maximum Mean Discrepancy metric, but requires only this sketch, which makes it time- and memory-efficient to optimize.

Vincent Schellekens, Laurent Jacques

Compressive learning is a framework where (so far unsupervised) learning tasks use not the entire dataset but a compressed summary (sketch) of it. We propose a compressive learning classification method, and a novel sketch function for images.

Sandrine Anthoine, Yannick Boursier, Laurent Jacques

The iTWIST workshop series aim at fostering collaboration between international scientific teams for developing new theories, applications and generalizations of low-complexity models. These events emphasize dissemination of ideas through both specific oral and poster presentations, as well as free discussions. For this fourth edition, iTWIST'18 gathered in CIRM, Marseille, France, 74 international participants and featured 7 invited talks, 16 oral presentations, and 21 posters. From iTWIST'18, the scientific committee has decided that the workshop proceedings will adopt the episcience.org philosophy, combined with arXiv.org: in a nutshell, "the proceedings are equivalent to an overlay page, built above arXiv.org; they add value to these archives by attaching a scientific caution to the validated papers." This means that all papers listed in the HTML page of this arxiv publication (see the menu on the right) have been thoroughly evaluated and approved by two independent reviewers, and authors have revised their work according to the comments provided by these reviewers.

Amirafshar Moshtaghpour, José M. Bioucas-Dias, Laurent Jacques

Single Pixel (SP) imaging is now a reality in many applications, e.g., biomedical ultrathin endoscope and fluorescent spectroscopy. In this context, many schemes exist to improve the light throughput of these device, e.g., using structured illumination driven by compressive sensing theory. In this work, we consider the combination of SP imaging with Fourier Transform Interferometry (SP-FTI) to reach high-resolution HyperSpectral (HS) imaging, as desirable, e.g., in fluorescent spectroscopy. While this association is not new, we here focus on optimizing the spatial illumination, structured as Hadamard patterns, during the optical path progression. We follow a variable density sampling strategy for space-time coding of the light illumination, and show theoretically and numerically that this scheme allows us to reduce the number of measurements and light-exposure of the observed object compared to conventional compressive SP-FTI.

Stéphanie Guérit, Siddharth Sivankutty, Camille Scotté et al.

The lensless endoscope is a promising device designed to image tissues in vivo at the cellular scale. The traditional acquisition setup consists in raster scanning during which the focused light beam from the optical fiber illuminates sequentially each pixel of the field of view (FOV). The calibration step to focus the beam and the sampling scheme both take time. In this preliminary work, we propose a scanning method based on compressive sampling theory. The method does not rely on a focused beam but rather on the random illumination patterns generated by the single-mode fibers. Experiments are performed on synthetic data for different compression rates (from 10 to 100% of the FOV).

Amirafshar Moshtaghpour, José M. Bioucas-Dias, Laurent Jacques

This paper introduces a single-pixel HyperSpectral (HS) imaging framework based on Fourier Transform Interferometry (FTI). By combining a space-time coding of the light illumination with partial interferometric observations of a collimated light beam (observed by a single pixel), our system benefits from (i) reduced measurement rate and light-exposure of the observed object compared to common (Nyquist) FTI imagers, and (ii) high spectral resolution as desirable in, e.g., Fluorescence Spectroscopy (FS). From the principles of compressive sensing with multilevel sampling, our method leverages the sparsity "in level" of FS data, both in the spectral and the spatial domains. This allows us to optimize the space-time light coding using time-modulated Hadamard patterns. We confirm the effectiveness of our approach by a few numerical experiments.

Vincent Schellekens, Laurent Jacques

The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it estimates the centroids of data clusters from pooled, non-linear, random signatures of the learning examples. While this approach significantly reduces computational time on very large datasets, its digital implementation wastes acquisition resources because the learning examples are compressed only after the sensing stage. The present work generalizes the sketching procedure initially defined in Compressive K-Means to a large class of periodic nonlinearities including hardware-friendly implementations that compressively acquire entire datasets. This idea is exemplified in a Quantized Compressive K-Means procedure, a variant of CKM that leverages 1-bit universal quantization (i.e. retaining the least significant bit of a standard uniform quantizer) as the periodic sketch nonlinearity. Trading for this resource-efficient signature (standard in most acquisition schemes) has almost no impact on the clustering performances, as illustrated by numerical experiments.

Kévin Degraux, Valerio Cambareri, Bert Geelen et al.

This paper introduces two acquisition device architectures for multispectral compressive imaging. Unlike most existing methods, the proposed computational imaging techniques do not include any dispersive element, as they use a dedicated sensor which integrates narrowband Fabry-Pérot spectral filters at the pixel level. The first scheme leverages joint inpainting and super-resolution to fill in those voxels that are missing due to the device's limited pixel count. The second scheme, in link with compressed sensing, introduces spatial random convolutions, but is more complex and may be affected by diffraction. In both cases we solve the associated inverse problems by using the same signal prior. Specifically, we propose a redundant analysis signal prior in a convex formulation. Through numerical simulations, we explore different realistic setups. Our objective is also to highlight some practical guidelines and discuss their complexity trade-offs to integrate these schemes into actual computational imaging systems. Our conclusion is that the second technique performs best at high compression levels, in a properly sized and calibrated setup. Otherwise, the first, simpler technique should be favored.

Stéphanie Guérit, Adriana González, Anne Bol et al.

Images from positron emission tomography (PET) provide metabolic information about the human body. They present, however, a spatial resolution that is limited by physical and instrumental factors often modeled by a blurring function. Since this function is typically unknown, blind deconvolution (BD) techniques are needed in order to produce a useful restored PET image. In this work, we propose a general BD technique that restores a low resolution blurry image using information from data acquired with a high resolution modality (e.g., CT-based delineation of regions with uniform activity in PET images). The proposed BD method is validated on synthetic and actual phantoms.

Adriana Gonzalez, Hong Jiang, Gang Huang et al.

We consider the problem of reconstructing an image from compressive measurements using a multi-resolution grid. In this context, the reconstructed image is divided into multiple regions, each one with a different resolution. This problem arises in situations where the image to reconstruct contains a certain region of interest (RoI) that is more important than the rest. Through a theoretical analysis and simulation experiments we show that the multi-resolution reconstruction provides a higher quality of the RoI compared to the traditional single-resolution approach.

Arnaud Browet, Christophe De Vleeschouwer, Laurent Jacques et al.

The progress in imaging techniques have allowed the study of various aspect of cellular mechanisms. To isolate individual cells in live imaging data, we introduce an elegant image segmentation framework that effectively extracts cell boundaries, even in the presence of poor edge details. Our approach works in two stages. First, we estimate pixel interior/border/exterior class probabilities using random ferns. Then, we use an energy minimization framework to compute boundaries whose localization is compliant with the pixel class probabilities. We validate our approach on a manually annotated dataset.

Stéphanie Guérit, Laurent Jacques, Benoît Macq et al.

Improving the quality of positron emission tomography (PET) images, affected by low resolution and high level of noise, is a challenging task in nuclear medicine and radiotherapy. This work proposes a restoration method, achieved after tomographic reconstruction of the images and targeting clinical situations where raw data are often not accessible. Based on inverse problem methods, our contribution introduces the recently developed total generalized variation (TGV) norm to regularize PET image deconvolution. Moreover, we stabilize this procedure with additional image constraints such as positivity and photometry invariance. A criterion for updating and adjusting automatically the regularization parameter in case of Poisson noise is also presented. Experiments are conducted on both synthetic data and real patient images.

Amit Kumar K. C., Laurent Jacques, Christophe De Vleeschouwer

Given a set of detections, detected at each time instant independently, we investigate how to associate them across time. This is done by propagating labels on a set of graphs, each graph capturing how either the spatio-temporal or the appearance cues promote the assignment of identical or distinct labels to a pair of detections. The graph construction is motivated by a locally linear embedding of the detection features. Interestingly, the neighborhood of a node in appearance graph is defined to include all the nodes for which the appearance feature is available (even if they are temporally distant). This gives our framework the uncommon ability to exploit the appearance features that are available only sporadically. Once the graphs have been defined, multi-object tracking is formulated as the problem of finding a label assignment that is consistent with the constraints captured each graph, which results into a difference of convex (DC) program. We propose to decompose the global objective function into node-wise sub-problems. This not only allows a computationally efficient solution, but also supports an incremental and scalable construction of the graph, thereby making the framework applicable to large graphs and practical tracking scenarios. Moreover, it opens the possibility of parallel implementation.

Adriana Gonzalez, Véronique Delouille, Laurent Jacques

Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF). Additionally, the image acquisition process is also contaminated by other sources of noise (read-out, photon-counting). The problem of estimating both the PSF and a denoised image is called blind deconvolution and is ill-posed. Aims: We propose a blind deconvolution scheme that relies on image regularization. Contrarily to most methods presented in the literature, our method does not assume a parametric model of the PSF and can thus be applied to any telescope. Methods: Our scheme uses a wavelet analysis prior model on the image and weak assumptions on the PSF. We use observations from a celestial transit, where the occulting body can be assumed to be a black disk. These constraints allow us to retain meaningful solutions for the filter and the image, eliminating trivial, translated and interchanged solutions. Under an additive Gaussian noise assumption, they also enforce noise canceling and avoid reconstruction artifacts by promoting the whiteness of the residual between the blurred observations and the cleaned data. Results: Our method is applied to synthetic and experimental data. The PSF is estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for SDO/AIA using the 2012 Venus transit. Results show that the proposed non-parametric blind deconvolution method is able to estimate the core of the PSF with a similar quality to parametric methods proposed in the literature. We also show that, if these parametric estimations are incorporated in the acquisition model, the resulting PSF outperforms both the parametric and non-parametric methods.

Prasad Sudhakar, Laurent Jacques, Xavier Dubois et al.

Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which describes the pattern of deflections in various directions. This article presents a novel method to efficiently acquire and reconstruct sparse deflection spectra induced by smooth object surfaces. To this end, we leverage the framework of Compressed Sensing (CS) in a particular implementation of a schlieren deflectometer, i.e., an optical system providing linear measurements of deflection spectra with programmable spatial light modulation patterns. We design those modulation patterns on the principle of spread spectrum CS for reducing the number of observations. The ability of our device to simultaneously observe the deflection spectra on a dense discretization of the object surface is related to a Multiple Measurement Vector (MMV) model. This scheme allows us to estimate both the noise power and the instrumental point spread function. We formulate the spectrum reconstruction task as the solving of a linear inverse problem regularized by an analysis sparsity prior using a translation invariant wavelet frame. Our results demonstrate the capability and advantages of using a CS based approach for deflectometric imaging both on simulated data and experimental deflectometric data. Finally, the paper presents an extension of our method showing how we can extract the main deflection direction in each point of the object surface from a few compressive measurements, without needing any costly reconstruction procedures. This compressive characterization is then confirmed with experimental results on simple plano-convex and multifocal intra-ocular lenses studying the evolution of the main deflection as a function of the object point location.

Srdjan Kitić, Laurent Jacques, Nilesh Madhu et al.

Clipping or saturation in audio signals is a very common problem in signal processing, for which, in the severe case, there is still no satisfactory solution. In such case, there is a tremendous loss of information, and traditional methods fail to appropriately recover the signal. We propose a novel approach for this signal restoration problem based on the framework of Iterative Hard Thresholding. This approach, which enforces the consistency of the reconstructed signal with the clipped observations, shows superior performance in comparison to the state-of-the-art declipping algorithms. This is confirmed on synthetic and on actual high-dimensional audio data processing, both on SNR and on subjective user listening evaluations.

Adriana Gonzalez, Laurent Jacques, Christophe De Vleeschouwer et al.

Optical Deflectometric Tomography (ODT) provides an accurate characterization of transparent materials whose complex surfaces present a real challenge for manufacture and control. In ODT, the refractive index map (RIM) of a transparent object is reconstructed by measuring light deflection under multiple orientations. We show that this imaging modality can be made "compressive", i.e., a correct RIM reconstruction is achievable with far less observations than required by traditional Filtered Back Projection (FBP) methods. Assuming a cartoon-shape RIM model, this reconstruction is driven by minimizing the map Total-Variation under a fidelity constraint with the available observations. Moreover, two other realistic assumptions are added to improve the stability of our approach: the map positivity and a frontier condition. Numerically, our method relies on an accurate ODT sensing model and on a primal-dual minimization scheme, including easily the sensing operator and the proposed RIM constraints. We conclude this paper by demonstrating the power of our method on synthetic and experimental data under various compressive scenarios. In particular, the compressiveness of the stabilized ODT problem is demonstrated by observing a typical gain of 20 dB compared to FBP at only 5% of 360 incident light angles for moderately noisy sensing.