arXiv subjects

Laurent Jacques

Publications and source records attributed to Laurent Jacques.

At least 37 records · Page 2Linked to original sources

arXiv2024

Interferometric lensless imaging: rank-one projections of image frequencies with speckle illuminations

Lensless illumination single-pixel imaging with a multicore fiber (MCF) is a computational imaging technique that enables potential endoscopic observations of biological samples at cellular scale. In this work, we show that this technique is tantamount to collecting multiple symmetric rank-one projections (SROP) of an interferometric matrix--a matrix encoding the spectral content of the sample image. In this model, each SROP is induced by the complex sketching vector shaping the incident light wavefront with a spatial light modulator (SLM), while the projected interferometric matrix collects up to $O(Q^2)$ image frequencies for a $Q$-core MCF. While this scheme subsumes previous sensing modalities, such as raster scanning (RS) imaging with beamformed illumination, we demonstrate that collecting the measurements of $M$ random SLM configurations--and thus acquiring $M$ SROPs--allows us to estimate an image of interest if $M$ and $Q$ scale log-linearly with the image sparsity level This demonstration is achieved both theoretically, with a specific restricted isometry analysis of the sensing scheme, and with extensive Monte Carlo experiments. On a practical side, we perform a single calibration of the sensing system robust to certain deviations to the theoretical model and independent of the sketching vectors used during the imaging phase. Experimental results made on an actual MCF system demonstrate the effectiveness of this imaging procedure on a benchmark image.

eess.IV↗

arXiv2024

Fully Differentiable Ray Tracing via Discontinuity Smoothing for Radio Network Optimization

Recently, Differentiable Ray Tracing has been successfully applied in the field of wireless communications for learning radio materials or optimizing the transmitter orientation. However, in the frame of gradient based optimization, obstruction of the rays by objects can cause sudden variations in the related objective functions or create entire regions where the gradient is zero. As these issues can dramatically impact convergence, this paper presents a novel Ray Tracing framework that is fully differentiable with respect to any scene parameter, but also provides a loss function continuous everywhere, thanks to specific local smoothing techniques. Previously non-continuous functions are replaced by a smoothing function, that can be exchanged with any function having similar properties. This function is also configurable via a parameter that determines how smooth the approximation should be. The present method is applied on a basic one-transmitter-multi-receiver scenario, and shows that it can successfully find the optimal solution. As a complementary resource, a 2D Python library, DiffeRT2d, is provided in Open Access, with examples and a comprehensive documentation.

eess.SP↗

arXiv2023

Learning to Reconstruct Signals From Binary Measurements

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.

eess.SP↗

arXiv2023

Grid Hopping: Accelerating Direct Estimation Algorithms for Multistatic FMCW Radar

This paper presents a novel signal processing technique, coined grid hopping, as well as an active multistatic Frequency-Modulated Continuous Wave (FMCW) radar system designed to evaluate its performance. The design of grid hopping is motivated by two existing estimation algorithms. The first one is the indirect algorithm estimating ranges and speeds separately for each received signal, before combining them to obtain location and velocity estimates. The second one is the direct method jointly processing the received signals to directly estimate target location and velocity. While the direct method is known to provide better performance, it is seldom used because of its high computation time. Our grid hopping approach, which relies on interpolation strategies, offers a reduced computation time while its performance stays on par with the direct method. We validate the efficiency of this technique on actual FMCW radar measurements and compare it with other methods.

eess.SP↗

arXiv2023

Signal processing after quadratic random sketching with optical units

Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the possibility of performing data processing (such as pattern detection or classification) directly in the sketched domain without accessing the original data was previously achieved for linear random sketching methods and compressive sensing. In this work, we show how to estimate simple signal processing tasks (such as deducing local variations in a image) directly using random quadratic projections achieved by an optical processing unit. The same approach allows for naive data classification methods directly operated in the sketched domain. We report several experiments confirming the power of our approach.

eess.SP↗

arXiv2023

Interferometric single-pixel imaging with a multicore fiber

Lensless illumination single-pixel imaging with a multicore fiber (MCF) is a computational imaging technique that enables potential endoscopic observations of biological samples at cellular scale. In this work, we show that this technique is tantamount to collecting multiple symmetric rank-one projections (SROP) of a Hermitian \emph{interferometric} matrix -- a matrix encoding the spectral content of the sample image. In this model, each SROP is induced by the complex \emph{sketching} vector shaping the incident light wavefront with a spatial light modulator (SLM), while the projected interferometric matrix collects up to $O(Q^2)$ image frequencies for a $Q$-core MCF. While this scheme subsumes previous sensing modalities, such as raster scanning (RS) imaging with beamformed illumination, we demonstrate that collecting the measurements of $M$ random SLM configurations -- and thus acquiring $M$ SROPs -- allows us to estimate an image of interest if $M$ and $Q$ scale linearly (up to log factors) with the image sparsity level, hence requiring much fewer observations than RS imaging or a complete Nyquist sampling of the $Q \times Q$ interferometric matrix. This demonstration is achieved both theoretically, with a specific restricted isometry analysis of the sensing scheme, and with extensive Monte Carlo experiments. Experimental results made on an actual MCF system finally demonstrate the effectiveness of this imaging procedure on a benchmark image.

eess.SP↗

arXiv2023

Signal processing with optical quadratic random sketches

eess.SP↗

arXiv2023

Low-rank plus sparse trajectory decomposition for direct exoplanet imaging

We propose a direct imaging method for the detection of exoplanets based on a combined low-rank plus structured sparse model. For this task, we develop a dictionary of possible effective circular trajectories a planet can take during the observation time, elements of which can be efficiently computed using rotation and convolution operation. We design a simple alternating iterative hard-thresholding algorithm that jointly promotes a low-rank background and a sparse exoplanet foreground, to solve the non-convex optimisation problem. The experimental comparison on the $β$-Pictoris exoplanet benchmark dataset shows that our method has the potential to outperform the widely used Annular PCA for specific planet light intensities in terms of the Receiver operating characteristic (ROC) curves.

astro-ph.IM↗

arXiv2023

Min-Path-Tracing: A Diffraction Aware Alternative to Image Method in Ray Tracing

For more than twenty years, Ray Tracing methods have continued to improve on both accuracy and computational time aspects. However, most state-of-the-art image-based ray tracers still rely on a description of the environment that only contains planar surfaces. They are also limited by the number of diffractions they can simulate. We present Min-Path-Tracing (MPT), an alternative to the image method that can handle diffractions seamlessly, while also leveraging the possibility to use different geometries for surfaces or edges, such as parabolic mirrors. MPT uses implicit representations of objects to write the path finding challenge as a minimization problem. We further show that multiple diffractions can be important in some situations, which MPT is capable to simulate without increasing neither the computational nor the implementation complexity.

eess.SP↗

arXiv2022

The Separation Capacity of Random Neural Networks

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.

cs.LG↗

arXiv2022

ROP inception: signal estimation with quadratic random sketching

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.

eess.SP↗

arXiv2021

Sketching Datasets for Large-Scale Learning (long version)

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.

stat.ML↗

arXiv2021

Compressive lensless endoscopy with partial speckle scanning

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.

physics.optics↗

arXiv2021

Asymmetric compressive learning guarantees with applications to quantized sketches

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.

stat.ML↗

arXiv2021

Breaking the waves: asymmetric random periodic features for low-bitrate kernel machines

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.

eess.SP↗

arXiv2021

MAYONNAISE: a morphological components analysis pipeline for circumstellar disks and exoplanets imaging in the near infrared

Imaging circumstellar disks in the near-infrared provides unprecedented information about the formation and evolution of planetary systems. However, current post-processing techniques for high-contrast imaging using ground-based telescopes have a limited sensitivity to extended signals and their morphology is often plagued with strong morphological distortions. Moreover, it is challenging to disentangle planetary signals from the disk when the two components are close or intertwined. We propose a pipeline that is capable of detecting a wide variety of disks and preserving their shapes and flux distributions. By construction, our approach separates planets from disks. After analyzing the distortions induced by the current angular differential imaging (ADI) post-processing techniques, we establish a direct model of the different components constituting a temporal sequence of high-contrast images. In an inverse problem framework, we jointly estimate the starlight residuals and the potential extended sources and point sources hidden in the images, using low-complexity priors for each signal. To verify and estimate the performance of our approach, we tested it on VLT/SPHERE-IRDIS data, in which we injected synthetic disks and planets. We also applied our approach on observations containing real disks. Our technique makes it possible to detect disks from ADI datasets of a contrast above $3\times10^{-6}$ with respect to the host star. As no specific shape of the disks is assumed, we are capable of extracting a wide diversity of disks, including face-on disks. The intensity distribution of the detected disk is accurately preserved and point sources are distinguished, even close to the disk.

astro-ph.IM↗

arXiv2021

Sparse Factorization-based Detection of Off-the-Grid Moving targets using FMCW radars

In this paper, we investigate the application of continuous sparse signal reconstruction algorithms for the estimation of the ranges and speeds of multiple moving targets using an FMCW radar. Conventionally, to be reconstructed, continuous sparse signals are approximated by a discrete representation. This discretization of the signal's parameter domain leads to mismatches with the actual signal. While increasing the grid density mitigates these errors, it dramatically increases the algorithmic complexity of the reconstruction. To overcome this issue, we propose a fast greedy algorithm for off-the-grid detection of multiple moving targets. This algorithm extends existing continuous greedy algorithms to the framework of factorized sparse representations of the signals. This factorized representation is obtained from simplifications of the radar signal model which, up to a model mismatch, strongly reduces the dimensionality of the problem. Monte-Carlo simulations of a K-band radar system validate the ability of our method to produce more accurate estimations with less computation time than the on-the-grid methods and than methods based on non-factorized representations.

eess.SP↗

arXiv2021

Morphological components analysis for circumstellar disks imaging

Recent developments in astronomical observations enable direct imaging of circumstellar disks. Precise characterization of such extended structure is essential to our understanding of stellar systems. However, the faint intensity of the circumstellar disks compared to the brightness of the host star compels astronomers to use tailored observation strategies, in addition to state-of-the-art optical devices. Even then, extracting the signal of circumstellar disks heavily relies on post-processing techniques. In this work, we propose a morphological component analysis (MCA) approach that leverages low-complexity models of both the disks and the stellar light corrupting the data. In addition to disks, our method allows to image exoplanets. Our approach is tested through numerical experiments.

astro-ph.IM↗