Angélique Drémeau

Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques

This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. On the sensor side, without a reference beam, the CCD camera provides only intensity measurements. Within this framework, this paper shows that the TM can still be retrieved, through signal processing techniques of phase retrieval. This is experimentally validated on three criteria : quality of prediction, distribution of singular values, and quality of focusing.

Boltzmann Machine and Mean-Field Approximation for Structured Sparse Decompositions

Taking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a marginalized maximum a posteriori problem. To solve this problem, we resort to a mean-field approximation and the “variational Bayes expectation-maximization” algorithm. This approach results in a soft procedure making no hard decision on the support or the values of the sparse representation. We show that this characteristic leads to an improvement of the performance over state-of-the-art algorithms.

Approximate Message Passing with Restricted Boltzmann Machine Priors

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.

Phase recovery from a Bayesian point of view: The variational approach

In this paper, we consider the phase recovery problem, where a complex signal vector has to be estimated from the knowledge of the modulus of its linear projections, from a naive variational Bayesian point of view. In particular, we derive an iterative algorithm following the minimization of the Kullback-Leibler divergence under the mean-field assumption, and show on synthetic data with random projections that this approach leads to an efficient and robust procedure, with a reasonable computational cost.

Sparse optimization with directional DCT bases for image compression

This paper proposes a new compression algorithm based on the directional DCT (DDCT) bases introduced in. We first explain how to extend the DDCT concept to rectangular bases and exploit them to build a set of bases using a bintree segmentation. We then use dynamic programming to select a basis from this set according to a rate-distortion criterion. Comparisons in terms of rate-distortion performance are finally made with the current compression standards JPEG and JPEG2000.

An EM-algorithm approach for the design of orthonormal bases adapted to sparse representations

In this paper, we consider the problem of dictionary learning for sparse representations. Several algorithms dealing with this problem can be found in the literature. One of them, introduced by Sezer et al. in optimizes a dictionary made up of the union of orthonormal bases. In this paper, we propose a probabilistic interpretation of Sezers algorithm and suggest a novel optimization procedure based on the EM algorithm. Comparisons of the performance in terms of missed detection rate show a clear superiority of the proposed approach.

Sparse representation algorithms based on mean-field approximations

In this paper we address the problem of sparse representation (SR) within a Bayesian framework. We assume that the observations are generated from a Bernoulli-Gaussian process and consider the corresponding Bayesian inference problem. Tractable solutions are then proposed based on the “mean-field” approximation and the variational Bayes EM algorithm. The resulting SR algorithms are shown to have a tractable complexity and very good performance over a wide range of sparsity levels. In particular, they significantly improve the critical sparsity upon state-of-the-art SR algorithms.

Random projections through multiple optical scattering: Approximating Kernels at the speed of light

Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the computational and memory costs. Here, we overcome this difficulty by proposing an analog, optical device, that performs the random projections literally at the speed of light without having to store any matrix in memory. This is achieved using the physical properties of multiple coherent scattering of coherent light in random media. We use this device on a simple task of classification with a kernel machine, and we show that, on the MNIST database, the experimental results closely match the theoretical performance of the corresponding kernel. This framework can help make kernel methods practical for applications that have large training sets and/or require real-time prediction. We discuss possible extensions of the method in terms of a class of kernels, speed, memory consumption and different problems.

Auditory Sketches: Sparse Representations of Sounds Based on Perceptual Models

An important question for both signal processing and auditory science is to understand which features of a sound carry the most important information for the listener. Here we approach the issue by introducing the idea of auditory sketches: sparse representations of sounds, severely impoverished compared to the original, which nevertheless afford good performance on a given perceptual task. Starting from biologically-grounded representations auditory models, a sketch is obtained by reconstructing a highly under-sampled selection of elementary atoms. Then, the sketch is evaluated with a psychophysical experiment involving human listeners. The process can be repeated iteratively. As a proof of concept, we present data for an emotion recognition task with short non-verbal sounds. We investigate 1/ the type of auditory representation that can be used for sketches 2/ the selection procedure to sparsify such representations 3/ the smallest number of atoms that can be kept 4/ the robustness to noise. Results indicate that it is possible to produce recognizable sketches with a very small number of atoms per second. Furthermore, at least in our experimental setup, a simple and fast under-sampling method based on selecting local maxima of the representation seems to perform as well or better than a more traditional algorithm aimed at minimizing the reconstruction error. Thus, auditory sketches may be a useful tool for choosing sparse dictionaries, and also for identifying the minimal set of features required in a specific perceptual task.

Soft Bayesian pursuit algorithm for sparse representations

This paper deals with sparse representations within a Bayesian framework. For a Bernoulli-Gaussian model, we here propose a method based on a mean-field approximation to estimate the support of the signal. In numerical tests involving a recovery problem, the resulting algorithm is shown to have good performance over a wide range of sparsity levels, compared to various state-of-the-art algorithms.