Manuel Moussallam

Matching Pursuits with random sequential subdictionaries

Matching Pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be computationally costly for large dictionaries and burdens their competitiveness in coding applications. We propose using a non-adaptive random sequence of subdictionaries in the decomposition process, thus parsing a large dictionary in a probabilistic fashion with no additional projection cost nor parameter estimation. A theoretical modeling based on order statistics is provided, along with experimental evidence showing that the novel algorithm can be efficiently used on sparse approximation problems. An application to audio signal compression with multiscale time-frequency dictionaries is presented, along with a discussion of the complexity and practical implementations.

Blind Denoising with Random Greedy Pursuits

Denoising methods require some assumptions about the signal of interest and the noise. While most denoising procedures require some knowledge about the noise level, which may be unknown in practice, here we assume that the signal expansion in a given dictionary has a distribution that is more heavy-tailed than the noise. We show how this hypothesis leads to a stopping criterion for greedy pursuit algorithms which is independent from the noise level. Inspired by the success of ensemble methods in machine learning, we propose a strategy to reduce the variance of greedy estimates by averaging pursuits obtained from randomly subsampled dictionaries. We call this denoising procedure Blind Random Pursuit Denoising (BIRD). We offer a generalization to multidimensional signals, with a structured sparse model (S-BIRD). The relevance of this approach is demonstrated on synthetic and experimental MEG signals where, without any parameter tuning, BIRD outperforms state-of-the-art algorithms even when they are informed by the noise level. Code is available to reproduce all experiments.

Sound enhancement using sparse approximation with speclets

This paper addresses an innovative approach to informed enhancement of damaged sound. It uses sparse approximations with a learned dictionary of atoms modeling the main components of the undamaged source spectra. The decomposition process aims at finding which of the atoms could constitute the decomposition of the undamaged source in order to recover it. The decomposition of the damaged signal is done with a Matching Pursuit algorithm and involves an adaptation of the dictionary learned on undamaged sources. Evaluation is performed on a bandwidth extension task for various classes of signals.

A general framework for dictionary based audio fingerprinting

Fingerprint-based Audio recognition system must address concurrent objectives. Indeed, fingerprints must be both robust to distortions and discriminative while their dimension must remain to allow fast comparison. This paper proposes to restate these objectives as a penalized sparse representation problem. On top of this dictionary-based approach, we propose a structured sparsity model in the form of a probabilistic distribution for the sparse support. A practical suboptimal greedy algorithm is then presented and evaluated on robustness and recognition tasks. We show that some existing methods can be seen as particular cases of this algorithm and that the general framework allows to reach other points of a Pareto-like continuum.

Codec independent lossy audio compression detection

In this paper, we propose a method for detecting marks of lossy compression encoding, such as MP3 or AAC, from PCM audio. The method is based on a convolutional neural network (CNN) applied to audio spectrograms and trained with the output of various lossy audio codecs and bitrates. Our method shows good performances on a large database and robustness to codec type and resampling.

Random time-frequency subdictionary design for sparse representations with greedy algorithms

Sparse signal approximation can be used to design efficient low bit-rate coding schemes. It heavily relies on the ability to design appropriate dictionaries and corresponding decomposition algorithms. The size of the dictionary, and therefore its resolution, is a key parameter that handles the tradeoff between sparsity and tractability. This work proposes the use of a non adaptive random sequence of subdictionaries in a greedy decomposition process, thus browsing a larger dictionary space in a probabilistic fashion with no additional projection cost nor parameter estimation. This technique leads to very sparse decompositions, at a controlled computational complexity. Experimental evaluation is provided as proof of concept for low bit rate compression of audio signals.

AUDIO SIGNAL REPRESENTATIONS FOR FACTORIZATION IN THE SPARSE DOMAIN

In this paper, a new class of audio representations is introduced, together with a corresponding fast decomposition algorithm. The main feature of these representations is that they are both sparse and approximately shift-invariant, which allows similarity search in a sparse domain. The common sparse support of detected similar patterns is then used to factorize their representations. The potential of this method for simultaneous structural analysis and compressing tasks is illustrated by preliminary experiments on simple musical data.