Research Area
Sparse signal decompositions
Overview

I have been (and still am) very interested in sparse decomposition algorithms, especially greedy ones and essentially on Audio/Acoustics signals (e.g. 1D data)
During my PhD I have developped a variant of the Matching Pursuit (MP) algorithm, which is called Random Sequential Subdictionaries Matching Pursuit (RSSMP). It mainly uses randomness to artificially increase the number of atoms among which the algorithm is allowed to choose.
I then used this algorithm to enhance low bitrate audio compression schemes.

Papers and support material
  • The paper explaining the algorithm is here
  • Audio samples illustrating the results can be found here (to be transfered)
  • Matlab code for the algorithm is available on FileExchange
Audio Source Separation
Overview
Source Separation is the process of retrieving mixed signals given only their mixtures. This typically the case of musical signals where multiple instruments play simultaneously and only the mix is available. Recently a lot of interest in repetition-based method encouraged me to propose separation algorithm that exploits the knowledge of repeating musical patterns. Combined with a classical sparse prior on the source, a structured sparsity model can be derived. The problem becomes an instance of a Multiple Measurement Vector (MMV) case and can be addressed using a greedy algorithm.
Papers and support material
  • The paper explaining the algorithm is here
Blind Denoising of time series
Overview
Denoising with sparse approximation is a fairly mature field since the wavelet thresholding era. Most state-of-the-art techniques, however, require the knowledge of the noise characteristics and/or statistical properties, which might not be available in practice. Instead, we can assume that the informative part of the signal is sparse in some known basis, on which the additive noise is incoherent. When a greedy algorithm is used for denoising, these assumptions provide a self-stopping criterion, without knowledge of the noise level. Combined with a randomization of the dictionary at each iteration, this forms the basis of a new denoising procedure, called Blind Random Pursuit Denoising (BIRD). It can be generalized to the denoising of multidimensional signals, with a structured sparse model (S-BIRD). The relevance of this approach is demonstrated on synthetic and experimental M/EEG signals, where BIRD outperforms state-of-the-art algorithms, even with an oracle knowledge of the noise level.
Papers and support material
  • The paper explaining the algorithm is here
  • A conference paper (in french) is availablehere
Reproducing research and code

A Python package for greedy decomposition (including RSSMP) is available in the form of the PyMP package (on github). I try to provide extensive documentation and even wrote tutorials to reproduce some results from the paper.

Source code for our denoising algorithm BIRD is available in two flavour: an optimized version takes advantage of the PyMP package to perform fast FFT operations, a simpler pure-python package is now available on github (Join work with A. Gramfort)

If you're interested in getting code from my other work please feel free to contact me.