SPARSE DECOMPOSITION OF AUDIO SIGNALS USING A PERCEPTUAL MEASURE OF DISTORTION. APPLICATION TO LOSSY AUDIO CODING.

International audienceState-of the art audio codecs use time-frequency transforms derived from cosine bases, followed by a quantification stage. The quantization steps are set according to perceptual considerations. In the last decade, several studies applied adaptive sparse time-frequency transforms to audio coding, e.g. on unions of cosine bases using a Matching-Pursuit-derived algorithm. This was shown to significantly improve the coding efficiency. We propose another approach based on a variational algorithm, i.e. the optimization of a cost function taking into account both a perceptual distortion measure derived form a hearing model and a sparsity constraint, which favors the coding efficiency. In this early version, we show that, using a coding scheme without perceptual control of quantization, our method outperforms a codec from the literature with the same quantization scheme. In future work, a more sophisticated quantization scheme would probably allow our method to challenge standard codecs e.g. AAC

A review of blind source separation in NMR spectroscopy

27 pagesInternational audienceFourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits. Blind source separation is a very broad definition regrouping several classes of mathematical methods for complex signal decomposition that use no hypothesis on the form of the data. Developed outside NMR, these algorithms have been increasingly tested on spectra of mixtures. In this review, we shall provide an historical overview of the application of blind source separation methodologies to NMR, including methods specifically designed for the specificity of this spectroscopy

Decomposition methods of NMR signal of complex mixtures : models ans applications

L'objectif de ce travail était de tester des méthodes de SAS pour la séparation des spectres complexes RMN de mélanges dans les plus simples des composés purs. Dans une première partie, les méthodes à savoir JADE et NNSC ont été appliqué es dans le cadre de la DOSY , une application aux données CPMG était démontrée. Dans une deuxième partie, on s'est concentré sur le développement d'un algorithme efficace "beta-SNMF" . Ceci s'est montré plus performant que NNSC pour beta inférieure ou égale à 2. Etant donné que dans la littérature, le choix de beta a été adapté aux hypothèses statistiques sur le bruit additif, une étude statistique du bruit RMN de la DOSY a été faite pour obtenir une image plus complète de nos données RMN étudiées.The objective of the work was to test BSS methods for the separation of the complex NMR spectra of mixtures into the simpler ones of the pure compounds. In a first part, known methods namely JADE and NNSC were applied in conjunction for DOSY , performing applications for CPMG were demonstrated. In a second part, we focused on developing an effective algorithm "beta- SNMF ". This was demonstrated to outperform NNSC for beta less or equal to 2. Since in the literature, the choice of beta has been adapted to the statistical assumptions on the additive noise, a statistical study of NMR DOSY noise was done to get a more complete picture about our studied NMR data

Audio inpainting based on joint-sparse modeling

We present a new framework for the restoration of missing samples in audio signals. It consists in locating audio frames that share similar sparse structures and in applying a joint-sparse algorithm to estimate the missing samples. Such similar frames are found in audio signals due to the signals' intrinsic structures: across channels, in the temporal neighboring of each frame and, since patterns are repeated non-locally. We propose a fast and robust strategy for locating the similar frames by introducing a spectral cosine similarity that is more suitable than the usual correlation similarity. We present and compare the inpainting versions of three known joint-sparse algorithms and show how they lead to a better reconstruction of the missing parts. Experimental results reveal that by selecting only a few similar frames, joint-sparse audio inpainting outperform the state-of-the-art OMP inpainting method by up to 5 dB, and that improvements cumulatively result from non-local and inter-channel joint decomposition

Joint-sparse modeling for audio inpainting

International audienceWe exploit the common sparse structure between similar audio frames in order to reconstruct missing samples in audio signals.While joint-sparse models and related algorithms have been widely studied, one important challenge is to locate such similar frames in a fast way and when some samples are missing.We propose and compare several similarity measures dedicated to this task.We then show how this leads to better reconstruction results than when processing the audio frames independently

Sparse non-local similarity modeling for audio inpainting

International audienceAudio signals are highly structured from a low, signal level to high cognitive aspects. We investigate how to exploit the common sparse structure between similar audio frames in order to reconstruct missing data in audio signals. While joint sparse models and related algorithms have been widely studied, one important challenge is to locate such similar frames : the search must be adapted to the joint-sparse model and should be fast and one must deal with missing data in the frames. We propose, compare and discuss several similarity measures dedicated to this task. We then show how this strategy can lead to better reconstruction of missing data in audio signals

Effective processing of pulse field gradient NMR of mixtures by blind source separation.

International audienceNMR diffusometry and its flagship layout, diffusion-ordered spectroscopy (DOSY), are versatile for studying mixtures of bioorganic and synthetic molecules, but a limiting factor of its applicability is the requirement of a mathematical treatment capable of distinguishing molecules with similar spectra or diffusion constants. We present here a processing strategy for DOSY, a synergy of two high-performance blind source separation (BSS) techniques: non-negative matrix factorization (NMF) using additional sparse conditioning (SC), and the JADE (joint approximate diagonalization of eigenmatrices) declination of independent component analysis (ICA). While the first approach has an intrinsic affinity for NMR data, the latter one can be orders of magnitude computationally faster and can be used to simplify the parametrization of the former

Effective Processing of Pulse Field Gradient NMR of Mixtures by Blind Source Separation

NMR diffusometry and its flagship layout, diffusion-ordered spectroscopy (DOSY), are versatile for studying mixtures of bioorganic and synthetic molecules, but a limiting factor of its applicability is the requirement of a mathematical treatment capable of distinguishing molecules with similar spectra or diffusion constants. We present here a processing strategy for DOSY, a synergy of two high-performance blind source separation (BSS) techniques: non-negative matrix factorization (NMF) using additional sparse conditioning (SC), and the JADE (joint approximate diagonalization of eigenmatrices) declination of independent component analysis (ICA). While the first approach has an intrinsic affinity for NMR data, the latter one can be orders of magnitude computationally faster and can be used to simplify the parametrization of the former