Sparsity and persistence in time-frequency sound representations

13 pagesInternational audienceIt is a well known fact that the time-frequency domain is very well adapted for representing audio signals. The main two features of time-frequency representations of many classes of audio signals are sparsity (signals are generally well approximated using a small number of coefficients) and persistence (significant coefficients are not isolated, and tend to form clusters). This contribution presents signal approximation algorithms that exploit these properties, in the framework of hierarchical probabilistic models. Given a time-frequency frame (i.e. a Gabor frame, or a union of several Gabor frames or time-frequency bases), coefficients are first gathered into groups. A group of coefficients is then modeled as a random vector, whose distribution is governed by a hidden state associated with the group. Algorithms for parameter inference and hidden state estimation from analysis coefficients are described. The role of the chosen dictionary, and more particularly its structure, is also investigated. The proposed approach bears some resemblance with variational approaches previously proposed by the authors (in particular the variational approach exploiting mixed norms based regularization terms). In the framework of audio signal applications, the time-frequency frame under consideration is a union of two MDCT bases or two Gabor frames, in order to generate estimates for tonal and transient layers. Groups corresponding to tonal (resp. transient) coefficients are constant frequency (resp. constant time) time-frequency coefficients of a frequency-selective (resp. time-selective) MDCT basis or Gabor frame

Sparse signal decomposition on hybrid dictionaries using musical priors

International audienceThis paper investigates the use of musical priors for sparse expansion of audio signals of music on overcomplete dictionaries taken from the union of two orthonormal bases. More specifically, chord information is used to build structured model that take into account dependencies between coefficients of the decomposition. Evaluation on various music signals shows that our approach provides results whose quality measured by the signal-to-noise ratio corresponds to state-of-the-art approaches, and shows that our model is relevant to represent audio signals of Western tonal music and opens new perspectives

Sparse and structured decomposition of audio signals on hybrid dictionaries using musical priors

International audienceThis paper investigates the use of musical priors for sparse expansion of audio signals of music, on an overcomplete dual-resolution dictionary taken from the union of two orthonormal bases that can describe both transient and tonal components of a music audio signal. More specifically, chord and metrical structure information are used to build a structured model that takes into account dependencies between coefficients of the decomposition, both for the tonal and for the transient layer. The denoising task application is used to provide a proof of concept of the proposed musical priors. Several configurations of the model are analyzed. Evaluation on monophonic and complex polyphonic excerpts of real music signals shows that the proposed approach provides results whose quality measured by the signal-to-noise ratio is competitive with state-of-the-art approaches, and more coherent with the semantic content of the signal. A detailed analysis of the model in terms of sparsity and in terms of interpretability of the representation is also provided, and shows that the model is capable of giving a relevant and legible representation of Western tonal music audio signals

Towards a Hybrid Audio Coder

International audienceThe main features of a novel approach for audio signal encoding are described. The approach combines non-linear transform coding and structured approximation techniques, together with hybrid modeling of the signal class under consideration. Essentially, several different components of the signal are estimated and transform coded using an appropriately chosen orthonormal basis. Different models and estimation procedures are discussed, and numerical results are provided

Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients

nombre de pages : 14International audienceSparse regression often uses $\ell_p$ norm priors (with p<2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of $\ell_{1,2}$ and $\ell_{2,1}$ norms lead to new group shrinkage operators. Mixed norm priors are shown to be particularly efficient in a generalized basis pursuit denoising approach, and are also used in a context of morphological component analysis. A suitable version of the Block Coordinate Relaxation algorithm is derived for the latter. The group-shrinkage operators are then modified to overcome some limitations of the mixed-norms. The proposed group shrinkage operators are tested on simulated signals in specific situations, to illustrate their different behaviors. Results on real data are also used to illustrate the relevance of the approach

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.Comment: 20 pages - accepted 2nd April 2012 at Elsevier Signal Processin

Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Structured Compressed Sensing: From Theory to Applications

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal Processin