Hybrid sparse and low-rank time-frequency signal decomposition

Abstract : We propose a new hybrid (or morphological) generative model that decomposes a signal into two (and possibly more) layers. Each layer is a linear combination of localised atoms from a time-frequency dictionary. One layer has a low-rank time-frequency structure while the other as a sparse structure. The time-frequency resolutions of the dictionaries describing each layer may be different. Our contribution builds on the recently introduced Low-Rank Time-Frequency Synthesis (LRTFS) model and proposes an iterative algorithm similar to the popular iterative shrinkage/thresholding algorithm. We illustrate the capacities of the proposed model and estimation procedure on a tonal + transient audio decomposition example. Index Terms— Low-rank time-frequency synthesis, sparse component analysis, hybrid/morphological decom-positions, non-negative matrix factorisation.
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Cédric Févotte, Matthieu Kowalski. Hybrid sparse and low-rank time-frequency signal decomposition. 23rd European Signal Processing Conference (EUSIPCO 2015), Aug 2015, Nice, France. ⟨hal-01199622⟩

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