Low Rank and Sparsity Analysis Applied to Speech Enhancement via Online Estimated Dictionary

In this letter, we propose an online estimated local dictionary based single-channel speech enhancement algorithm, which focuses on low-rank and sparse matrix decomposition. In the proposed algorithm, a noisy speech spectrogram can be decomposed into low-rank background noise components and an activation of the online speech dictionary, on which both low-rank and sparsity constraints are imposed. This decomposition takes the advantage of local estimated exemplar’s high expressiveness on speech components and also accommodates nonstationary background noise. The local dictionary can be obtained through estimating the speech presence probability (SPP) by applying expectation–maximal algorithm, in which a generalized Gamma prior for speech magnitude spectrum is used. The proposed algorithm is evaluated using signal-to-distortion ratio, and perceptual evaluation of speech quality. The results show that the proposed algorithm achieves significant improvements at various SNRs when compared to four other speech enhancement algorithms, including improved Karhunen–Loeve transform approach, SPP-based MMSE, nonnegative matrix factorization-based robust principal component analysis (RPCA), and RPCA

Using Underapproximations for Sparse Nonnegative Matrix Factorization

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g., text mining, image processing, microarray data analysis, collaborative filtering, etc. We introduce a novel approach to solve NMF problems, based on the use of an underapproximation technique, and show its effectiveness to obtain sparse solutions. This approach, based on Lagrangian relaxation, allows the resolution of NMF problems in a recursive fashion. We also prove that the underapproximation problem is NP-hard for any fixed factorization rank, using a reduction of the maximum edge biclique problem in bipartite graphs. We test two variants of our underapproximation approach on several standard image datasets and show that they provide sparse part-based representations with low reconstruction error. Our results are comparable and sometimes superior to those obtained by two standard Sparse Nonnegative Matrix Factorization techniques.Comment: Version 2 removed the section about convex reformulations, which was not central to the development of our main results; added material to the introduction; added a review of previous related work (section 2.3); completely rewritten the last part (section 4) to provide extensive numerical results supporting our claims. Accepted in J. of Pattern Recognitio

Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images