A CONSTRAINED MATCHING PURSUIT APPROACH TO AUDIO DECLIPPING

© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Audio Inpainting

(c) 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Published version: IEEE Transactions on Audio, Speech and Language Processing 20(3): 922-932, Mar 2012. DOI: 10.1090/TASL.2011.2168211

A Proper version of Synthesis-based Sparse Audio Declipper

Methods based on sparse representation have found great use in the recovery of audio signals degraded by clipping. The state of the art in declipping has been achieved by the SPADE algorithm by Kiti\'c et. al. (LVA/ICA2015). Our recent study (LVA/ICA2018) has shown that although the original S-SPADE can be improved such that it converges significantly faster than the A-SPADE, the restoration quality is significantly worse. In the present paper, we propose a new version of S-SPADE. Experiments show that the novel version of S-SPADE outperforms its old version in terms of restoration quality, and that it is comparable with the A-SPADE while being even slightly faster than A-SPADE

Sparsity and cosparsity for audio declipping: a flexible non-convex approach

This work investigates the empirical performance of the sparse synthesis versus sparse analysis regularization for the ill-posed inverse problem of audio declipping. We develop a versatile non-convex heuristics which can be readily used with both data models. Based on this algorithm, we report that, in most cases, the two models perform almost similarly in terms of signal enhancement. However, the analysis version is shown to be amenable for real time audio processing, when certain analysis operators are considered. Both versions outperform state-of-the-art methods in the field, especially for the severely saturated signals

Revisiting Synthesis Model of Sparse Audio Declipper

The state of the art in audio declipping has currently been achieved by SPADE (SParse Audio DEclipper) algorithm by Kiti\'c et al. Until now, the synthesis/sparse variant, S-SPADE, has been considered significantly slower than its analysis/cosparse counterpart, A-SPADE. It turns out that the opposite is true: by exploiting a recent projection lemma, individual iterations of both algorithms can be made equally computationally expensive, while S-SPADE tends to require considerably fewer iterations to converge. In this paper, the two algorithms are compared across a range of parameters such as the window length, window overlap and redundancy of the transform. The experiments show that although S-SPADE typically converges faster, the average performance in terms of restoration quality is not superior to A-SPADE

Audio Declipping with Social Sparsity

International audienceWe consider the audio declipping problem by using iterative thresholding algorithms and the principle of social sparsity. This recently introduced approach features thresholding/shrinkage operators which allow to model dependencies between neighboring coefficients in expansions with time-frequency dictionaries. A new unconstrained convex formulation of the audio declipping problem is introduced. The chosen structured thresholding operators are the so called \emph{windowed group-Lasso} and the \emph{persistent empirical Wiener}. The usage of these operators significantly improves the quality of the reconstruction, compared to simple soft-thresholding. The resulting algorithm is fast, simple to implement, and it outperforms the state of the art in terms of signal to noise ratio

Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information

Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in the measurement vector leading to a poor performance when the noise no longer follows the Gaussian assumption but, instead, is better characterized by heavier-than-Gaussian tailed distributions. In this paper, we propose a robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse signals in the presence of impulsive noise. To address this problem, we use a Lorentzian cost function instead of the $L_2$ cost function employed by the traditional IHT algorithm. We also modify the algorithm to incorporate prior signal information in the recovery process. Specifically, we study the case of CS with partially known support. The proposed algorithm is a fast method with computational load comparable to the LS based IHT, whilst having the advantage of robustness against heavy-tailed impulsive noise. Sufficient conditions for stability are studied and a reconstruction error bound is derived. We also derive sufficient conditions for stable sparse signal recovery with partially known support. Theoretical analysis shows that including prior support information relaxes the conditions for successful reconstruction. Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments. Numerical results also demonstrate that the partially known support inclusion improves the performance of the proposed algorithm, thereby requiring fewer samples to yield an approximate reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal Processin