Audio declipping with social sparsity

We 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 windowed group-Lasso and the 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.

[1]  Anestis Antoniadis,et al.  Wavelet methods in statistics: Some recent developments and their applications , 2007, 0712.0283.

[2]  Jean-Philippe Vert,et al.  Group Lasso with Overlaps: the Latent Group Lasso approach , 2011, ArXiv.

[3]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[4]  R. Schiffer,et al.  INTRODUCTION , 1988, Neurology.

[5]  Simon J. Godsill,et al.  A Bayesian approach to the restoration of degraded audio signals , 1995, IEEE Trans. Speech Audio Process..

[6]  T. Blumensath,et al.  Iterative Thresholding for Sparse Approximations , 2008 .

[7]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[8]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[9]  D. Donoho,et al.  Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) , 2005 .

[10]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[11]  Richard G. Baraniuk,et al.  Improved wavelet denoising via empirical Wiener filtering , 1997, Optics & Photonics.

[12]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[13]  Jean-Philippe Vert,et al.  Group lasso with overlap and graph lasso , 2009, ICML '09.

[14]  Laurent Jacques,et al.  Consistent iterative hard thresholding for signal declipping , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[15]  Julius O. Smith,et al.  Restoring a clipped signal , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[16]  Ilker Bayram,et al.  Mixed norms with overlapping groups as signal priors , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[17]  Raymond N. J. Veldhuis,et al.  Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes , 1986, IEEE Trans. Acoust. Speech Signal Process..

[18]  Monika Dörfler,et al.  Time-Frequency Analysis for Music Signals: A Mathematical Approach , 2001 .

[19]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[20]  I. Loris.  On the performance of algorithms for the minimization of ℓ1-penalized functionals , 2007, 0710.4082.

[21]  Kai Siedenburg,et al.  Social Sparsity! Neighborhood Systems Enrich Structured Shrinkage Operators , 2013, IEEE Transactions on Signal Processing.

[22]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[23]  Nelly Pustelnik,et al.  Nested Iterative Algorithms for Convex Constrained Image Recovery Problems , 2008, SIAM J. Imaging Sci..

[24]  Monika Dörfler,et al.  Persistent Time-Frequency Shrinkage for Audio Denoising , 2013 .

[25]  Liva Ralaivola,et al.  Multiple indefinite kernel learning with mixed norm regularization , 2009, ICML '09.

[26]  Michael Elad,et al.  Audio Inpainting , 2012, IEEE Transactions on Audio, Speech, and Language Processing.

[27]  Marc Moonen,et al.  Declipping of Audio Signals Using Perceptual Compressed Sensing , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[28]  Bruno Torrésani,et al.  Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients , 2009, Signal Image Video Process..