Abstract
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.
R. Gribonval—This work was supported in part by the European Research Council, PLEASE project (ERC-StG-2011-277906).
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Notes
- 1.
Observe that if D and A are unitary matrices, the two problems become identical.
- 2.
Recall that the matrices \({{{\varvec{M}}}_\mathrm{r}}\), \({{{\varvec{M}}}_\mathrm{c}^+}\) and \({{{\varvec{M}}}_\mathrm{c}^-}\) are tight frames by design.
- 3.
We use the implementation kindly provided by the authors.
- 4.
All algorithms were implemented in Matlab®, and run in single-thread mode.
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Kitić, S., Bertin, N., Gribonval, R. (2015). Sparsity and Cosparsity for Audio Declipping: A Flexible Non-convex Approach. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_28
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