Wavelet shrinkage using adaptive structured sparsity constraints

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Wavelet shrinkage using adaptive structured sparsity constraints

Tomassi, D; Milone, D; Nelson, JDB; (2015) Wavelet shrinkage using adaptive structured sparsity constraints. Signal Processing , 106 73 - 87. 10.1016/j.sigpro.2014.07.001. Green open access

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Abstract

Structured sparsity approaches have recently received much attention in the statistics, machine learning, and signal processing communities. A common strategy is to exploit or assume prior information about structural dependencies inherent in the data; the solution is encouraged to behave as such by the inclusion of an appropriate regularisation term which enforces structured sparsity constraints over sub-groups of data. An important variant of this idea considers the tree-like dependency structures often apparent in wavelet decompositions. However, both the constituent groups and their associated weights in the regularisation term are typically defined a priori. We here introduce an adaptive wavelet denoising framework whereby a sparsity-inducing regulariser is modified based on information extracted from the signal itself. In particular, we use the same wavelet decomposition to detect the location of salient features in the signal, such as jumps or sharp bumps. Given these locations, the weights in the regulariser associated to the groups of coefficients that cover these time locations are modified in order to favour retention of those coefficients. Denoising experiments show that, not only does the adaptive method preserve the salient features better than the non-adaptive constraints, but it also delivers significantly better shrinkage over the signal as a whole.

Type:	Article
Title:	Wavelet shrinkage using adaptive structured sparsity constraints
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1016/j.sigpro.2014.07.001
Publisher version:	http://dx.doi.org/10.1136/jech-2013-20305710.1016/...
Language:	English
Additional information:	This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords:	Structured sparsity, Regularised regression, Denoising, Dual-tree complex wavelet transform
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI:	https://discovery.ucl.ac.uk/id/eprint/1469014