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Total Variation minimization for Compressed Sensing with "smoothly'' varying covariates.

Chretien, S; Harris, P M; Tawil, R* (2016) Total Variation minimization for Compressed Sensing with "smoothly'' varying covariates. In: 19th IEEE International Conference on Computational Science and Engineering (CSE), IEEE 14th International Conference on Embedded and Ubiquitous Computing (EUC) and 15th International Symposium on Distributed Computing and Applications for Business Engine, 24-26 August 2016, Paris, France.

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Abstract

The LASSO is a variable subset selection procedure in statistical linear regression based on sparsity promoting l1 penalization of the least-squares operator. In many applications, the design matrix has strongly correlated columns which are smoothly evolving with the column index. For such applications, the standard LASSO does not provide satisfactory solutions in practice because some incoherence is often needed for support recovery of sparse vectors. In this paper, we circumvent this problem by using a Total Variation penalty and obtain adaptive confidence intervals for the nonzero components of the signal. The relaxation parameter is calibrated by a new multiscale data acquisition scheme. This approach is illustrated by some simulations results for a source localization problem in a marine environment.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Subjects: Mathematics and Scientific Computing
Mathematics and Scientific Computing > Signal Processing
Identification number/DOI: 10.1109/CSE-EUC-DCABES.2016.233
Last Modified: 02 Feb 2018 13:13
URI: http://eprintspublications.npl.co.uk/id/eprint/7668

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