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Iterative Soft/Hard Thresholding with Homotopy Continuation for Sparse Recovery

Jin, B; Jiao, Y; Lu, X; (2017) Iterative Soft/Hard Thresholding with Homotopy Continuation for Sparse Recovery. IEEE Signal Processing Letters , 24 (6) pp. 784-788. 10.1109/LSP.2017.2693406. Green open access

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Abstract

In this note, we analyze an iterative soft/hard thresholding algorithm with homotopy continuation for recovering a sparse signal x† from noisy data of a noise level . Under suitable regularity and sparsity conditions, we design a path, along which the algorithm can find a solution x∗, which admits a sharp reconstruction error x∗ − x†∞ = O() with an iteration complexity O( ln ln γ np), where n and p are problem dimensionality and γ ∈ (0, 1) controls the length of the path. Numerical examples are given to illustrate its performance.

Type: Article
Title: Iterative Soft/Hard Thresholding with Homotopy Continuation for Sparse Recovery
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/LSP.2017.2693406
Publisher version: http://doi.org/10.1109/LSP.2017.2693406
Language: English
Additional information: © 2017 IEEE. This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Continuation, convergence, iterative soft/hard thresholding (IST/IHT), solution path
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1551711
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