Reprint of “Nesterov’s algorithm solving dual formulation for compressed sensing”,☆☆

Dedicated to Professor Benyu Guo on the occasion of his seventieth birthday with friendship and esteem
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Abstract

We develop efficient algorithms for solving the compressed sensing problem. We modify the standard 1 regularization model for compressed sensing by adding a quadratic term to its objective function so that the objective function of the dual formulation of the modified model is Lipschitz continuous. In this way, we can apply the well-known Nesterov algorithm to solve the dual formulation and the resulting algorithms have a quadratic convergence. Numerical results presented in this paper show that the proposed algorithms outperform significantly the state-of-the-art algorithm NESTA in accuracy.

Keywords

Nesterov’s algorithm
Proximity operator
Moreau envelope
1 regularization
Compressed sensing

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A publishers’ error resulted in this article appearing in the wrong issue. The article is reprinted here for the reader’s convenience and for the continuity of the special issue. For citation purposes, please use the original publication details; Journal of Computational and Applied Mathematics 260, pp. 1–17.

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This research is supported in part by 2012 Air Force Visiting Faculty Research Program, by the US National Science Foundation under grant DMS-1115523, by US Air Force Office of Scientific Research under grant FA9550-09-1-0511.