Nesterov's algorithm solving dual formulation for compressed sensing

• Autores: Feishe Chen, Lixin Shen, Bruce W. Suter, Yuesheng Xu
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 260, Nº 1, 2014, págs. 1-17
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.09.032
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• Resumen

  • We develop efficient algorithms for solving the compressed sensing problem. We modify the standard l1 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.