Nesterov’s algorithm solving dual formulation for compressed sensing

Feishe Chen (current student), Lixin Shen, Bruce W. Suter, Yuesheng Xu

Abstract: 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.

Journal: Journal of Computational and Applied Mathematics 260 (2014), 1–17

DOI: 10.1016/j.cam.2013.09.032