Nesterov’s algorithm solving dual formulation for compressed sensing

We develop efficient algorithms for solving the compressed sensing problem. We modify the standard ℓ1ℓ1 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.