Fast Source Reconstruction via ADMM with Elastic Net Regularization

Norm-1 regularized optimization algorithms are commonly used for Compressive Sensing applications. In this paper, an optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) together with the Elastic Net regularization is presented. This type of regularization is a linear combination of the norm-1 and norm-2 regularizations, allowing a solution between the sparsest and the minimum energy solutions, but still enforcing some sparsivity. The combination of these two regularizations and the distributive capabilities of the ADMM algorithm enables a fast sparse signal recovering with minimum error.