Smoothed sparse recovery via locally competitive algorithm and forward Euler discretization method.

•An ADMM-based method is devised to solve the general nonsmooth minimization with ℓ1/ℓ0-norm, without requiring direct computation of subdifferential.•We are the first to combine the LCA and ADMM to solve the smoothed ℓ1/ℓ0-norm minimization. A challenge is that the LCA is a continuous-time algorithm, and in this paper, we exploit the forward Euler discretization method to approximate the ℓ1/ℓ0-norm penalty function.•An iterative method has been developed to approximate the matrix inverse for computationally efficient calculation, which is different with the existing ADMM-based algorithms.