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

Highlights • An ADMM-based method is devised to solve the general nonsmooth minimization with ℓ 1 /ℓ 0 -norm, without requiring direct computation of subdifferential. • We are the first to combine the LCA and ADMM to solve the smoothed ℓ 1 /ℓ 0 -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 ℓ 1 /ℓ 0 -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. Abstract This paper considers the problem of sparse recovery whose optimization cost function is a linear combination of a nonsmooth sparsity-inducing term and an ℓ 2 -norm as the metric for the residual error. Since the resultant sparse approximation involves nondifferentiable functions, locally competitive algorithm and forward Euler discretization method are exploited to approximate the nonsmooth objective function, yielding a smooth optimization problem. Alternating direction method of multipliers is then applied as the solver, and Nesterov acceleration trick is integrated for speeding up the computation process. Numerical simulations demonstrate the superiority of the proposed method over several popular sparse recovery schemes in terms of computational complexity and support recovery. [ABSTRACT FROM AUTHOR]