Mixed $${L}_{1}$$ L 1 norm and $${L}_{2}$$ L 2 norm regularized sparsity adaptive matching pursuit algorithm

Abstract

The sparsity adaptive matching pursuit (SAMP) algorithm has an advantage of reconstructing signals without the prior information of the sparsity level. However, the required computational power is high and the reconstruction performance is not satisfied for perturbed systems. This is because this algorithm is based on the expectation maximization algorithm. Also, a pseudo-inverse operation of the matrix is employed to select the element candidates of the sensing matrix in each iteration. In this paper, a mixed $$L_{1}$$ norm and $$L_{2}$$ norm regularized algorithm is proposed to address these issues. Similar to the SAMP algorithm, the regularized algorithm also reconstructs the signals without the prior information of the sparsity level. Different from the SAMP algorithm, the element candidates of the sensing matrix are selected by the $$L_{2}$$ norm strategy in each iteration. Experiments are performed on an ideal simulation system, a perturbed simulation system and real image reconstruction. Simulation and real image reconstruction experimental results indicate that the regularized algorithm has lower computational power than the SAMP algorithm. Also, the proposed algorithm has better reconstruction performance on the perturbed system compared to the SAMP algorithm.