A Sparsity-Based Design of Regularization Parameter for Adaptive Proximal Forward-Backward Splitting Algorithm

In this paper, a novel regularization-parameter design for the adaptive proximal forward-backward splitting algorithm is proposed for sparse system identification. The regularization parameter is controlled adaptively based on sparsity of an estimated unknown system. The regularizer is designed by approximating an !p quasi-norm (0 < p < 1) linearly. Numerical examples show that the proposed algorithm is robust to the variation of the system sparsity.