Diffusion fused sparse LMS algorithm over networks

Abstract

The problem of distributed estimation for sparse parameter has attracted much attention in recent years due to its wide applications. In some cases, the sparsity feature may also be found in the differences of successive components of the true parameter, i.e. the non-zero components may be assembled in one or more regions of the true parameter. In this paper, we propose the fused sparse diffusion LMS algorithm for recovering such parameter. The proposed algorithm relies on a sparse regularization term to enforce sparsity of components themselves, and fused sparse regularization term to enforce similarity of adjacent non-zero components. We then provide the condition of the proposed algorithm converging in the mean sense and study mean-square behaviors, which include mean square deviation (MSD) and individual weight error variance (IWEV). To further enhance estimation performance of the fused sparse diffusion algorithm, we provide an adaptive strategy in which the optimal regularization factors can be adjusted at each iteration. Finally, numerical simulations are conducted to show the superiority of our proposed algorithm over several other algorithms.