Distributed estimation for sparse parameter based on fused-lasso technique

Abstract

Estimation for sparse parameter in adaptive networks has become a hot topic recently in the field of adaptive filtering. In some cases, the sparsity feature may also be found in the differences of successive entries of the true parameter, i.e. the non-zero elements 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 sparse regularization term to enforce sparsity of entries themselves, and fused sparse regularization term to enforce similarity of adjacent non-zero entries. We then provide the conditions for the convergence of the proposed algorithm in the mean sense. Numerical simulations are conducted to show the superiority of our proposed algorithm over several other algorithms.