Iterative Weighted Method of Sparse Decomposition and Preliminary Application
Dezhong Yao · Dianzi xuebao · 2004
A weighted algorithm of sparse decomposition is developed for recovery of signal in strong background noise. To find the real components in a complete dictionary, the cost function can be constructed by a weighted sum of the / - 2 norm of residual errors and l-1 norm of sparse components. Taking complete dictionary as the multiresolution wavelets, a feasible penalty formula is deduced according to two-scale relation of additive noise in wavelets dictionary. Analyzing the resolving process of minimum l -1 problem, proposed is the difference of l - 1 norm of signal components as converge condition, where the difference is derived from the results of successive two iterative steps.The method is confirmed by both simulated and real data.