FU Ting, YAO De-zhong. Iterative Weighted Method of Sparse Decomposition and Preliminary Application[J]. Acta Electronica Sinica, 2004, 32(4): 567-570.
FU Ting, YAO De-zhong. Iterative Weighted Method of Sparse Decomposition and Preliminary Application[J]. Acta Electronica Sinica, 2004, 32(4): 567-570.DOI：
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
l
-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.
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