Signal Separation Using Re-weighted and Adaptive Morphological Component Analysis

Morphological component analysis (MCA) for signal separation decomposes a signal into a superposition of morphological subcomponents, each of which is approximately sparse in a certain dictionary. Some of the dictionaries can also be modified to make them adaptive to local structure in images. We show that signal separation performance can be improved over the previous MCA approaches by replacing L1 norm optimization with “weighted” L1 norm optimization and replacing their dictionary adaptation with regularized dictionary adaptation. The weight on an atom for sparse coding is commonly derived from the corresponding coefficient’s value. In contrast, the weight of an atom in a dictionary for signal separation is derived from the mutual coherence between the atom and the atoms in the other dictionaries. The proposed solution for regularized dictionary adaptation is an extension of the K-SVD method, where the dictionary and “weighted” sparse coefficients are estimated simultaneously. We present a series of experiments demonstrating the significant performance improvement of the proposed algorithm over the previous approaches for signal separation.