Stagewise ridge pursuit of isolated singularities signals
孤立奇异性信号的分段脊寻踪*

In the area of overcomplete representation, the atom selection strategies of most of the existing greedy pursuit methods, such as matching pursuit and orthogonal matching pursuit, which are aiming at the general signals and dictionaries, have poor sparsity-conserving property and slow convergence for signals and dictionaries which have special structures. For isolated singularities signals and multiscale dictionaries, this paper introduced a new stagewise matching pursuit, called stagewise ridge pursuit(StRP), based on stagewise orthogonal matching pursuit(StOMP) and the theory of modulus maxima of wavelet transform. Since StRP calculated the minimum (e)_2 solutions by pseudoinverse, gave the sufficient and necessary condition of the minimum (e)_2 solutions were the minimum (e)_0 solutions, which showed that the analysis results of StRP were always equal to the minimum (e)_0 solutions as long as the exact positions of the singularity points could be found. Numerical experiments furthermore show that the sparsity-conserving property, supperresolution and convergence of StRP are superior to all of the existing methods when analyzing isolated singularities signals.