The application of sparse component decomposition in the over-complete dictionary to signal representation

Sparse component analysis (SCA) is a new and promising method for signal processing. With SCA, a sparse and compact expression of signal can be achieved. In this paper, Matching Pursuit (MP), one of the popularly used SCA methods, was adopted to decompose the signals in the wavelet over-complete dictionary for a sparse expression and high-ratio compression. By comparison of the decomposition and reconstruction results between wavelet used in the JPEG2000 compression and MP, we see that the pulse signal which is not sparse in the wavelet dictionary may have a more sparse expression in the over-complete dictionary, and when signal is recovered with the same number of atoms or coefficients, the construction result with MP decomposition is superior to that with wavelet decomposition.