Abstract: In this article, we first presented the basic principle and theoretical model of the compressed sensing, and then we elaborated the matching pursuit (MP) and the orthogonal matching pursuit (OMP)，at the last we proposed a new algorithm based on the wavelet transformed by OMP (WOMP). In this algorithm we transform the signal with singlelayer wavclet, after that, we reserved the approximation coefficients and compress the detail coefficients only. OMP is used to recovery the detail one. In the end all the coefficients can be reconstructed by the inverse wavelet transform. Our simulation experiment indicated that, in the same measurements and iterations, WOMP behaved more outstandingly compared with traditional MP and OMP. The recovery rate reached up to 95.2%.

Key words: Compressed sensing,Sparse representation,Recovery algorithm,Wavelet transform