Data compression based on compressed sensing and wavelet transform

The recovery can be achieved from the undersampling signal in compressed sensing theory relying on the sparsity and incoherent characteristics of the signal. A data compression algorithm is advanced in this article, based on compressed sensing and wavelet transform. Firstly the framework of the compressed sensing theory is introduced, and then a one-dimension and a two-dimension wavelet transform matrixes are constructed respectively, which leads two compressed algorithms based on modulus and original data separately. At last, the compression characteristics are simulated and compared using one-dimension signal and two-dimension images separately, at the same time, the validity is proved by those results.