Abstract: Combining Bayesian learning and compressive sensing,an image compression and reconstruction method based on wavelet transform was proposed in this article．Utilizing the specific structure and correlation of wavelet transforming coefficients,this method improves the image compression rate and reconstruction accuracy effectively.At same time,a regression model based on prediction is adopted in coefficient reconstruction．Gaussian mixture parameters are used to predefine the prior conditional density of the unknown parameters in order to enforce the sparsity．This method can get a group of model with high probability of the coefficients,and result in reconstruction of the image in sense of MMSE．Compared with other image compression methods and CS based image reconstruction methods,the proposed method can get reconstruction images with high quality and get bigger compression rate.

Key words: Compressive sensing,Wavelet,Image compression,Bayesian