A Bayesian compressive sensing algorithm for natural images based on sparse filtering in directional lifting wavelet transform domain

A Bayesian compressive sensing algorithm based on sparse-filtering in directional lifting wavelet transform (DLWT) domain for natural images (DLWT-SF-TSW-BCS) is proposed to overcome the problem that the wavelet coefficients of natural images are not sparse. The DLWT is applied to natural images to get wavelet coefficients. Then, sparse-filtering is used to cut off the small DLWT coefficients before random measurement, so that the interference of the small coefficients on the reconstruction of important coefficients is eliminated. Finally, the Bayesian compressive sensing algorithm with wavelet tree structure is employed to reconstruct the image. Experimental results show that the proposed algorithm significantly outperforms various other state-of-the-art CS reconstruction schemes. In particular, the peak signal-to-noise ratio increases 10 dB over the tree structured wavelet compressive sensing (TSW-CS) algorithm.