A reconstruction algorithm with Bayesian compressive sensing for synthetic aperture radar images

A reconstruction algorithm with Bayesian compressive sensing for synthetic aperture radar (SAR) images (DLWT-TDC) is proposed to solve the problem that the dependencies of wavelet coefficients are not fully exploited by existing compressive sensing (CS) reconstruction algorithms. The new algorithm exploits both the interscale attenuation and the intrascale directional clustering property of the directional lifting wavelet transform (DLWT) coefficients. The DLWT is used for SAR image's sparse representation, and then, 3×5, 5×3 and 5×5 neighboring blocks are used to design prior probability models with local adaptivity in both the direction and space. Then the Bayesian inference via Markov chain Monte Carlo sampling is used to recover the image's wavelet coefficients and the reconstructed image is generated in turn. Experimental results show that the DLWT-TDC achieves high reconstruction performance when the sampling percentage is in the range from 50% to 90%. Comparisons with the Bayesian tree-structured wavelet compressive sensing algorithm, which only uses the interscale dependencies, show that the proposed algorithm improves the peak-signal-to-noise-ratio by about 3 dB when the sampling percentage is 90%.