Sparsity Fine Tuning in Wavelet Domain With Application to Compressive Image Reconstruction

In compressive sensing, wavelet space is widely used to generate sparse signal (image signal in particular) representations. In this paper, we propose a novel approach of statistical context modeling to increase the level of sparsity of wavelet image representations. It is shown, contrary to a widely held assumption, that high-frequency wavelet coefficients have nonzero mean distributions if conditioned on local image structures. Removing this bias can make wavelet image representations sparser, i.e., having a greater number of zero and closeto-zero coefficients. The resulting unbiased probability models can significantly improve the performance of existing wavelet-based compressive image reconstruction methods in both PSNR and visual quality. An efficient algorithm is presented to solve the compressive image recovery (CIR) problem using the refined models. Experimental results on both simulated compressive sensing (CS) image data and real CS image data show that the new CIR method significantly outperforms existing CIR methods in both PSNR and visual quality.