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 work, 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 non-zero 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 close-to-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.