Block Compressed Sensing of Natural Images

Compressed sensing (CS) is a new technique for simultaneous data sampling and compression. In this paper, we propose and study block compressed sensing for natural images, where image acquisition is conducted in a block-by-block manner through the same operator. While simpler and more efficient than other CS techniques, the proposed scheme can sufficiently capture the complicated geometric structures of natural images. Our image reconstruction algorithm involves both linear and nonlinear operations such as Wiener filtering, projection onto the convex set and hard thresholding in the transform domain. Several numerical experiments demonstrate that the proposed block CS compares favorably with existing schemes at a much lower implementation cost.