Compressed sensing by collaborative reconstruction

Abstract The main idea behind collaborative reconstruction is to determine the atomic combination for an image block not only by the measurement of itself, but also by the collaboration of a group of other blocks sharing similar structures to it. Using collaborative models, the information and constraints for individual image blocks are increased, while the uncertainty and the degree of freedom of the reconstruction problems are decreased. Compressed sensing is a set of signal sampling theory based on signal sparsity. The sparse signal is projected into a low-dimensional space using linear transformation. Random linear projection contains most of the information of the signal. The original signal can be accurately recovered using a nonlinear decoding method (or reconstruction algorithm).