A new type of multilevel system for image sparse recovery

This work focuses on image sparse recovery problem. First, we construct a new kind of pseudo-directional multilevel system, which forms a tight frame in [Formula: see text]. Different from the widely used directional multilevel transforms curvelts and shearlets, whose subbands are neat and nonsensitive to the energy distribution of signals in Fourier domain, the proposed multilevel system is designed to have subbands with specific shape, the shape is oriented by the energy distribution. Thus, we can obtain more sparse structure of signals and low computation for the multilevel transform. Moreover, to detect directional singularities of signals effectively, a local directional gradient operator is introduced to catch the signal variation along different directions, it can be seen as the generalized gradient. Then we proposed a simple but efficient method for image sparse recovery, the split Bregman algorithm is employed to solve the proposed convex model which guarantees the global optimal solution. Some contrast experiments suggest that the sparse recovery by the proposed method performs well in artifacts’ suppressing and details’ extraction.