Fractal pursuit for compressive sensing signal recovery

Abstract

Basis pursuit (BP) and matching pursuit (MP) are two important basic recovery methods in compressive sensing (CS) research. BP can compute the global optimal solution in CS recovery problem, but its computational complexity is high and dimensional universality (regardless of 1D or 2D or higher dimensions) is not good. On the other side, the computational cost of MP is lower than BP, but the sparsity of signal needs to be known beforehand and its solution may not necessarily be global optimal. In this paper, a new CS recovery method is proposed, termed fractal pursuit (FP) which integrates the advantage of BP and MP. It acquires the prior knowledge of signal by fractal recognition to cut down the computational cost of pursuit operation, and uses fractal minimization in place of l1-norm minimization for improving the recovery quality and dimensional universality in CS framework. Two experiments show the feasibility and performance of FP in CS recovery.