Accelerated Split Bregman Method for Image Compressive Sensing Recovery under Sparse Representation

Compared with traditional patch-based sparse representation, recent studies have concluded that group-based sparse representation (GSR) can simultaneously enforce the intrinsic local sparsity and nonlocal self-similarity of images within a unified framework. This article investigates an accelerated split Bregman method (SBM) that is based on GSR which exploits image compressive sensing (CS). The computational efficiency of accelerated SBM for the measurement matrix of a partial Fourier matrix can be further improved by the introduction of a fast Fourier transform (FFT) to derive the enhanced algorithm. In addition, we provide convergence analysis for the proposed method. Experimental results demonstrate that accelerated SBM is potentially faster than some existing image CS reconstruction methods.