Compressed sensing image reconstruction in multiple sparse spaces

Most traditional compressed sensing(CS) reconstruction algorithms only exploit the sparsity of a natural signal in a single sparse space. However, since natural signals often exhibit spatially varying characteristics, the single space sparse representation fails to well characterize the local signal structures. The mismatch between sparse representation in the single space and the varying local structures make the reconstruction algorithms fail to exploit the local sparsity, leading to low reconstruction quality. In this paper, we propose a new image signal reconstruction method based on multiple sparse spaces(MSS) to overcome this defect of the CS reconstruction algorithms in the single space, where a signal is adaptively characterized by the total variation(TV) model or the piecewise autoregressive(PAR) model according to its local structures. The objective function of the proposed MSS-based CS reconstruction is then formulated as a multiple l₁-norm and l₂-norm minimization problem. To efficiently solve the proposed objective function, an alternating direction method(ADM) is used. Experimental results show that compared with the single space methods the proposed MSS-based reconstruction method achieves a much better visual quality and a higher PSNR. The PSNR improvements over TV and AR based methods can be up to 7dB and 1dB, respectively.