The restoration of compressed images typically focuses on the removing of spatial artifacts caused by quantization error rather than the recovery of spectral information in compressed images. In this paper, we attempt to solve the compressed image restoration by considering the recovery of spectral information in compressed images. To this end, we convert this recovery problem to a route searching process in the high dimensional vector space spanned by all DCT coefficients. Since there are huge number of routes in the search space, we present two crucial issues in route construction: how to decide the nodes along the searching route and how to restrict the route within a reasonable sub-space. Total variation (TV) based regularization is applied to determine all the nodes in the searching process, and two constraints on the DCT coefficients are proposed to prune the searching space. Experimental results of our algorithm show a remarkable improvement in both PSNR and visual quality.