A learning-based method for compressive image recovery

Compressive sensing (CS) theory dictates that a sparse signal can be reconstructed from a few random measurements. An important issue of compressive image recovery (CIR) is that the optimal sparse space is usually unknown and/or it often varies spatially for non-stationary signals (e.g., natural images). In this paper, apart from fixed sparse spaces, prior models, specifically a set of piecewise autoregressive (AR) models that encode the common statistics of image micro-structures, are learned from example image patches, and they are then used to construct adaptive sparsity regularizers for CIR. Furthermore, a complementary non-local structural sparsity regularizer is also incorporated into the CIR process to improve the robustness. The regularization by local AR model and non-local redundancy makes the proposed CIR very effective. Experimental results on benchmark images validate that the proposed algorithm can outperform significantly previous CIR methods in terms of both PSNR and visual quality.