Compressive sensing reconstruction via decomposition

When recovering images from a small number of Compressive Sensing (CS) measurements, a problem arises whereby image features (e.g., smoothness, edges, textures) cannot be preserved well in reconstruction, especially textures at small-scale. Since the missing information still remains in the residual measurement, we propose a novel Decomposition-based CS-recovery framework (DCR) which utilizes residual reconstruction and state-of-the-art filters. The proposed method iteratively refines residual measurement which is closely related to the denoise-boosting techniques. DCR is further incorporated with a weighted total variation and nonlocal structures in the gradient domain as priors to form the proposed Decomposition based Texture preserving Reconstruction (DETER). We subsequently demonstrate robustness of the proposed framework to noise and its superiority over the other state-of-the-art methods, especially at low subrates. Its fast implementation based on the split Bregman technique is also presented.