Compressive sampling (CS) is a new technique for simultaneous sampling and compression of signals in which the sampling rate can be very small under certain conditions. Due to the limited number of samples, image reconstruction based on CS samples is a challenging task. Most of the existing CS image reconstruction methods have a high computational complexity as they are applied on the entire image. To reduce this complexity, block-based CS (BCS) image reconstruction algorithms have been developed in which the image sampling and reconstruction processes are applied on a block by block basis. In almost all the existing BCS methods, a fixed transform is used to achieve a sparse representation of the image. however such fixed transforms usually do not achieve very sparse representations, thereby degrading the reconstruction quality. To remedy this problem, we propose an adaptive block-based transform, which exploits the correlation and similarity of neighboring blocks to achieve sparser transform coefficients. We also propose an adaptive soft-thresholding operator to process the transform coefficients to reduce any potential noise and perturbations that may be produced during the reconstruction process, and also impose sparsity. Experimental results indicate that the proposed method outperforms several prominent existing methods using four different popular image quality assessment metrics.
