Compressive sensing image recovery using dictionary learning and shape-adaptive DCT thresholding

Compressed sensing (CS) has shown to be a successful technique for image recovery. Designing an effective regularization term reflecting the image sparse prior information plays a critical role in this field. Dictionary learning (DL) strategy alleviates the drawback of fixed bases. But the structure information of the image is easy to be blurred in complex regions due to the absence of sparsity in dictionary learning. This paper proposes a novel joint dictionary learning and Shape-Adaptive DCT (SADCT) thresholding method. We first propose to exploit sparsity of image in shape-adaptive regions, which is beneficial to medical images of complex textures. In this framework, the local sparsity depicts the smoothness redundancies exploited by dictionary learning. Moreover, the sparsity is enhanced especially in detail areas by the newly introduced SADCT thresholding. The attenuated SADCT coefficients are used to reconstruct a local estimation of the signal within the adaptive-shape support. Image is represented sparser in SADCT transform domain and the details of the image information can be kept with a much larger probability. Based on split Bregman iterations, an efficient alternating minimization algorithm is developed to solve the proposed CS medical image recovery problem. The results of various experiments on MR images consistently demonstrate that the proposed algorithm efficiently recovers MR images and shows advantages over the current leading CS reconstruction approaches.