Adaptive dictionary learning in sparse gradient domain for CT reconstruction

Image recovery from undersampled data has always been a challenging and fascinating task due to its implicit ill-posed nature and significance accompanied with the emerging compressed sensing (CS) theory. This paper proposes a novel Gradient based Dictionary Learning method for CT image Reconstruction (GradDL-CT), which alleviates the drawback of the popular total variation (TV) regularization by employing dictionary learning technique. Specifically, we firstly train dictionaries from the horizontal and vertical gradients of the image respectively, and then reconstruct the desired image using the sparse representations of both derivatives, exploiting gradient magnitude image sparsity for reduction in the number of projections or the X-ray dose. Preliminary results on phantom and real CT images demonstrate that the proposed method can efficiently recover images and presents advantages over the current state-of-the-art reconstruction approaches.