Image restoration approach using a joint sparse representation in 3D-transform domain

Image restoration is a crucial problem in image processing and a necessary step before the image segmentation and recognition. A new framework for image restoration in 3D transform domain terms as joint sparse representation (JSR) is proposed in this work. The proposed JSR is able to represent image more sparsely and more precisely in the transform domain by performing 3D transform on each set of similar blocks. In addition to that, in order to overcome the issues of defective block matching and spurious artifact in the 3D sparse representation, JSR introduces a new nonlocal regularization term which characterizes the statistics of the nonlocal image to improve the accuracy of the estimated coefficients. The parameters of regularization terms are calculated based on Bayesian philosophy, and a split Bregman-based technique is developed to obtain the solution in a tractable and robust manner. Extensive experiments on image denoising, image inpainting and image deblurring demonstrate that the proposed JSR algorithm outperforms current state-of-the-art approaches in terms of peak signal-to-noise ratio and visual quality.