New image restoration method associated with tetrolets shrinkage and weighted anisotropic total variation

Image restoration is one of the most classical problems in image processing. The main issues of image restoration are deblurring, denoising and preserving fine details. In order to obtain good restored images, we propose a new image restoration method based on a compound regularization model associated with the weighted anisotropic total variation (WATV) and the tetrolets-based sparsity. The WATV recovers sharp edges by embedding two directional gradient operators into the original anisotropic total variation (ATV), and the tetrolet transform adapts its basis to the local image structures. Thus, our model can preserve details such as textures and edges in the processing of image restoration by combining the WATV with the tetrolets-based sparsity. We present an alternate iterative scheme which consists of the variable splitting method and the operator splitting method to solve the proposed minimization problem. Experimental results demonstrate the efficiency of our image restoration method for preserving the structure details and the sharp edges of image.