Image Restoration based on Double Sparse Model and ADMM Optimization

Image restoration algorithms based on sparse representation generally use the whole sparsity or the local sparsity of the image, while not make full use of prior knowledge of the image. Based on this, in the framework of sparse representation, this article proposed a new image restoration algorithm introducing both the Cosparse analysis model leading to a sparse representation of each image patch and translation invariant wavelet transform leading to a sparse representation over the whole image. In the algorithm, the problem of image restoration is expressed as the double sparse regularization problem. To solve the complex double sparse optimization problem, the alternating direction method of multipliers is introduced to decompose the issue into equivalent sub-problems. By alternatively and iteratively solving the sub-problems, the restored image is obtained. In the experiments, the images blurred by different type of blur are restored. The experimental results show that, the proposed algorithm outperforms the existing restoration algorithms. Thus, the effectiveness of the proposed algorithm is verified.