Image Denoising Using Adaptive Algorithm Based On Sparse Representation

With the development of the sparse representation theory in image processing field, the sparse denoising method becomes a hot issue of the current researches. It gives full consideration to the characteristics of image internal structures. The atoms in the dictionary are the prototypes of image internal structures. And the noise in the image obeys random distribution without structural characteristics. Therefore, there exists a set of linear combinations of the atoms in the appropriate over-complete dictionary, which can efficiently represent images, so as to achieve the purpose of removing noise.What decides the success of the sparse denoising algorithm performance is dictionary selecting and sparse coding. Therefore, in this paper we consider an algorithm combining the dictionary learning methods of K-Singular Value Decomposition(K-SVD) and Sparse K-SVD(SK-SVD). Our algorithm can learn adaptive sparse over-complete dictionary by alternative optimization ideas in the sparsity-based Bayesian reconstruction framework. As the dictionary structure itself has sparsity, it can effectively separate the useful information and noise data in the images, and improve the robustness of the algorithm; In the sparse coding stage, this paper apply the full least squares-orthogonal matching pursuit algorithm (Least Square-OMP, LS-OMP) to decompose images under the sparse dictionary. The LS-OMP algorithm whose reconstruction error is smaller than that of the orthogonal matching pursuit algorithm (Orthogonal Matching Pursuit, OMP) can adaptively select atoms with the most similar structure with the image. At the same time, it conducts image denoising processing using the adaptive threshold which is based on the statistical characteristics of the noise. Thus, the proposed algorithm can be well approximated to the original image. Considering the complex calculation of pseudo-inverse in the algorithm, In this paper, we can reduce the reconstruction error while shortening the running time of the algorithm by Cholesky decomposition of matrix to simplify computing.The experimental results show that when compared with the traditional fixed dictionary/OMP, K-SVD/OMP and SK-SVD/OMP learning dictionary, the proposed algorithm captures detailed information of images, gains higher peak signal to noise ration (PSNR) and shows better adaptability.