Research On Image Denoising Method Based On Sparse Representation And Dictionary Learning

Accompany the development of compressive sensing theory, sparse representation theory has become a hot research and has been thoroughly studied,which used in image processing fields constantly, like image de-noising, image deblurring. The essence of signal sparse representation is using sparse coefficient represents the signal, meanwhile maintaining the signal structural characteristics. In general, the traditional image denoising method is based on the assumption that image and noise bands can be separated, but in fact this assumption does cause the damage of the original image. The key of Sparse representation based de-noising method is to find a dictionary to adapt the structure of the image information, using as little atom linear combination as possible to represent the image information; according to the theory that the random noise can’t be represented by atom linear combination, by which could separate the signal and noise.On the basis of sparse representation and dictionary learning, the paper proposes a fast dictionary learning algorithm by combing with convex optimization problem solving and apply it to the image de-noising based on sparse representation which achieved better test results. This paper mainly consists of the following three parts:1. The description and detailed analysis of sparse representation basic theory, sparse decomposition algorithm and denoising model based on the theory.2. Having a deep study on dictionary learning Dictionary learning concerns the accomplishment of sparsest representation, to some extent, determines the quality of the signal restoration and reconstruction. Based on the analysis of dictionary learning theory and its model, introducing several classical dictionary learning algorithms. Under the description and analysis of the classical dictionary learning algorithms, we apply proximal gradient to solve the optimization problem produced by dictionary model to gain the learned dictionary; it is a new dictionary learning algorithm, called FDL_PG (Fast Dictionary Learning algorithm based on Proximal Gradient), which has advantages in the complexity, computation time, global convergence and other aspects of performance.3. Applying the dictionary learning algorithm to image de-noising based on sparse representation. After the brief introduction of image sparse representation, we expound the model of image de-noising based on sparse representation and its progress of solving. We take the image denoising experiment under the model mentioned above with the learned dictionary, which got by the dictionary learning algorithm proposed in this paper. It turns out that the proposed algorithm has a better de-noising performance than the method based on K-SVD, OLM algorithms.