Laplacian Graph Regularized Dictionary Learning Image Denoising Algorithm Research

Image restoration is a problem in the image processing field all the time. Image denoising is one of main researches in the image restoration. In recent years, a variety of image denoising algorithms have been proposed. Wavelets and curvelets can achieve a good image denoising performance. These regular bases can be easily constructed, but the representation form of the signal is too unitary and not self-adaptive. To improve the self-adaptivity, Olshausen proposed the initial idea to learn the dictionary for the different images. Mallet proposed the sparse representation theory, in which two alternative update processes sparse coding and dictionary learning make more self-adaptive dictionary and sparse coefficient for the denoised image.Wavelet threshold filtering based on regular bases can remove the noise, which can not adapt to all images. Because the regular bases are not self-adaptive. In this paper, denoising model based on dictionary learning can learn more self-adaptive dictionary, which can achieve a good denoising performance for different images. Image denoising is an under-determined problem, defining appropriate image priors to regularize the problem plays an important role. Recently a popular one among proposed image priors is the graph Laplacian regularizer, where a given pixel patch is assumed to be smooth in the space domain. In this paper, graph Laplacian is introduced into the regularizer term to establish a model that can improve the denoising quality. The main work is as follow:First we carry out the wavelet threshold filtering experiment based on regular bases and analyse the merits and drawbacks. Then we study the convex optimization model based on sparse representation and the Douglas algorithm in details. Moreover, we apply Douglas algorithm when dictionary learning and sparse coding. The experimental results show that the image restoration quality can get improved remarkably.A new model is proposed for restoring the original image by introducing the graph Laplacian into the regularizer term and combining with the general sparse representation denoising model, which consists of the data fidelity term, the graph Laplacian regularizer term and the sparse representation term. First we conduct the bilateral filtering and divide the filtered image into blocks for clustering. Then the graph Laplacian matrix of the cluster is calculated and substituted into the model Lagrange form. Finally, we conduct the dictionary learning for denoising. Specifically, the eigenvectors of the normalized graph Laplacian matrix are choosed as the initial dictionary to perform the denoising task. The experimental results show that the proposed model achieves a good denoising performance objectively and subjectively.