Image Denoising Via Sparse And Redundant Representations Over K-SVD Algorithm And Residual Ratio Iteration Termination

Multimedia technology is an important part of information technology. In recentyears, the rapid development of multimedia technology has become an significant wayfor people’s acceptance of complex information. Digital image processing, with greatscientific and social value, has changed the way of people’s lives deeply.Image denoising is the basic aspect of image processing, and it makes directimpact on the success of other subsequent aspects. Therefore image denoising is one ofthe central issues in image processing. In recent years, the theory of sparsedecomposition via over complete atom dictionaries has become a new way of signal’srepresentation. The theory has attracted lots of scholars’ attention and developedrapidly. The theory has been used for image denoising and performed not bad. In thispaper, the traditional image denoising algorithms, especially for the ones based ontransform domains are reviewed briefly. Then introduced image denoising algorithmsvia sparse decomposition on over complete atom dictionaries in detail. The maincontents are as follows:①Briefly introduced the image noise’s impacts, noise model and the imagequality criteria. The relative researches on image denoising algorithms and sparsedecomposition on over complete atom dictionaries are summarized.②Several common image transforms in frequency domain are reviewed.Elaborated the theoretical system of signal decomposition via over completedictionaries. Discussed the decomposition, reconstruction and complexity oforthogonal matching pursuit (Orthogonal Matching Pursuit is OMP) algorithm. Thenintroduced the K-SVD(Singular Value Decomposition) algorithm, described how itworks and it’s significance in practical use.③One of the core issue in image denoising is how to distinguish the image’seffective information and the image noise. In this paper, two algorithms based ontraditional threshold as the end condition of decomposition are introduced and theweakness of them are pointed out. Meanwhile, algorithms based on coherent ratio andresidual ratio as the iteration termination are introduced, and their superiorities arediscussed as well. Especially for the low SNR image denoising problem, details of theimage noise’s influences are analyzed. ④For the low SNR(Signal to Noise Ratio) images denoising, a new algorithm isproposed based on K-SVD and residual ratio iteration termination. Firstly, an initialredundant dictionary is produced under the DCT framework and the dictionary is trainedby K-SVD algorithm through the noisy image. A new dictionary that reflects thestructure of the image effectively is produced. Then, the residual ratio is used as theiteration termination of OMP algorithm to remove the zero-mean white andhomogeneous Gaussian additive noise from a given image. Different kinds of imageswith different noise levels are used to test the algorithm. The results show that thealgorithm has strong robustness and performs better than the image denoising algorithmusing Symlets wavelet, Contourlet and sparse representation based on DCT redundantdictionary.⑤An overall review of the paper is made and the forecast of studies in the futureis proposed as well.