An Adaptive Hybrid Threshold Denoising Algorithm Based On Singular Value Decomposition

In the process of image acquisition and transmission,image is inevitably contami-nated by noise.In order to improve the visual effect of image and to facilitate subsequent processing of image,we need to perform noise reduction and enhancement processing on noisy image.As a kind of subspace algorithm for dimensionality reduction,singular val-ue decomposition(SVD)-based threshold shrinkage technique has been widely used in image denoising.This method decomposes noisy signal vector space into two subspaces dominated by the real signal and noise signal respectively,and then estimates the real signal by removing the noisy signal components that fall in the "noise space".The singular value threshold shrinkage method based on low rank prior is used to decompose noisy image Y into the form of Y = UT AV,where U and V are orthogonal matrices,and A is the eigenvalue matrix of noisy image matrix Y.And then,a shrinkage processing achieves the purpose of noise reduction by selecting appropriate thresholds for eigenvalues on the diagonal of matrix A.A hard or soft threshold shrinkage method is adopted in general low-rank approximation denoising algorithm;however,they are not the optimal image denoising method.At the same time,in order to enhance image denoising effect,the traditional algorithm uses the observation image and the interme-diate estimation results to construct the backprojection iteration process,and gradually achieves better image denoising results.Although the iterative process of backprojection can improve the denoising effect to some extent,the fixed paramet.er settings make the algorithm itself lack of adaptability,resulting in some weaknesses such as more iterations,longer running time and denoising effect to be improved.In order to improve the general low-rank approximation denoising,in this thesis innovates from two aspects are conducted to improve the effectiveness of denoising algo-rithm.(1)Denoising method by the hybrid threshold shrinkage of singular values.After constructing low-rank matrices using image self-similarity,low-rank image denoising is performed by singular value threshold shrinkage.In order to restore important feature structures of images,the threshold shrinkage is achieved using a combination of soft and hard thresholds,which changes the traditional idea of using a single threshold.On the one hand,the hard threshold selection method is based on hard threshold approximation using non-local self-similarity and low rank approximation.On the other hand,the soft threshold selection method is based on the random matrix and asymptotic matrix reconstruction theory.(2)Backprojection iteration method based on image phase consistency and gradi-ent calculation.In the process of iterative back projection reconstruction,image phase consistency,gradient calculation and projection enhancement techniques ar used to con-struct an adaptive function that adapts to image features,resulting in adaptive input images which participate in the iterative process.This method changes the traditional fixed-factor backprojection method,reduces the number of iterative operations to some extent and achieves much more better image denoising effect.A large number of natural images are denoised and enhanced by using the adaptive hybrid threshold denoising algorithm based on singular value decomposition.The experi-mental results show that the proposed algorithm has a certain improvement in subjective visual effects and objective quantitative indicators compared with some related advanced denoising algorithms.The research of this dissertation further strengthens the collaborative innovation between computational mathematics and information science,deepens and enriches the research of image denoising technology and is expected to be further extended to medical image processing and other application fields.