Research On Image Denoising Algorithm Based On Image Self-similarity And Singular Value Decomposition

In the process of image generation and network transmission,images are always contaminated by noise due to various conditions and external interference.Noise causes some image information to be masked.Even in severe cases,images will be distorted and lost their original meanings.By using greater hardware equipment to improve image quality,it will cost a lot of money.However,in practice,it is difficult to significantly reduce external interference to improve image quality.Therefore,image denoising technology was born.The technology is an image pre-processing technology that devoted to removing the noise part from the known images containing noise to restore the true information of images.Using image denoising technology to process an image can not only restore the original information carried by the image,but also provide important basic guarantees for subsequent image processing processes,such as image segmentation and feature recognition.The self-similarity of images,which depicts the similarity of the structure or pixel of the image in local or non-local,is an image prior that has attracted much attention in the research of image denoising algorithms in the past decade.The property means that similar patch matrices can be constructed from similar image patches in the image,which are low-rank to some extent For low-rank matrices,the method of singular value decomposition(SVD)can provide optimal energy compression in the least squares sense.Unlike other SVD-based denoising methods,the low-rank approximation method in the SVD domain avoids the huge computational cost caused by learning the local basis used to represent image patches.For low-rank approximation denoising methods based on SVD,the ability to accurately construct similar patch matrices with noise and handle singular values are keys.The thesis focuses on the self-similarity and singular value decomposition to study the denoising algorithm,and uses the SVD optimal energy compression characteristic to derive a low-rank approximation matrix of the similar patch matrix.Then,an image denoising algorithm based on adaptive clustering and singular value decomposition is proposed.The algorithm combines the prior information of images and adopts a two-stage clustering method to adaptively construct low-rank similar patch matrices.The similar patch matrices constructed by our clustering method is anti-noise.That is to say,the low-rank matrices constructed by our clustering method is more accurate than the low-rank matrices constructed by other methods.In addition,the advantage of accuracy will become more obvious as the noise level increases.Then,the algorithm uses singular value decomposition to perform low-rank estimation on similar patch matrices.And according to the geometric meanings of singular values and singular vectors,we correct the singular vectors of the estimation matrices derived from low-rank estimation,so that the residual noise in the low-rank estimations is further suppressed.For back projection,we use the original noise level and the residual image to adaptively determine projection parameters and new noise levels.So,our back projection can provide a good foundation for our denoising algorithm,and it makes our algorithm remove noise better and preserve more image details.The adaptive clustering method with noise immunity proposed in this thesis can adaptively and accurately classify image patches and construct low-rank similar patch matrices,which provides a new idea for image patch classification based on similarity.Meanwhile,the correction of singular vectors proposed in this thesis also provides a new direction for the study of image denoising algorithms based on singular value decomposition.Experimental results show that compared with the existing state-of-the-art denoising algorithms,the proposed algorithm achieves competitive denoising performances in terms of quantitative metrics and preserving details.Especially,with the increase of noise,the competitiveness of our algorithm is gradually enhanced.