Research On Sparse Representation And Low-rank Approximation Algorithm And Its Application In Image Denoising

The preprocessing of image data sets is an important step for image denoising.Appropriate similarity image block selection method can improve the similarity accuracy of image blocks.The classic Euclidean distance method for judging similarity only considers the similarity of pixels,which leads to insufficient similarity between preprocessed image blocks,which affects the denoising result.Therefore,combined with the turning to kernel regression method,the pixel similarity and geometric similarity between image blocks are considered when judging the similarity of image blocks,so that the column correlation of the combined matrix obtained after grouping is higher,and the rank of the matrix is also lower.The denoising effect is better.After the denoising operation is completed,an iterative back-projection algorithm is introduced to remove residual noise.The new grouping method is applied to the singular value decomposition theory of low-rank approximation,and good experimental results have been obtained.The traditional low-rank approximation denoising algorithm defaults the noise energy in the singular value decomposition domain to concentrate on a few smaller singular values,so set the last few smaller singular values to zero to get a low-rank noise-free matrix.This method ignores the true distribution of noise energy.Therefore,combining the physical meaning of the singular value and the actual distribution of noise,this paper proposes a method to estimate the singular value of the noise-free matrix for denoising.In the same image data set,add the current noise that is a multiple of the intensity,and observe the influence of high-intensity noise on low-intensity noise,that is,the difference between the singular values of the block matrices formed by each of them,and use this as a reference to estimate the noisy image The effect on the noise-free image,and the denoised image is obtained.After the above denoising operation is completed,an iterative back-projection algorithm is introduced to remove residual noise.Grayscale images include many texture parts,flat parts and edge parts.Traditional dictionary learning trains a dictionary for the entire image,which will cause partial distortion of the image texture.Therefore,this paper proposes a method of adaptively training a dictionary for different regions of the image to perform denoising operations.First,the image is divided into several groups during image preprocessing.For the image block groups of the flat group and the edge group,a dictionary with a suitable atomic size is selected for denoising,and for the image block group of the texture group,a double sparse dictionary training is adopted.The method denoises the texture part of the image,combines a fixed dictionary with a learning dictionary,so that the dictionary meets the denoising requirements of different regions.The experimental results show that the denoising results of the image,especially the texture part,retain more details.The results of simulation experiments prove that the improved denoising algorithm under the framework of sparse representation and low-rank matrix restoration theory has a good denoising effect,and has excellent subjective and objective performance indicators,which is better than the existing classic algorithms.