Research On Sparse Representation Algorithm And Its Application In Image Denoising

The update of the dictionary in dictionary learning is an important issue for the sparse representation model.A suitable dictionary can increase the sparsity and thus better achieve image noise removal.The classic dictionary learning method K-SVD requires a column-by-column update dictionary,resulting in high computational complexity and slower denoising.Therefore,combined with the approximate K-SVD algorithm,the sparse representation coefficients and the overcomplete dictionary are updated using the quadratic programming idea and the norm sparse constraint.Improves the denoising speed while maintaining image detail and texture information more effectively.In the low rank matrix recovery theory,the nuclear norm is generally used instead of the norm to achieve the low rank constraint.However,the convex relaxation problem of the kernel norm usually only obtains the suboptimal solution of the original rank minimization problem.Therefore,this paper uses the non-local similarity of the low-rank image and the non-convex substitution function of the norm to approximate the rank minimization and construct the non-convex low rank minimization problem.The fixed point iterative algorithm is used to solve the algorithm,supplemented by a new image aggregation algorithm.The simulation results show that it has better denoising performance than the traditional low rank matrix recovery algorithm.Combining the total variational norm and non-convex function,a new low rank matrix recovery algorithn is proposed.Thereby,it is possible to utilize the low rank property of the natural image,enhance structural smoothness,and eliminate sparse noise and various mixed noises.Using the alternating direction iterative algorithm(ADMM)and the fast gradient projection algorithm,the challenging non-convex optimization problem is solved smoothly.This paper proposes a color image denoising algorithm that combines multi-channel optimization and non-convex low-rank matrix approximation.Considering that the noise variances in the three channels are not the same,three weights(in inverse proportion to the noise variance)are introduced to balance the effects of noise differences.The non-convex function MCP is used to avoid local optimal solutions and over-penalty problems.Finally,the improved model is reconstructed into a linear equality constrained optimization problem and solved by ADMM algorithm.Experiments on simulated color noise and real color noise image datasets show that after denoising by the algorithm,there is less noise residue,clearer detail texture,and no chromatic aberration.The peak signal-to-noise ratio of the image is increased by an average of 0.20 dB and 1.59 dB compared to the existing advanced algorithms.The simulation experiment and real color image denoising experiments show that the improved algorithm in the framework of sparse representation and low rank matrix recovery has good denoising effect for both gray noise image and color noise image.Practical application value.