Research On Image Denoising Based On Maximum A Posteriori Criterion

Image denoising is a classical and well-studied problem in image processing,and is known to be closely related to sparse coding.Essentially,image denoising is a problem of maximum a posteriori(MAP)estimation.According to the noisy observed image and the original image priors,the most probable potential real image is estimated.In this work,based on sparse coding and maximum a posteriori criterion,two competitive image denoising algorithms and one generalized image restoration algorithm are proposed.The novelty of this work is as follows.(1)Use Gaussian scale mixture to model sparse coefficients.Based on the key observation that the probability density function of image patch is relevant to the maximum a posteriori estimation of sparse coefficients,we get an efficient approximation of the probability density of image patch using the density of a linear transform,and introduce it into the MAP estimation of sparse coefficients.Then a nonlocal image denoising method: Improved Simultaneous Sparse Coding with Gaussian Scale Mixture(ISSC-GSM)is proposed.The preprocessing of centering for a collection of similar patches saves expensive computation and admits biased-mean of sparse coefficients.Our formulation can be transformed into two subproblems and efficiently computed by alternating minimization,and both subproblems have analytical solutions using the orthogonal PCA dictionary.When applied to noise removal,the proposed ISSC-GSM has achieved highly competitive denoising performance with often higher subjective and objective qualities than other competing approaches.(2)Noticing that the Laplacian distribution has a strong sparseness,we use Laplacian scale mixture to model sparse coefficients.With an appropriate estimate of the prior probability density function of an image,we introduce prior information of the image into MAP estimation of sparse coefficients.Extending to structured sparsity,a nonlocal image denoising method: Improved Simultaneous Sparse Coding with Laplacian Scale Mixture(ISSC-LSM)is proposed.The centering preprocessing reduces computational complexity.By alternating minimization and learning an orthogonal PCA dictionary,an efficient algorithm with closed-form solutions is proposed.Structured sparsity is capable of capturing structured image features such as abundant self-repeating patterns including textures and strong edges,and the adoption of image prior information produces a further gain.Our proposed ISSC-LSM often delivers denoised images with the best visual quality,and is most suitable for processing images with abundant self-repeating patterns by effectively suppressing undesirable artifacts while maintaining the textures and edges.(3)The idea of the proposed denoising algorithms above is generalized to the general image restoration problem.The alternating direction method of multipliers(ADMM)is widely applied to solve constrained optimization problems in image restoration.Its modular plug-and-play structure allows the proposed denoising algorithm as a plugin to solve the subproblem in ADMM algorithm.To avoid the shortcoming that original ADMM is sensitive to the initial value of the parameter,a parameter-adaptive idea is considered.Besides,the MAP-based improved simultaneous sparse coding denoising algorithm is introduced as a “plug and play” denoising operator.Then we propose an image restoration algorithm called parameter-adaptive ADMM based Improved Simultaneous Sparse Coding(ADMM-ISSC).Thus,the idea of using image prior information and structured sparsity is extended to more general image restoration problems.Experimental results of image restoration show that the proposed ADMM-ISSC algorithm is robust to initial parameters with fast convergence and high stability,and can achieve satisfactory performance in objective evaluation indexes and subjective visual presentation.