Medical Image Denoising Via Matrix Norm Minimization Problems

This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given matrix keeps the important information in the image and removing the unwanted information by solving the matrix completion problem that is defined by P. The quadratic programming use to solve the given three norm-based minimization problems. To improve the optimal solution a weighted exponential is used to compute the weighted vector of spectral that use to improve the threshold of optimal low rank that getting from solving the nuclear norm and spectral norm problems. The result of applying the proposed method on different types of images is given by adopting some metrics. The results showed the ability of the given methods.

Inverse Halftoning Based on Weighted Nuclear Norm Minimization

The inverse halftoning technology refers to restore a continuous-tone image from a halftone image with only bi-level pixes. However, recovering the continuous images from their halftoned ones is normally ill-posed, which making the inverse halftoning algorithm very challenging. In this paper, we propose an optimization model with two alternate projections (TAP) for image inverse halftoning under the weighted nuclear norm minimization (WNNM) framework. The main contributions are two-folds. First, the WNNM nonlocal regularization term is established, which offers a powerful mechanism of nonlocal self-similarity to ensure a more reliable estimation. Second, the alternate minimization projections are formulated for solving the image inverse halftoning, which reconstructs the continuous-tone image without destroying the image details and structures. The experiment results shown that the proposed method outperformed the state of the arts in terms of both objective measurements and subjective visual performance.

Sobel Edge Detection Based on Weighted Nuclear Norm Minimization Image Denoising

As a classic and effective edge detection operator, the Sobel operator has been widely used in image segmentation and other image processing technologies. This operator has obvious advantages in the speed of extracting the edge of images, but it also has the disadvantage that the detection effect is not ideal when the image contains noise. In order to solve this problem, this paper proposes an optimized scheme for edge detection. In this scheme, the weighted nuclear norm minimization (WNNM) image denoising algorithm is combined with the Sobel edge detection algorithm, and the excellent denoising performance of the WNNM algorithm in a noise environment is utilized to improve the anti-noise performance of the Sobel operator. The experimental results show that the optimization algorithm can obtain better detection results when processing noisy images, and the advantages of the algorithm become more obvious with the increase of noise intensity.