Narrow Results

In recent years, image denoising methods based on total variational regularization have attracted extensive attention. However, the traditional total variational regularization method is an approximate solution based on convex method, and does not consider the particularity of the region with rich details. In this paper, the adaptive total-variation and nonconvex low-rank model for image denoising is proposed, which is a hybrid regularization model. First, the image is decomposed into sparse terms and low rank terms, and then the total variational regularization is used to denoise. At the same time, an adaptive coefficient based on gradient is constructed to adaptively judge the flat area and detail texture area, slow down the denoising intensity of detail area, and then play the role of preserving detail information. Finally, by constructing a nonconvex function, the optimal solution of the function is obtained by using the alternating minimization method. This method not only effectively removes the image noise, but also retains the detailed information of the image. The experimental results show the effectiveness of the proposed model, and SNR and SSIM of the denoised image are improved.

Designing an efficient filtering technique is an ill-posed problem especially for image affected from high density of noise. The majority of existing techniques suffer from edge degradation and texture distortion issues. Therefore, in this paper, an efficient weighted nuclear norm minimization (NNM)-based filtering technique to preserve the edges and texture information of filtered images is proposed. The proposed technique significantly improves the quantitative improvements on the low rank approximation of nonlocal self-similarity matrices to deal with the overshrink problem. Extensive experiments reveal that the proposed technique preserves edges and texture details of filtered image with lesser number of visual artifacts on visual quality. The proposed technique outperforms the existing techniques over the competitive filtering techniques in terms of structural similarity index metric (SSIM), peak signal-to-noise ratio (PSNR) and edge preservation index (EPI).

Low-rank matrix completion, which aims to recover a matrix with many missing values, has attracted much attention in many fields of computer science. A low-rank matrix fitting (LMaFit) method has been proposed for fast matrix completion recently. However, this method cannot converge accurately on matrices of real-world images. For improving the accuracy of LMaFit method, an improved low-rank matrix fitting (ILMF) method based on the weighted $L_{1,p}$ norm minimization is proposed in this paper, where the $L_{1,p}$ norm is the summation of the $p$-power $(0<p<2)$ of $L_1$ norms of rows in a matrix. In the proposed method, i.e. the ILMF method, the incomplete matrix that may be corrupted by noises is decomposed into the summation of a low-rank matrix and a noise matrix at first. Then, a weighted $L_{1,p}$ norm minimization problem is solved by using an alternating direction method for improving the accuracy of matrix completion. Experimental results on real-world images show that the ILMF method has much better performances in terms of both the convergence accuracy and convergence speed than the compared methods.

Pseudoskeleton approximation and some other problems require the knowledge of sufficiently well-conditioned submatrix in a largescale matrix. The quality of a submatrix can be measured by modulus of its determinant, also known as volume. In this paper we discuss a search algorithm for the maximum-volume submatrix which already proved to be useful in several matrix and tensor approximation algorithms. We investigate the behavior of this algorithm on random matrices and present some of its applications, including maximization of a bivariate functional.

In the field of image saliency detection, previous approaches are mostly built on the low level priors like color and space contrast, boundary or connectivity prior, which are not sufficient to differentiate real salient regions from other independent or high-contrast parts. In this paper, we propose a novel approach which utilizes both high level and low level priors or cues to generate a salient map. Specifically, we obtain a foreground likelihood map via low rank matrix recovery, which incorporates traditional low-level features with higher-level guidance. Then, we compute a background likelihood map via principal component analysis and k-means clustering, which utilize two low level priors: distribution and boundary priors. Finally, the salient values of one image are calculated based on the two likelihood maps via a modified optimization framework. Extensive experiments on numerous publicly available datasets demonstrate that our proposed algorithm outperforms state-of-the-art methods.