Matrix Completion Using Graph Total Variation Based on Directed Laplacian Matrix

2021 ◽  
Author(s):  
Alireza Ahmadi ◽  
Sina Majidian ◽  
Mohammad Hossein Kahaei
Keyword(s):  
Total Variation ◽  
Matrix Completion ◽  
Laplacian Matrix

scholarly journals Millimeter-Wave InSAR Image Reconstruction Approach by Total Variation Regularized Matrix Completion

2018 ◽  
Vol 10 (7) ◽  
pp. 1053 ◽  
Author(s):  
Yilong Zhang ◽  
Wei Miao ◽  
Zhenhui Lin ◽  
Hao Gao ◽  
Shengcai Shi
Keyword(s):  
Image Reconstruction ◽  
Total Variation ◽  
Millimeter Wave ◽  
Matrix Completion

scholarly journals Enhancing Matrix Completion Using a Modified Second-Order Total Variation

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wendong Wang ◽  
Jianjun Wang
Keyword(s):  
Total Variation ◽  
Optimization Problem ◽  
State Of The Art ◽  
Matrix Completion ◽  
Second Order ◽  
Low Rank ◽  
Superior Performance ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix

In this paper, we propose a new method to deal with the matrix completion problem. Different from most existing matrix completion methods that only pursue the low rank of underlying matrices, the proposed method simultaneously optimizes their low rank and smoothness such that they mutually help each other and hence yield a better performance. In particular, the proposed method becomes very competitive with the introduction of a modified second-order total variation, even when it is compared with some recently emerged matrix completion methods that also combine the low rank and smoothness priors of matrices together. An efficient algorithm is developed to solve the induced optimization problem. The extensive experiments further confirm the superior performance of the proposed method over many state-of-the-art methods.

scholarly journals Linear Total Variation Approximate Regularized Nuclear Norm Optimization for Matrix Completion

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xu Han ◽  
Jiasong Wu ◽  
Lu Wang ◽  
Yang Chen ◽  
Lotfi Senhadji ◽  
...  
Keyword(s):  
Total Variation ◽  
Missing Values ◽  
Matrix Completion ◽  
Nuclear Norm ◽  
Low Rank ◽  
Visual Data ◽  
Total Variation Norm ◽  
Rank Matrix ◽  
Variation Norm ◽  
Low Rank Matrix

Matrix completion that estimates missing values in visual data is an important topic in computer vision. Most of the recent studies focused on the low rank matrix approximation via the nuclear norm. However, the visual data, such as images, is rich in texture which may not be well approximated by low rank constraint. In this paper, we propose a novel matrix completion method, which combines the nuclear norm with the local geometric regularizer to solve the problem of matrix completion for redundant texture images. And in this paper we mainly consider one of the most commonly graph regularized parameters: the total variation norm which is a widely used measure for enforcing intensity continuity and recovering a piecewise smooth image. The experimental results show that the encouraging results can be obtained by the proposed method on real texture images compared to the state-of-the-art methods.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

DE-NOISING OF CT IMAGES USING COMBINED BIVARIATE SHRINKAGE AND ENHANCED TOTAL VARIATION TECHNIQUE

2018 ◽  
Vol 8 (4) ◽  
pp. 12
Author(s):  
DEVANAND BHONSLE ◽  
VIVEK KUMAR CHANDRA ◽  
SINHA G. R. ◽  
◽  
◽  
...  
Keyword(s):  
Total Variation ◽  
Ct Images ◽  
Bivariate Shrinkage ◽  
Variation Technique
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