scholarly journals Adaptive Image Restoration via a Relaxed Regularization of Mean Curvature

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mingxi Ma ◽  
Jun Zhang ◽  
Chengzhi Deng ◽  
Zhaoyang Liu ◽  
Yuanyun Wang
Keyword(s):  
Image Restoration ◽  
Mean Curvature ◽  
Complexity Analysis ◽  
State Of The Art ◽  
Alternating Direction Method ◽  
Natural Images ◽  
Convergence Theory ◽  
Relaxation Model ◽  
Alternating Direction ◽  
Effectiveness And Efficiency

In this paper, a new relaxation model based on mean curvature for adaptive image restoration is proposed. To solve the problem efficiently, an alternating direction method of multipliers (ADMMs) is proposed. Furthermore, a rigorous convergence theory of the proposed algorithm is established. We also give the complexity analysis of our proposed method. Experimental results are provided to demonstrate the effectiveness and efficiency of the proposed method over a state-of-the-art method on synthetic and natural images.

scholarly journals Fusing Multiple Multiband Images

2018 ◽  
Vol 4 (10) ◽  
pp. 118 ◽  
Author(s):  
Reza Arablouei
Keyword(s):  
State Of The Art ◽  
Likelihood Estimation ◽  
Alternating Direction Method ◽  
Natural Images ◽  
Hyperspectral Images ◽  
Superior Performance ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Abrupt Changes ◽  
Fused Image

High-resolution hyperspectral images are in great demand but hard to acquire due to several existing fundamental and technical limitations. A practical way around this is to fuse multiple multiband images of the same scene with complementary spatial and spectral resolutions. We propose an algorithm for fusing an arbitrary number of coregistered multiband, i.e., panchromatic, multispectral, or hyperspectral, images through estimating the endmember and their abundances in the fused image. To this end, we use the forward observation and linear mixture models and formulate an appropriate maximum-likelihood estimation problem. Then, we regularize the problem via a vector total-variation penalty and the non-negativity/sum-to-one constraints on the endmember abundances and solve it using the alternating direction method of multipliers. The regularization facilitates exploiting the prior knowledge that natural images are mostly composed of piecewise smooth regions with limited abrupt changes, i.e., edges, as well as coping with potential ill-posedness of the fusion problem. Experiments with multiband images constructed from real-world hyperspectral images reveal the superior performance of the proposed algorithm in comparison with the state-of-the-art algorithms, which need to be used in tandem to fuse more than two multiband images.

scholarly journals Two Efficient Algorithms for Orthogonal Nonnegative Matrix Factorization

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jing Wu ◽  
Bin Chen ◽  
Tao Han
Keyword(s):  
Gene Expression ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Alternating Direction Method ◽  
Data Matrix ◽  
Popular Method ◽  
Alternating Direction ◽  
Expression Classification

Nonnegative matrix factorization (NMF) is a popular method for the multivariate analysis of nonnegative data. It involves decomposing a data matrix into a product of two factor matrices with all entries restricted to being nonnegative. Orthogonal nonnegative matrix factorization (ONMF) has been introduced recently. This method has demonstrated remarkable performance in clustering tasks, such as gene expression classification. In this study, we introduce two convergence methods for solving ONMF. First, we design a convergent orthogonal algorithm based on the Lagrange multiplier method. Second, we propose an approach that is based on the alternating direction method. Finally, we demonstrate that the two proposed approaches tend to deliver higher-quality solutions and perform better in clustering tasks compared with a state-of-the-art ONMF.

scholarly journals Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1623
Author(s):  
Jie Chen ◽  
Ryosuke Shimmura ◽  
Joe Suzuki
Keyword(s):  
Graphical Model ◽  
State Of The Art ◽  
High Accuracy ◽  
Alternating Direction Method ◽  
Main Approach ◽  
First Order ◽  
Gradient Algorithms ◽  
Graphical Lasso ◽  
Alternating Direction ◽  
Accuracy And Precision

We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

scholarly journals An adaptive algorithm for restoring image corrupted by mixed noise

2019 ◽  
pp. 73-82
Author(s):  
Pham Cong Thang ◽  
Tran Thi Thu Thao ◽  
Phan Tran Dang Khoa ◽  
Dinh Viet Sang ◽  
Pham Minh Tuan ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Digital Images ◽  
State Of The Art ◽  
Natural Images ◽  
Total Variation Regularization ◽  
Edge Preservation ◽  
Spatially Adaptive ◽  
Alternating Direction ◽  
Mixed Noise ◽  
Adaptive Total Variation

Image denoising is one of the fundamental problems in image processing. Digital images are often contaminated by noise due to the image acquisition process under poor conditions. In this paper, we propose an effective approach to remove mixed Poisson-Gaussian noise in digital images. Particularly, we propose to use a spatially adaptive total variation regularization term in order to enhance the ability of edge preservation. We also propose an instance of the alternating direction algorithm to solve the proposed denoising model as an optimization problem. The experiments on popular natural images demonstrate that our approach achieves superior accuracy than other recent state-of-the-art techniques.

Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method

2020 ◽  
Author(s):  
Thomas Kleinert ◽  
Martin Schmidt
Keyword(s):  
Optimization Problems ◽  
Mathematical Optimization ◽  
Alternating Direction Method ◽  
Convergence Theory ◽  
Mixed Integer ◽  
Solution Quality ◽  
Alternating Direction ◽  
Bilevel Problems ◽  
Primal Heuristics ◽  
Feasible Points

Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, and so on. Often these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization, one develops primal heuristics in order to obtain feasible points of good quality quickly or to enhance the search process of exact global methods. However, there are comparably few heuristics for bilevel problems. In this paper, we develop such a primal heuristic for bilevel problems with a mixed-integer linear or quadratic upper level and a linear or quadratic lower level. The heuristic is based on a penalty alternating direction method, which allows for a theoretical analysis. We derive a convergence theory stating that the method converges to a stationary point of an equivalent single-level reformulation of the bilevel problem and extensively test the method on a test set of more than 2,800 instances—which is one of the largest computational test sets ever used in bilevel programming. The study illustrates the very good performance of the proposed method in terms of both running times and solution quality. This renders the method a suitable subroutine in global bilevel solvers as well as a reasonable standalone approach. Summary of Contribution: Bilevel optimization problems form a very important class of optimization problems in the field of operations research, which is mainly due to their capability of modeling hierarchical decision processes. However, real-world bilevel problems are usually very hard to solve—especially in the case in which additional mixed-integer aspects are included in the modeling. Hence, the development of fast and reliable primal heuristics for this class of problems is very important. This paper presents such a method.

scholarly journals An Alternating Direction Method for Mixed Gaussian Plus Impulse Noise Removal

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Si Wang ◽  
Ting-Zhu Huang ◽  
Xi-le Zhao ◽  
Jun Liu
Keyword(s):  
Total Variation ◽  
Numerical Experiments ◽  
Impulse Noise ◽  
State Of The Art ◽  
Noise Removal ◽  
Alternating Direction Method ◽  
Impulse Noise Removal ◽  
Alternating Direction ◽  
Total Variation Model ◽  
Blurred Images

A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by impulse noise or mixed Gaussian plus impulse noise. We attack the proposed scheme with an alternating direction method of multipliers (ADMM). Numerical experiments demonstrate the efficiency of the proposed method and the performance of the proposed method is competitive with the existing state-of-the-art methods.

Sign in / Sign up

Export Citation Format

Share Document