Log in

Relevant bibliographies by topics / Bregman algorithms / Journal articles

To see the other types of publications on this topic, follow the link: Bregman algorithms.

Journal articles on the topic 'Bregman algorithms'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Bregman algorithms.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Bauschke, Heinz H., Jonathan M. Borwein, and Patrick L. Combettes. "Bregman Monotone Optimization Algorithms." SIAM Journal on Control and Optimization 42, no. 2 (2003): 596–636. http://dx.doi.org/10.1137/s0363012902407120.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Chen, Jiawei, Zhongping Wan, Liuyang Yuan, and Yue Zheng. "Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–23. http://dx.doi.org/10.1155/2011/420192.

Full text

Abstract:

We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings in Banach spaces. The strong convergence theorems for weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings are derived under some suitable assumptions

APA, Harvard, Vancouver, ISO, and other styles

3

Wu, Qiang, Jinchao Feng, Kebin Jia, and Xiangyu Wang. "Improved Reconstruction Quality of Bioluminescent Images by Combining SP3Equations and Bregman Iteration Method." Computational and Mathematical Methods in Medicine 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/767296.

Full text

Abstract:

Bioluminescence tomography (BLT) has a great potential to provide a powerful tool for tumor detection, monitoring tumor therapy progress, and drug development; developing new reconstruction algorithms will advance the technique to practical applications. In the paper, we propose a BLT reconstruction algorithm by combining SP3equations and Bregman iteration method to improve the quality of reconstructed sources. The numerical results for homogeneous and heterogeneous phantoms are very encouraging and give significant improvement over the algorithms without the use of SP3equations and Bregman it

APA, Harvard, Vancouver, ISO, and other styles

4

Zhu, Wei, Shi Shu, and Lizhi Cheng. "An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration." Advances in Applied Mathematics and Mechanics 6, no. 2 (2014): 145–64. http://dx.doi.org/10.4208/aamm.2013.m175.

Full text

Abstract:

AbstractIn this paper, we propose a fast proximity point algorithm and apply it to total variation (TV) based image restoration. The novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation (TV) based image restoration have been proposed. Many current algorithms for TV-based image restoration, such as Chambolle’s projection algorithm, the split Bregman algorithm, the Bermúdez-Moreno algorithm, the Jia-Zhao denoising algorithm, and the fixed point algorithm, can be viewed as special cases of the

APA, Harvard, Vancouver, ISO, and other styles

5

Jolaoso, Lateef Olakunle, Maggie Aphane, and Safeer Hussain Khan. "Two Bregman Projection Methods for Solving Variational Inequality Problems in Hilbert Spaces with Applications to Signal Processing." Symmetry 12, no. 12 (2020): 2007. http://dx.doi.org/10.3390/sym12122007.

Full text

Abstract:

Studying Bregman distance iterative methods for solving optimization problems has become an important and very interesting topic because of the numerous applications of the Bregman distance techniques. These applications are based on the type of convex functions associated with the Bregman distance. In this paper, two different extragraident methods were proposed for studying pseudomonotone variational inequality problems using Bregman distance in real Hilbert spaces. The first algorithm uses a fixed stepsize which depends on a prior estimate of the Lipschitz constant of the cost operator. The

APA, Harvard, Vancouver, ISO, and other styles

6

ABDULLAH, AMIRALI, JOHN MOELLER, and SURESH VENKATASUBRAMANIAN. "APPROXIMATE BREGMAN NEAR NEIGHBORS IN SUBLINEAR TIME: BEYOND THE TRIANGLE INEQUALITY." International Journal of Computational Geometry & Applications 23, no. 04n05 (2013): 253–301. http://dx.doi.org/10.1142/s0218195913600066.

Full text

Abstract:

Bregman divergences are important distance measures that are used extensively in data-driven applications such as computer vision, text mining, and speech processing, and are a key focus of interest in machine learning. Answering nearest neighbor (NN) queries under these measures is very important in these applications and has been the subject of extensive study, but is problematic because these distance measures lack metric properties like symmetry and the triangle inequality. In this paper, we present the first provably approximate nearest-neighbor (ANN) algorithms for a broad sub-class of B

APA, Harvard, Vancouver, ISO, and other styles

7

Kuo, Li-Wei, and D. R. Sahu. "Bregman Distance and Strong Convergence of Proximal-Type Algorithms." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/590519.

Full text

Abstract:

The purpose of this paper is to discuss some fundamental properties of Bregman distance, generalized projection operators, firmly nonexpansive mappings, and resolvent operators of set-valued monotone operators corresponding to a functionalΦ(∥·∥). We further study some proximal point algorithms for finding zeros of monotone operators and solving generalized mixed equilibrium problems in Banach spaces. Our results improve and extend some recent results concerning generalized projection operators corresponding to Bregman distance.

APA, Harvard, Vancouver, ISO, and other styles

8

Hidalgo-Silva, Hugo, and E. Gómez-Treviño. "Bregman iterative algorithms for 2D geosounding inversion." Inverse Problems in Science and Engineering 23, no. 6 (2014): 1085–99. http://dx.doi.org/10.1080/17415977.2014.991729.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Censor, Yair, and Gabor T. Herman. "Block-Iterative Algorithms with Underrelaxed Bregman Projections." SIAM Journal on Optimization 13, no. 1 (2002): 283–97. http://dx.doi.org/10.1137/s1052623401389439.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Xiong, Zhao, Shi, and Wang. "A Convex Optimization Algorithm for Compressed Sensing in a Complex Domain: The Complex-Valued Split Bregman Method." Sensors 19, no. 20 (2019): 4540. http://dx.doi.org/10.3390/s19204540.

Full text

Abstract:

The Split Bregman method (SBM), a popular and universal CS reconstruction algorithm for inverse problems with both l1-norm and TV-norm regularization, has been extensively applied in complex domains through the complex-to-real transforming technique, e.g., MRI imaging and radar. However, SBM still has great potential in complex applications due to the following two points; Bregman Iteration (BI), employed in SBM, may not make good use of the phase information for complex variables. In addition, the converting technique may consume more time. To address that, this paper presents the complex-val

APA, Harvard, Vancouver, ISO, and other styles

11

Pang, Chin-Tzong, Eskandar Naraghirad, and Ching-Feng Wen. "Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/573075.

Full text

Abstract:

We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize ma

APA, Harvard, Vancouver, ISO, and other styles

12

Wang, Shenghua, and Shin Min Kang. "Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/619762.

Full text

Abstract:

We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.

APA, Harvard, Vancouver, ISO, and other styles

13

Zou, Jian, Yuli Fu, Qiheng Zhang, and Haifeng Li. "Split Bregman algorithms for multiple measurement vector problem." Multidimensional Systems and Signal Processing 26, no. 1 (2013): 207–24. http://dx.doi.org/10.1007/s11045-013-0251-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Eckstein, Jonathan. "Approximate iterations in Bregman-function-based proximal algorithms." Mathematical Programming 83, no. 1-3 (1998): 113–23. http://dx.doi.org/10.1007/bf02680553.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Liu, Chunsheng, Hong Shan, and Bin Wang. "Wireless Sensor Network Localization via Matrix Completion Based on Bregman Divergence." Sensors 18, no. 9 (2018): 2974. http://dx.doi.org/10.3390/s18092974.

Full text

Abstract:

One of the main challenges faced by wireless sensor network (WSN) localization is the positioning accuracy of the WSN node. The existing algorithms are arduous to use for dealing with the pulse noise that is universal and ineluctable in practical considerations, resulting in lower positioning accuracy. Aimed at this problem and introducing Bregman divergence, we propose in this paper a novel WSN localization algorithm via matrix completion (LBDMC). Based on the natural low-rank character of the Euclidean Distance Matrix (EDM), the problem of EDM recovery is formulated as an issue of matrix com

APA, Harvard, Vancouver, ISO, and other styles

16

Thibault, Alexis, Lénaïc Chizat, Charles Dossal, and Nicolas Papadakis. "Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport." Algorithms 14, no. 5 (2021): 143. http://dx.doi.org/10.3390/a14050143.

Full text

Abstract:

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple metho

APA, Harvard, Vancouver, ISO, and other styles

17

Butnariu, Dan, and Elena Resmerita. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces." Abstract and Applied Analysis 2006 (2006): 1–39. http://dx.doi.org/10.1155/aaa/2006/84919.

Full text

Abstract:

The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.

APA, Harvard, Vancouver, ISO, and other styles

18

Murata, Noboru, Takashi Takenouchi, Takafumi Kanamori, and Shinto Eguchi. "Information Geometry of U-Boost and Bregman Divergence." Neural Computation 16, no. 7 (2004): 1437–81. http://dx.doi.org/10.1162/089976604323057452.

Full text

Abstract:

We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over a label set. We propose two versions of U-Boost learning algorithms by taking account of whether the domain is restricted to the space of probability functions. In the sequential step, we observe that the two adjacent and the initial classifiers

APA, Harvard, Vancouver, ISO, and other styles

19

Kabbadj, S. "Theoretical Aspect of Diagonal Bregman Proximal Methods." Journal of Applied Mathematics 2020 (January 17, 2020): 1–9. http://dx.doi.org/10.1155/2020/3108056.

Full text

Abstract:

In this paper, we propose and study a diagonal inexact version of Bregman proximal methods, to solve convex optimization problems with and without constraints. The proposed method forms a unified framework for existing algorithms by providing others.

APA, Harvard, Vancouver, ISO, and other styles

20

Pang, Zhi-Feng, Li-Lian Wang, and Yu-Fei Yang. "Fast Algorithms for the Anisotropic LLT Model in Image Denoising." East Asian Journal on Applied Mathematics 1, no. 3 (2011): 264–83. http://dx.doi.org/10.4208/eajam.231210.260411a.

Full text

Abstract:

AbstractIn this paper, we propose a new projection method for solving a general minimization problems with twoL1-regularization terms for image denoising. It is related to the split Bregman method, but it avoids solving PDEs in the iteration. We employ the fast iterative shrinkage-thresholding algorithm (FISTA) to speed up the proposed method to a convergence rateO(k−2). We also show the convergence of the algorithms. Finally, we apply the methods to the anisotropic Lysaker, Lundervold and Tai (LLT) model and demonstrate their efficiency.

APA, Harvard, Vancouver, ISO, and other styles

21

Zegeye, Habtu. "Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces." Filomat 28, no. 7 (2014): 1525–36. http://dx.doi.org/10.2298/fil1407525z.

Full text

Abstract:

In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove convergence theorem for a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

APA, Harvard, Vancouver, ISO, and other styles

22

Xiao, Su. "Deblurring by Solving a TVp-Regularized Optimization Problem Using Split Bregman Method." Advances in Multimedia 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/906464.

Full text

Abstract:

Image deblurring is formulated as an unconstrained minimization problem, and its penalty function is the sum of the error term and TVp-regularizers with0<p<1. Although TVp-regularizer is a powerful tool that can significantly promote the sparseness of image gradients, it is neither convex nor smooth, thus making the presented optimization problem more difficult to deal with. To solve this minimization problem efficiently, such problem is first reformulated as an equivalent constrained minimization problem by introducing new variables and new constraints. Thereafter, the split Bregman met

APA, Harvard, Vancouver, ISO, and other styles

23

Lu, Lian, Guowei Tong, Ge Guo, and Shi Liu. "Split Bregman iteration based reconstruction algorithm for electrical capacitance tomography." Transactions of the Institute of Measurement and Control 41, no. 9 (2018): 2389–99. http://dx.doi.org/10.1177/0142331218799841.

Full text

Abstract:

The electrical capacitance tomography (ECT) technique uses the measured capacitance data to reconstruct the permittivity distribution in a specific measurement area, in which the performances of reconstruction algorithms play a crucial role in the reliability of measurement results. According to the Tikhonov regularization technique, a new cost function with the total least squares technique and the ℓ1-norm based regularizer is presented, in which measurement noises, model deviations and the influence of the outliers in the measurement data are simultaneously considered. The split Bregman tech

APA, Harvard, Vancouver, ISO, and other styles

24

Ochs, Peter, Jalal Fadili, and Thomas Brox. "Non-smooth Non-convex Bregman Minimization: Unification and New Algorithms." Journal of Optimization Theory and Applications 181, no. 1 (2018): 244–78. http://dx.doi.org/10.1007/s10957-018-01452-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Wu, X., R. Zurita-Milla, M. J. Kraak, and E. Izquierdo-Verdiguier. "CLUSTERING-BASED APPROACHES TO THE EXPLORATION OF SPATIO-TEMPORAL DATA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W7 (September 14, 2017): 1387–91. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w7-1387-2017.

Full text

Abstract:

As one spatio-temporal data mining task, clustering helps the exploration of patterns in the data by grouping similar elements together. However, previous studies on spatial or temporal clustering are incapable of analysing complex patterns in spatio-temporal data. For instance, concurrent spatio-temporal patterns in 2D or 3D datasets. In this study we present two clustering algorithms for complex pattern analysis: (1) the Bregman block average co-clustering algorithm with I-divergence (BBAC_I) which enables the concurrent analysis of spatio-temporal patterns in 2D data matrix, and (2) the Bre

APA, Harvard, Vancouver, ISO, and other styles

26

Liu, Qiegen, Xi Peng, Jianbo Liu, Dingcheng Yang, and Dong Liang. "A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction." International Journal of Biomedical Imaging 2014 (2014): 1–23. http://dx.doi.org/10.1155/2014/128596.

Full text

Abstract:

Nonconvex optimization has shown that it needs substantially fewer measurements thanl1minimization for exact recovery under fixed transform/overcomplete dictionary. In this work, two efficient numerical algorithms which are unified by the method named weighted two-level Bregman method with dictionary updating (WTBMDU) are proposed for solvinglpoptimization under the dictionary learning model and subjecting the fidelity to the partial measurements. By incorporating the iteratively reweighted norm into the two-level Bregman iteration method with dictionary updating scheme (TBMDU), the modified a

APA, Harvard, Vancouver, ISO, and other styles

27

Teng, Yueyang, Nimu Yuan, Yaonan Zhang, Shouliang Qi, and Yan Kang. "Family of Iterative Reconstruction Algorithms for Medical Imaging with Bregman-Divergences." Journal of Medical Imaging and Health Informatics 5, no. 8 (2015): 1708–14. http://dx.doi.org/10.1166/jmihi.2015.1633.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Yin, Wotao, Stanley Osher, Donald Goldfarb, and Jerome Darbon. "Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing." SIAM Journal on Imaging Sciences 1, no. 1 (2008): 143–68. http://dx.doi.org/10.1137/070703983.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Naraghirad, Eskandar, and Sara Timnak. "Strong convergence theorems for equilibrium problems involving Bregman functions in Banach spaces." Tamkang Journal of Mathematics 48, no. 2 (2017): 159–84. http://dx.doi.org/10.5556/j.tkjm.48.2017.2299.

Full text

Abstract:

In this paper, using Bregman functions, we introduce new Halpern-type iterative algorithms for finding a solution of an equilibrium problem in Banach spaces. We prove the strong convergence of a modified Halpern-type scheme to an element of the set of solution of an equilibrium problem in a reflexive Banach space. This scheme has an advantage that we do not use any Bregman projection of a point on the intersection of closed and convex sets in a practical calculation of the iterative sequence. Finally, some application of our results to the problem of finding a minimizer of a continuously Fr\'{

APA, Harvard, Vancouver, ISO, and other styles

30

PLONKA, GERLIND, and JIANWEI MA. "CURVELET-WAVELET REGULARIZED SPLIT BREGMAN ITERATION FOR COMPRESSED SENSING." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (2011): 79–110. http://dx.doi.org/10.1142/s0219691311003955.

Full text

Abstract:

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon–Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity c

APA, Harvard, Vancouver, ISO, and other styles

31

Mukkamala, Mahesh Chandra, Peter Ochs, Thomas Pock, and Shoham Sabach. "Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Nonconvex Optimization." SIAM Journal on Mathematics of Data Science 2, no. 3 (2020): 658–82. http://dx.doi.org/10.1137/19m1298007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Eckstein, Jonathan. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming." Mathematics of Operations Research 18, no. 1 (1993): 202–26. http://dx.doi.org/10.1287/moor.18.1.202.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Zou, Jian, and Yuli Fu. "Split Bregman algorithms for sparse group Lasso with application to MRI reconstruction." Multidimensional Systems and Signal Processing 26, no. 3 (2014): 787–802. http://dx.doi.org/10.1007/s11045-014-0282-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Zhang, Yin, Qiping Zhang, Yongchao Zhang, Jifang Pei, Yulin Huang, and Jianyu Yang. "Fast Split Bregman Based Deconvolution Algorithm for Airborne Radar Imaging." Remote Sensing 12, no. 11 (2020): 1747. http://dx.doi.org/10.3390/rs12111747.

Full text

Abstract:

Deconvolution methods can be used to improve the azimuth resolution in airborne radar imaging. Due to the sparsity of targets in airborne radar imaging, an L 1 regularization problem usually needs to be solved. Recently, the Split Bregman algorithm (SBA) has been widely used to solve L 1 regularization problems. However, due to the high computational complexity of matrix inversion, the efficiency of the traditional SBA is low, which seriously restricts its real-time performance in airborne radar imaging. To overcome this disadvantage, a fast split Bregman algorithm (FSBA) is proposed in this p

APA, Harvard, Vancouver, ISO, and other styles

35

Wibisono, Andre, Ashia C. Wilson, and Michael I. Jordan. "A variational perspective on accelerated methods in optimization." Proceedings of the National Academy of Sciences 113, no. 47 (2016): E7351—E7358. http://dx.doi.org/10.1073/pnas.1614734113.

Full text

Abstract:

Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. Although many generalizations and extensions of Nesterov’s original acceleration method have been proposed, it is not yet clear what is the natural scope of the acceleration concept. In this paper, we study accelerated methods from a continuous-time perspective. We show that there is a Lagrangian functional that we call the Bregman Lagrangian, which generates a large class of accelerated methods in continuous time, including (but not limited to) accelerated gradient descent, its non-Eucl

APA, Harvard, Vancouver, ISO, and other styles

36

Zeng, Fanfan, Hongwei Du, Jiaquan Jin, Jinzhang Xu, and Bensheng Qiu. "Compressed Sensing MRI via Extended Anisotropic and Isotropic Total Variation." Journal of Medical Imaging and Health Informatics 9, no. 6 (2019): 1066–75. http://dx.doi.org/10.1166/jmihi.2019.2702.

Full text

Abstract:

Compressed sensing (CS) is a technique to reconstruct images from undersampling data, reducing the scanning time of magnetic resonance imaging (MRI). It utilizes the sparsity of images in some transform domains. Total variation (TV) has been applied to enforce sparsity. However, traditional TV based on the l1-norm is not the most direct way to induce sparsity, and it cannot offer a sufficiently sparse representation. Since the lp-norm (0< p < 1) promotes the sparsity better than that of the l1-norm, we propose two extended TV algorithms based on the lp-norm: anisotropic and isotropic tot

APA, Harvard, Vancouver, ISO, and other styles

37

Jiao, Shengxi, Lu Wen, and Haitao Guo. "Incomplete angle reconstruction algorithm with the sparse optimization and the image optimal criterions." International Journal of Advanced Robotic Systems 17, no. 3 (2020): 172988142091697. http://dx.doi.org/10.1177/1729881420916974.

Full text

Abstract:

To solve the problem of artifact and image degradation caused by incomplete angle projection, this article presents an incomplete angle reconstruction algorithm based on sparse optimization and image optimization criterion (SO-IOC). Firstly, the joint objective function model is established based on the projection sparsity and the natural features of images. Secondly, by means of the idea of alternating direction method of multipliers, the augmented Lagrange method is used to decompose the reconstruction model into simple subproblems and the modified genetic algorithm is used for solving those

APA, Harvard, Vancouver, ISO, and other styles

38

Tan, Lu, Wei Bo Wei, Zhen Kuan Pan, Wei Zhong Zhang, and Jin Ming Duan. "A High-Order Model of TV and its Augmented Lagrangian Algorithm." Applied Mechanics and Materials 568-570 (June 2014): 726–33. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.726.

Full text

Abstract:

In recent twenty years, image denoising method which is based on partial differential equations (PDE) has been developed rapidly. Due to its scientific and strong theoretical foundation, it owns accurate and stable results which can be got by efficient algorithms. But it still leaves some problems which need to be solved. The staircase effect is one of the most basic problems in the classical TV (Total Variation) model. This problem can be effectively solved by high-order model proposed in this paper. A fast and efficient numerical algorithm is designed to solve minimization problems related t

APA, Harvard, Vancouver, ISO, and other styles

39

Tembine, Hamidou. "Deep Learning Meets Game Theory: Bregman-Based Algorithms for Interactive Deep Generative Adversarial Networks." IEEE Transactions on Cybernetics 50, no. 3 (2020): 1132–45. http://dx.doi.org/10.1109/tcyb.2018.2886238.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Alghamdi, Mohammed Ali, Naseer Shahzad, and Habtu Zegeye. "Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/580686.

Full text

Abstract:

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved fo

APA, Harvard, Vancouver, ISO, and other styles

41

Li, Ao, and Hayaru Shouno. "Dictionary-Based Image Denoising by Fused-Lasso Atom Selection." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/368602.

Full text

Abstract:

We proposed an efficient image denoising scheme by fused lasso with dictionary learning. The scheme has two important contributions. The first one is that we learned the patch-based adaptive dictionary by principal component analysis (PCA) with clustering the image into many subsets, which can better preserve the local geometric structure. The second one is that we coded the patches in each subset by fused lasso with the clustering learned dictionary and proposed an iterative Split Bregman to solve it rapidly. We present the capabilities with several experiments. The results show that the prop

APA, Harvard, Vancouver, ISO, and other styles

42

BAUSCHKE, HEINZ H., JONATHAN M. BORWEIN, and PATRICK L. COMBETTES. "ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES." Communications in Contemporary Mathematics 03, no. 04 (2001): 615–47. http://dx.doi.org/10.1142/s0219199701000524.

Full text

Abstract:

The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamen

APA, Harvard, Vancouver, ISO, and other styles

43

Ji, Hui, Zuowei Shen, and Yuhong Xu. "Wavelet Based Restoration of Images with Missing or Damaged Pixels." East Asian Journal on Applied Mathematics 1, no. 2 (2011): 108–31. http://dx.doi.org/10.4208/eajam.020310.240610a.

Full text

Abstract:

AbstractThis paper addresses the problem of how to restore degraded images where the pixels have been partly lost during transmission or damaged by impulsive noise. A wide range of image restoration tasks is covered in the mathematical model considered in this paper - e.g. image deblurring, image inpainting and super-resolution imaging. Based on the assumption that natural images are likely to have a sparse representation in a wavelet tight frame domain, we propose a regularization-based approach to recover degraded images, by enforcing the analysis-based sparsity prior of images in a tight fr

APA, Harvard, Vancouver, ISO, and other styles

44

Shen, Zhengwei. "Construction of symmetric fractional over-complete wavelets and applications in image restoration." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 04 (2016): 1650020. http://dx.doi.org/10.1142/s021969131650020x.

Full text

Abstract:

In this work, a novel design scheme is proposed for the construction of symmetric fractional over-complete wavelet filter banks. We first provide solutions to the open problem of designing low-pass filters that are symmetric and of minimum-length. We then obtain the high high-pass filters via Toeplitz matrix factorization which is of less computational complexity than existing methods. The resulting filter banks are approximately shift-invariant. The designed filter banks are applied in image restoration that uses an analysis based model solved by split Bregman algorithms. The experiments show

APA, Harvard, Vancouver, ISO, and other styles

45

Cho, Sun. "A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space." Filomat 34, no. 5 (2020): 1487–97. http://dx.doi.org/10.2298/fil2005487c.

Full text

Abstract:

In this paper, a monotone Bregan projection algorithm is investigated for solving equilibrium problems and common fixed point problems of a family of closed multi-valued Bregman quasi-strict pseudocontractions. Strong convergence is guaranteed in the framework of reflexive Banach spaces.

APA, Harvard, Vancouver, ISO, and other styles

46

Zhou, Gang, Kai Zhong, Zhongwei Li, and Yusheng Shi. "Direct Least Absolute Deviation Fitting of Ellipses." Mathematical Problems in Engineering 2020 (July 11, 2020): 1–11. http://dx.doi.org/10.1155/2020/1317349.

Full text

Abstract:

Scattered data from edge detection usually involve undesired noise which seriously affects the accuracy of ellipse fitting. In order to alleviate this kind of degradation, a method of direct least absolute deviation ellipse fitting by minimizing the ℓ1 algebraic distance is presented. Unlike the conventional ℓ2 estimators which tend to produce a satisfied performance on ideal and Gaussian noise data, while do a poor job for non-Gaussian outliers, the proposed method shows very competitive results for non-Gaussian noise. In addition, an efficient numerical algorithm based on the split Bregman i

APA, Harvard, Vancouver, ISO, and other styles

47

Boffi, Nicholas M., and Jean-Jacques E. Slotine. "Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction." Neural Computation 33, no. 3 (2021): 590–673. http://dx.doi.org/10.1162/neco_a_01360.

Full text

Abstract:

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction. We begin by i

APA, Harvard, Vancouver, ISO, and other styles

48

Chen, Bo, Guowei Zhu, and Zhenqiang Yang. "Multidirectional Anisotropic Total Variation and Its Application in the Tomography of the Surrounding Rock of Coal Mining Faces." Shock and Vibration 2021 (September 6, 2021): 1–15. http://dx.doi.org/10.1155/2021/1138620.

Full text

Abstract:

The computed tomography (CT) reconstruction algorithm is one of the crucial components of the CT system. To date, total variation (TV) has been widely used in CT reconstruction algorithms. Although TV utilizes the a priori information of the longitudinal and lateral gradient sparsity of an image, it introduces some staircase artifacts. To overcome the current limitations of TV and improve imaging quality, we propose a multidirectional anisotropic total variation (MATV) that uses multidirectional gradient information. The surrounding rock of coal mining faces uses principles of tomography simil

APA, Harvard, Vancouver, ISO, and other styles

49

Tang, Jinping, Bo Han, Weimin Han, Bo Bi, and Li Li. "Mixed Total Variation and L1 Regularization Method for Optical Tomography Based on Radiative Transfer Equation." Computational and Mathematical Methods in Medicine 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2953560.

Full text

Abstract:

Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE). It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV) regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 no

APA, Harvard, Vancouver, ISO, and other styles

50

Marzouk, Mohamed, and Mahmoud Hassouna. "Quality analysis using three-dimensional modelling and image processing techniques." Construction Innovation 19, no. 4 (2019): 614–28. http://dx.doi.org/10.1108/ci-10-2018-0086.

Full text

Abstract:

Purpose This paper aims to propose a system for defect detection in constructed elements that is able to indicate deformity positions. It also evaluates the defects in finishing materials of constructed building elements to support the subjective visual quality investigation of the aesthetics of an architectural work. Design/methodology/approach This strategy depends on defect features analysis that evaluates the defect value in digital images using digital image processing methods. The research uses the three-dimensional (3D) modeling techniques and image processing algorithms to generate a s

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!