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A fixed-point algorithm for blind source separation with nonlinear autocorrelation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第2期223卷 908-915页

作者： Shi, Zhenwei Jiang, Zhiguo Zhou, Fugen Beijing Univ Aeronaut & Astronaut Image Proc Ctr Sch Astronaut Beijing 100083 Peoples R China

This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective function based on the nonlinear autocorrelation of sources. Maximizing the objective function, we propose a fixed-point source separation algorithm. Furthermore, we give some mathematical properties of the algorithm. Computer simulations for sources with square temporal autocorrelation and the real-world applications in the analysis of the magnetoencephalographic recordings (MEG) illustrate the efficiency of the proposed approach. Thus, the presented BSS algorithm, which is based on the nonlinear measure of temporal autocorrelation, provides a novel statistical property to perform BSS. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Blind source separation (BSS) Independent component analysis (ICA) Nonlinear autocorrelation fixed-point algorithm

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A new constrained fixed-point algorithm for ordering independent components

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第1-2期220卷 548-558页

作者： Zhang, Hongjuan Guo, Chonghui Shi, Zhenwei Feng, Enmin Dalian Univ Technol Inst Syst Engn Dalian 116024 Peoples R China Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China Beijing Univ Aeronaut & Astronaut Sch Astronaut Image Proc Ctr Beijing 100083 Peoples R China

Independent component analysis (ICA) aims to recover a set of unknown mutually independent components (ICs) from their observed mixtures without knowledge of the mixing coefficients. In the classical ICA model there exists ICs' indeterminacy on permutation and dilation. Constrained ICA is one of methods for solving this problem through introducing constraints into the classical ICA model. In this paper we first present a new constrained ICA model which composed of three pans: a maximum likelihood criterion as an objective function, statistical measures as inequality constraints and the normalization of demixing matrix as equality constraints. Next, we incorporate the new fixed-point (newFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm. Computation simulations on synthesized signals and speech signals demonstrate that this combination both can eliminate ICs' indeterminacy to a certain extent, and can provide better performance. Moreover, comparison results with the existing algorithm verify the efficiency of our new algorithm furthermore, and show that it is more simple to implement than the existing algorithm due to its advantage of not using the learning rate. Finally. this new algorithm is also applied for the real-world fetal ECG data. experiment results further indicate the efficiency of the new constrained fixed-point algorithm. (c) 2007 Published by Elsevier B.V.

关键词： independent component analysis constrained independent component analysis Lagrange multiplier method fixed-point algorithm

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A fixed-point algorithm for second-order total variation models in image denoising

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COMPUTATIONAL & APPLIED MATHEMATICS 2019年第1期38卷 1-14页

作者： Gao, Tianling Wang, Xiaofei Liu, Qiang Zhang, Zhiguang Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China

In this paper, we construct fixed-point algorithms for the second-order total variation models through discretization models and the subdifferential and proximity operators. Particularly, we focus on the convergence conditions of our algorithms by analyzing the eigenvalues of the difference matrix. The algorithms are tested on various images to verify our proposed convergence conditions. The experiments compared with the split Bregman algorithms demonstrate that fixed-point algorithms could solve the second-order functional minimization problem stably and effectively.

关键词： fixed-point algorithm Convergence High-order total variation Image denoising

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Convergence of the fixed-point algorithm in ISAR imaging

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REMOTE SENSING LETTERS 2023年第9期14卷 993-1001页

作者： Wang, Junfeng Shanghai Jiao Tong Univ Dept Elect Engn Shanghai Peoples R China Shanghai Jiao Tong Univ Dept Elect Engn 800 Dongchuan Rd Shanghai 200240 Peoples R China

In inverse synthetic aperture radar (ISAR) imaging, a lot of attention is paid to the sharpest-image phase adjustment for its good focus quality and robustness against noise and target scintillation. It can be done by the fixed-point algorithm, which is both universally applicable and computationally efficient. This paper develops this algorithm with a general sharpness measure and reveals that for this algorithm to converge stably and correctly, the sharpness measure should have a kernel function whose absolute derivative is an increasing function. Further, a sharpness measure is presented for the fixed-point algorithm. This sharpness measure leads to a good focus quality like the negative entropy because their kernel functions have similar second-order derivatives. Also, since this sharpness measure has a kernel function whose absolute derivative is an increasing function, the fixed-point algorithm with this sharpness measure converges stably and correctly.

关键词： ISAR sharpest-image phase adjustment fixed-point algorithm sharpness measure negative entropy

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Finding Dantzig selectors with a proximity operator based fixed-point algorithm

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2015年 90卷 36-46页

作者： Prater, Ashley Shen, Lixin Suter, Bruce W. Air Force Res Lab Informat Directorate Rome NY 13441 USA Syracuse Univ Dept Math Syracuse NY 13244 USA

A simple iterative method for finding the Dantzig selector, designed for linear regression problems, is introduced. The method consists of two stages. The first stage approximates the Dantzig selector through a fixed-point formulation of solutions to the Dantzig selector problem;the second stage constructs a new estimator by regressing data onto the support of the approximated Dantzig selector. The proposed method is compared to an alternating direction method. The results of numerical simulations using both the proposed method and the alternating direction method on synthetic and real-world data sets are presented. The numerical simulations demonstrate that the two methods produce results of similar quality;however the proposed method tends to be significantly faster. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Dantzig selector Proximity operator fixed-point algorithm Alternating direction method

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A new fixed-point algorithm for independent component analysis

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NEUROCOMPUTING 2004年第1期56卷 467-473页

作者： Shi, ZW Tang, HW Tang, YY Dalian Univ Technol Inst Neuroinformat Dalian 116023 Peoples R China Chinese Acad Sci Lab Visual Informat Proc Beijing 100101 Peoples R China Chinese Acad Sci Key Lab Mental Hlth Beijing 100101 Peoples R China Dalian Univ Technol Inst Computat Biol & Bioinformat Dalian 116023 Peoples R China

A new fixed-point algorithm for independent component analysis (ICA) is presented that is able blindly to separate mixed signals with sub- and super-Gaussian source distributions. The new fixed-point algorithm maximizes the likelihood of the ICA model under the constraint of decorrelation and uses the method of Lee et al. (Neural Comput. 11(2) (1999) 417) to switch between sub- and super-Gaussian regimes. The new fixed-point algorithm maximizes the likelihood very fast and reliably. The validity of this algorithm is confirmed by the simulations and experimental results. (C) 2003 Elsevier B.V. All rights reserved.

关键词： independent component analysis blind source separation fixed-point algorithm

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A New Riemannian Averaged fixed-point algorithm for MGGD Parameter Estimation

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IEEE SIGNAL PROCESSING LETTERS 2015年第12期22卷 2314-2318页

作者： Boukouvalas, Zois Said, Salem Bombrun, Lionel Berthoumieu, Yannick Adali, Tuelay Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA Univ Bordeaux Lab IMS Bordeaux France Univ Maryland Baltimore Cty Dept Comp Sci & Elect Engn Baltimore MD 21250 USA

Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few parameters, i.e., the scatter matrix and the shape parameter. Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter increases. Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value of the shape parameter. We provide the mathematical justification of the convergence of the RA-FP algorithm based on the Riemannian geometry of the space of symmetric positive definite matrices. We also show using numerical simulations that the RA-FP algorithm is invariant to the initialization of the scatter matrix and provides significantly improved performance over existing FP and method-of-moments (MoM) algorithms for the estimation of the scatter matrix.

关键词： fixed-point algorithm maximum likelihood estimation multivariate generalized Gaussian distribution Riemannian geometry symmetric positive definite matrix

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Convergence of a fixed-point algorithm under Maximum Correntropy Criterion

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IEEE SIGNAL PROCESSING LETTERS 2015年第10期22卷 1723-1727页

作者： Chen, Badong Wang, Jianji Zhao, Haiquan Zheng, Nanning Principe, Jose C. Xi An Jiao Tong Univ Inst Artificial Intelligence & Robot Xian Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu Peoples R China Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering algorithms under MCC have been developed and available for practical use. The fixed-point algorithms under MCC are, however, seldom studied. In particular, too little attention has been paid to the convergence issue of the fixed-point MCC algorithms. In this letter, we will study this problem and give a sufficient condition to guarantee the convergence of a fixed-point MCC algorithm.

关键词： fixed-point algorithm maximum correntropy criterion robust estimation

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A feature selection method using fixed-point algorithm for DNA microarray gene expression data

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INTERNATIONAL JOURNAL OF KNOWLEDGE-BASED AND INTELLIGENT ENGINEERING SYSTEMS 2014年第1期18卷 55-59页

作者： Sharma, Alok Paliwal, Kuldip K. Imoto, Seiya Miyano, Satoru Sharma, Vandana Ananthanarayanan, Rajeshkannan Univ Tokyo Ctr Human Genome Inst Med Sci Lab DNA Informat AnalMinato Ku 4-6-1 Shirokanedai Tokyo 1088639 Japan Griffith Univ Sch Engn Tokyo Japan Univ South Pacific Sch Engn & Phys Tokyo Japan Univ South Pacific Fiji Sch Med Tokyo Japan

As the performance of hardware is limited, the focus has been to develop objective, optimized and computationally efficient algorithms for a given task. To this extent, fixed-point and approximate algorithms have been developed and successfully applied in many areas of research. In this paper we propose a feature selection method based on fixed-point algorithm and show its application in the field of human cancer classification using DNA microarray gene expression data. In the fixed-point algorithm, we utilize between-class scatter matrix to compute the leading eigenvector. This eigenvector has been used to select genes. In the computation of the eigenvector, the eigenvalue decomposition of the scatter matrix is not required which significantly reduces its computational complexity and memory requirement.

关键词： Feature selection fixed-point algorithm DNA microarray gene expression data fast PCA

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A new robust fixed-point algorithm and its convergence analysis

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JOURNAL OF fixed point THEORY AND APPLICATIONS 2017年第4期19卷 3191-3215页

作者： Heravi, Ahmad Reza Hodtani, Ghosheh Abed Ferdowsi Univ Mashhad Dept Elect Engn Mashhad Iran

In recent years, research on information theoretic learning (ITL) criteria has become very popular and ITL concepts are widely exploited in several applications because of their robust properties in the presence of heavy-tailed noise distributions. Minimum error entropy with fiducial points (MEEF), as one of the ITL criteria, has not yet been well investigated in the literature. In this study, we suggest a new fixed-point MEEF (FP-MEEF) algorithm, and analyze its convergence based on Banach's theorem (contraction mapping theorem). Also, we discuss in detail the convergence rate of the proposed method, which is able to converge to the optimal solution quadratically with the appropriate selection of the kernel size. Numerical results confirm our theoretical analysis and also show the outperformance of FP-MEEF in comparison with FP-MSE in some non-Gaussian environments. In addition, the convergence rate of FP-MEEF and gradient descent-based MEEF is evaluated in some numerical examples.

关键词： fixed-point algorithm information theoretic learning convergence contraction mapping theorem order of convergence

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