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Fast high-order matched filter for hyperspectral image target detection

INFRARED PHYSICS & TECHNOLOGY 2018年 94卷 151-155页

作者： Yang, Shuo Song, Ziyang Yuan, Hongyi Zou, Zhengxia Shi, Zhenwei Beijing Electromech Engn Inst Beijing 100074 Peoples R China China Aerosp Sci & Ind Corp Ltd Acad 3 Satellite Operat Div HiWing Beijing 100070 Peoples R China Beihang Univ Sch Astronaut Image Proc Ctr Beijing 100191 Peoples R China

Hyperspectral image target detection is an important application for both of its civil and military uses. Traditional hyperspectral image target detection algorithms are usually designed based on the second-order statistics of the data where it is assumed that the target follows a Gaussian distribution. However, due to the low spatial resolution of the hyperspectral sensor, sometimes the targets of interest only occupy a few pixels. In this case, targets are more suitable to be described by high-order statistics. In this paper, we propose a fast high-order matched filter (FHMF) algorithm which describes the essence of the data more properly and then formulate the detection problem as an optimization problem. To solve the optimization problem efficiently, a fixed-point algorithm is proposed inspired by the FastICA algorithm of the signal processing field. The experiments are conducted with a synthetic hyperspectral image and a real hyperspectral image. The experiment results show that FHMF has better detection performance than other classical detection algorithms. In addition, the fast convergence speed also demonstrates the effectiveness of the proposed fixed-point algorithm.

关键词： Hyperspectral image Target detection Fast high-order matched filter (FHMF) fixed-point algorithm

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Complex correntropy function: Properties, and application to a channel equalization problem

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EXPERT SYSTEMS WITH APPLICATIONS 2018年 107卷 173-181页

作者： Guimaraes, Joao P. F. Fontes, Aluisio I. R. Rego, Joilson B. A. Martins, Allan de M. Principe, Jose C. Fed Inst Rio Grande Norte BR-59015300 Natal RN Brazil Univ Fed Rio Grande do Norte Dept Comp Engn & Automat BR-59078900 Natal RN Brazil Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

The use of correntropy as a similarity measure has been increasing in different scenarios due to the well-known ability to extract high-order statistic information from data. Recently, a new similarity measure between complex random variables was defined and called complex correntropy. Based on a Gaussian kernel, it extends the benefits of correntropy to complex-valued data. However, its properties have not yet been formalized. This paper studies the properties of this new similarity measure and extends this definition to positive-definite kernels. Complex correntropy is applied to a channel equalization problem as good results are achieved when compared with other algorithms such as the complex least mean square (CLMS), complex recursive least squares (CRLS), and least absolute deviation (LAD). (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Channel equalization Complex-valued data Correntropy fixed-point algorithm Maximum complex correntropy criterion Properties

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A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier-Stokes and Euler Equations on Unstructured Meshes

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JOURNAL OF SCIENTIFIC COMPUTING 2017年第3期71卷 1375-1411页

作者： Costa, Ricardo Clain, Stephane Machado, Gaspar J. Loubere, Raphael Univ Paul Sabatier Inst Math Toulouse F-31062 Toulouse France Univ Minho Ctr Matemat Campus Azurem P-4800058 Guimaraes Portugal

We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order convergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme.

关键词： Finite volume method High-order scheme Polynomial reconstruction Navier-Stokes equations Euler equations fixed-point algorithm

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Maximum correntropy Kalman filter

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AUTOMATICA 2017年 76卷 70-77页

作者： Chen, Badong Liu, Xi Zhao, Haiquan Principe, Jose C. Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu Peoples R China Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean vector and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is also given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Kalman filter Maximum correntropy criterion (MCC) fixed-point algorithm

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New algorithms for M-estimation of multivariate scatter and location

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JOURNAL OF MULTIVARIATE ANALYSIS 2016年 144卷 200-217页

作者： Duembgen, Lutz Nordhausen, Klaus Schuhmacher, Heike Univ Bern CH-3012 Bern Switzerland Univ Turku SF-20500 Turku Finland

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and other algorithms. The main idea is to utilize a Taylor expansion of second order of the target functional and devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially. (C) 2015 Elsevier Inc. All rights reserved.

关键词： fixed-point algorithm Matrix exponential function Newton-Raphson algorithm Taylor expansion

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A method to build non-scattering perturbations of two-dimensional acoustic waveguides

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2017年第2期40卷 335-349页

作者： Bonnet-Ben Dhia, A. S. Luneville, E. Mbeutchaa, Y. Nazarov, S. A. CNRS INRIA ENSTA UMR 7231 POEMS 828 Blvd Marechaux F-91762 Palaiseau France St Petersburg State Univ Univ Pr 28 St Petersburg 198504 Russia St Petersburg State Polytechn Univ Polytechnicheskaya Ul 29 St Petersburg Russia

We are interested in finding deformations of the rigid wall of a two-dimensional acoustic waveguide, which are not detectable in the far field, as they produce neither reflection nor conversion of propagative modes. A proof of existence of such invisible deformations has been presented in a previous paper. It combines elements of the asymptotic analysis for small deformations and a fixed-point argument. In the present paper, we give a systematic presentation of the method, and we prove that it works for all frequencies except a discrete set. A particular attention is devoted to the practical implementation of the method. The main difficulty concerns the building of a dual family to given oscillating functions. Advantages and limits of the method are illustrated by several numerical results. Copyright (C) 2015 JohnWiley & Sons, Ltd.

关键词： waveguide modal analysis scattering matrix asymptotic analysis cloaking fixed-point algorithm

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Regularized CT reconstruction on unstructured grid

Regularized CT reconstruction on unstructured grid

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Conference on Medical Imaging - Physics of Medical Imaging

作者： Chen, Yun Lu, Yao Ma, Xiangyuan Xu, Yuesheng Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou 510275 Guangdong Peoples R China Sun Yat Sen Univ Sch Math & Computat Sci Guangzhou 510275 Guangdong Peoples R China Guangdong Prov Key Lab Computat Sci Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781510600188

D Computed tomography (CT) is an ill-posed problem. Reconstruction on unstructured grid reduces the computational cost and alleviates the ill-posedness by decreasing the dimension of the solution space. However, there was no systematic study on edge-preserving regularization methods for CT reconstruction on unstructured grid. In this work, we propose a novel regularization method for CT reconstruction on unstructured grid, such as triangular or tetrahedral meshes generated from the initial images reconstructed via analysis reconstruction method (e.g., filtered back-projection). The proposed regularization method is modeled as a three-term optimization problem, containing a weighted least square fidelity term motivated by the simultaneous algebraic reconstruction technique (SART). The related cost function contains two non-differentiable terms, which bring difficulty to the development of the fast solver. A fixed-point proximity algorithm with SART is developed for solving the related optimization problem, and accelerating the convergence. Finally, we compare the regularized CT reconstruction method to SART with different regularization methods. Numerical experiments demonstrated that the proposed regularization method on unstructured grid is effective to suppress noise and preserve edge features.

关键词： CT reconstruction regularization unstructured grid proximity operator fixed-point algorithm

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STOCHASTIC QUASI-FEJER BLOCK-COORDINATE fixed point ITERATIONS WITH RANDOM SWEEPING

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SIAM JOURNAL ON OPTIMIZATION 2015年第2期25卷 1221-1248页

作者： Combettes, Patrick L. Pesquet, Jean-Christophe Univ Paris 06 Sorbonne Univ UMR 7598 Lab Jacques Louis Lions F-75005 Paris France Univ Paris Est CNRS UMR 8049 Lab Informat Gaspard Monge F-77454 Marne La Vallee 2 France

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fejer monotonicity, which is thoroughly investigated. The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. algorithms using quasi-nonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate. As a by-product, novel block-coordinate operator splitting methods are obtained for solving structured monotone inclusion and convex minimization problems. In particular, the proposed framework leads to random block-coordinate versions of the Douglas-Rachford and forward-backward algorithms and of some of their variants. In the standard case of m = 1 block, our results remain new as they incorporate stochastic perturbations.

关键词： arbitrary sampling block-coordinate algorithm fixed-point algorithm monotone operator splitting primal-dual algorithm stochastic quasi-Fejer sequence stochastic algorithm structured convex minimization problem

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Multi-step fixed-point proximity algorithms for solving a class of optimization problems arising from image processing

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2015年第2期41卷 387-422页

作者： Li, Qia Shen, Lixin Xu, Yuesheng Zhang, Na Sun Yat Sen Univ Sch Math & Computat Sci Guangdong Prov Key Lab Computat Sci Guangzhou 510275 Guangdong Peoples R China Syracuse Univ Dept Math Syracuse NY 13244 USA Sun Yat Sen Univ Sch Math & Computat Sci Guangzhou 510275 Guangdong Peoples R China

We introduce in this paper a class of multi-step fixed-point proximity algorithms for solving optimization problems in the context of image processing. The objective functions of such optimization problems are the sum of two convex functions having one composed with an affine transformation which is often the regularization term. We are particularly interested in the scenario when the convex functions involved in the objective function have low regularity (not differentiable) since many practical problems encountered in image processing have this nature. We characterize the solutions of the optimization problem as fixed-points of a mapping defined in terms of the proximity operators of the two convex functions. The algorithmic and mathematical challenges come from the fact that the mapping is a composition of a firmly non-expansive operator with an expansive affine transform. A class of multi-step iterative schemes are developed based on the fixed-point equations that characterize the solutions. For the purpose of studying convergence of the proposed algorithms, we introduce a notion of weakly firmly non-expansive mappings and establish under certain conditions that the sequence generated from a weakly firmly non-expansive mapping is convergent. We use this general convergence result to conclude that the proposed multi-step algorithms converge. We in particular design a class of two-step algorithms for solving the optimization problem which include several existing algorithms as special examples and at the same time offer novel algorithms. Moreover, we identify the well-known alternating split Bregman iteration method as a special case of the proposed algorithm and modify it to improve its convergence result. A class of two-step algorithms for the total variation based image restoration models are presented.

关键词： fixed-point algorithm Proximity operator Image processing Convex optimization

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CONVERGENCE RATE ANALYSIS OF THE FORWARD-DOUGLAS-RACHFORD SPLITTING SCHEME

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SIAM JOURNAL ON OPTIMIZATION 2015年第3期25卷 1760-1786页

作者： Davis, Damek Univ Calif Los Angeles Dept Math Los Angeles CA 90025 USA

Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable or distributed algorithms, which often obtain nearly state-of-the-art performance. In this paper, we analyze the convergence rate of the forward-Douglas-Rachford splitting (FDRS) algorithm, which is a generalization of the forward-backward splitting (FBS) and Douglas-Rachford splitting algorithms. Under general convexity assumptions, we derive the ergodic and nonergodic convergence rates of the FDRS algorithm, and show that these rates are the best possible. Under Lipschitz differentiability assumptions, we show that the best iterate of FDRS converges as quickly as the last iterate of the FBS algorithm. Under strong convexity assumptions, we derive convergence rates for a sequence that strongly converges to a minimizer. Under strong convexity and Lipschitz differentiability assumptions, we show that FDRS converges linearly. We also provide examples where the objective is strongly convex, yet FDRS converges arbitrarily slowly. Finally, we relate the FDRS algorithm to a primal-dual FBS scheme and clarify its place among existing splitting methods. Our results show that the FDRS algorithm automatically adapts to the regularity of the objective functions and achieves rates that improve upon the sharp worst case rates that hold in the absence of smoothness and strong convexity.

关键词： forward-Douglas-Rachford splitting Douglas-Rachford splitting forward-backward splitting generalized forward-backward splitting fixed-point algorithm primal-dual algorithm

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