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Fast Domain Decomposition for Global Image Smoothing

IEEE TRANSACTIONS ON IMAGE PROCESSING 2017年第8期26卷 4079-4091页

作者： Kim, Youngjung Min, Dongbo Ham, Bumsub Sohn, Kwanghoon Yonsei Univ Sch Elect & Elect Engn Seoul 120749 South Korea Chungnam Natl Univ Sch Comp Sci & Engn Taejon 305764 South Korea

Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and regularization terms. At the price of high-computational cost, this global EPS approach is more robust and versatile than a local one that typically has a form of weighted averaging. In this paper, we introduce an efficient decomposition-based method for global EPS that minimizes the objective function of L-2 data and (possibly non-smooth and non-convex) regularization terms in linear time. Different from previous decomposition-based methods, which require solving a large linear system, our approach solves an equivalent constrained optimization problem, resulting in a sequence of 1-D sub-problems. This enables applying fast linear time solver for weighted-least squares and -L-1 smoothing problems. An alternating direction method of multipliers algorithm is adopted to guarantee fast convergence. Our method is fully parallelizable, and its runtime is even comparable to the state-of-the-art local EPS approaches. We also propose a family of fast majorization-minimization algorithms that minimize an objective with non-convex regularization terms. Experimental results demonstrate the effectiveness and flexibility of our approach in a range of image processing and computational photography applications.

关键词： Edge-preserving image smoothing joint image filtering weighted-least squares alternating minimization majorization-minimization algorithm

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Traffic demand-aware topology control for enhanced energy-efficiency of cellular networks

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2016年第1期000卷 1-17页

作者： Pollakis, Emmanuel Cavalcante, Renato L. G. Stanczak, Slawomir Heinrich Hertz Inst Nachrichtentech Berlin GmbH Fraunhofer Inst Telecommun Einsteinufer 37 D-10587 Berlin Germany Tech Univ Berlin Commun & Informat Theory Grp Einsteinufer 25 D-10587 Berlin Germany

The service provided by current mobile networks is not adapted to spatio-temporal fluctuations in traffic demand, but such fluctuations offer opportunities for energy savings. In particular, significant gains in energy efficiency are realizable by disengaging temporarily redundant hardware components of base stations. We therefore propose a novel optimization framework that considers both the load-dependent energy radiated by the antennas and the remaining forms of energy needed for operating the base stations. The objective is to reduce the energy consumption of mobile networks, while ensuring that the data rate requirements of the users are met throughout the coverage area. Building upon sparse optimization techniques, we develop a majorization-minimization algorithm with the ability to identify energy-efficient network configurations. The iterative algorithm is load-aware, has low computational complexity, and can be implemented in an online fashion to exploit load fluctuations on a short time scale. Simulations show that the algorithm can find network configurations with the energy consumption similar to that obtained with global optimization tools, which cannot be applied to real large networks. Although we consider only one currently deployed cellular technology, the optimization framework is general, potentially applicable to a large class of access technologies.

关键词： Energy efficiency Optimization majorization-minimization algorithm

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Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2024年第3期18卷 597-625页

作者： Browne, Ryan P. Bagnato, Luca Punzo, Antonio Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON Canada Univ Cattolica Sacro Cuore Dept Econ & Social Sci Milan Italy Univ Catania Dept Econ & Business Catania Italy

Mixtures of multivariate leptokurtic-normal distributions have been recently introduced in the clustering literature based on mixtures of elliptical heavy-tailed distributions. They have the advantage of having parameters directly related to the moments of practical interest. We derive two estimation procedures for these mixtures. The first one is based on the majorization-minimization algorithm, while the second is based on a fixed point approximation. Moreover, we introduce parsimonious forms of the considered mixtures and we use the illustrated estimation procedures to fit them. We use simulated and real data sets to investigate various aspects of the proposed models and algorithms.

关键词： Leptokurtic-normal distribution majorization-minimization algorithm Mixture models Parsimony 62Hxx Multivariate analysis

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Fractional-order TV-L² model for image denoising

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CENTRAL EUROPEAN JOURNAL OF PHYSICS 2013年第10期11卷 1414-1422页

作者： Chen, Dali Sun, Shenshen Zhang, Congrong Chen, YangQuan Xue, Dingyu Northeastern Univ Shenyang 110819 Liaoning Peoples R China Univ Calif MESA Lab Merced CA 95343 USA

This paper proposes a new fractional order total variation (TV) denoising method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, regularization parameter selection and blocky effect. Two fractional order TV-L-2 models are constructed for image denoising. The majorization-minimization (MM) algorithm is used to decompose these two complex fractional TV optimization problems into a set of linear optimization problems which can be solved by the conjugate gradient algorithm. The final adaptive numerical procedure is given. Finally, we report experimental results which show that the proposed methodology avoids the blocky effect and achieves state-of-the-art performance. In addition, two medical image processing experiments are presented to demonstrate the validity of the proposed methodology.

关键词： image denoising fractional calculus total variation majorization-minimization algorithm

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Maximum smoothed likelihood component density estimation in mixture models with known mixing proportions

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ELECTRONIC JOURNAL OF STATISTICS 2019年第2期13卷 4035-4078页

作者： Yu, Tao Li, Pengfei Qin, Jing Natl Univ Singapore Dept Stat & Appl Probabil Singapore 117546 Singapore Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON N2L 3G1 Canada NIAID NIH 9000 Rockville Pike Bethesda MD 20892 USA

Mixture models appear in many research areas. In genetic and epidemiology applications, sometimes the mixture proportions may vary but are known. For such data, the existing methods for the underlying component density estimation may produce undesirable results: negative values in the density estimates. In this paper, we propose a maximum smoothed likelihood method to estimate these component density functions. The proposed estimates maximize a smoothed log likelihood function which can inherit all the important properties of probability density functions. A majorization-minimization algorithm is suggested to compute the proposed estimates numerically. We show that, starting from any initial value, the algorithm converges. Furthermore, we establish the asymptotic convergence rate of the L-1 errors of our proposed estimators. Our method provides a general framework for dealing with many similar mixture model problems. An adaptive procedure is suggested for choosing the bandwidths in our estimation procedure. Simulation studies show that the proposed method is very promising and can be much more efficient than the existing method in terms of the L-1 errors. A malaria data application shows the advantages of our method over others.

关键词： EM-like algorithm empirical process M-estimators majorization-minimization algorithm mixture data smoothed like-lihood function

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Maximum smoothed likelihood for multivariate mixtures

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BIOMETRIKA 2011年第2期98卷 403-416页

作者： Levine, M. Hunter, D. R. Chauveau, D. Purdue Univ Dept Stat W Lafayette IN 47907 USA Penn State Univ Dept Stat University Pk PA 16801 USA Univ Orleans Lab Math Anal F-45067 Orleans 2 France

We introduce an algorithm for estimating the parameters in a finite mixture of completely unspecified multivariate components in at least three dimensions under the assumption of conditionally independent coordinate dimensions. We prove that this algorithm, based on a majorization-minimization idea, possesses a desirable descent property just as any em algorithm does. We discuss the similarities between our algorithm and a related one, the so-called nonlinearly smoothed em algorithm for the non-mixture setting. We also demonstrate via simulation studies that the new algorithm gives very similar results to another algorithm that has been shown empirically to be effective but that does not satisfy any descent property. We provide code for implementing the new algorithm in a publicly available R package.

关键词： em algorithm majorization-minimization algorithm Nonlinearly smoothed EM algorithm Nonparametric mixture

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Compressive Sensing Reconstruction Based on Weighted Directional Total Variation

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Journal of Shanghai Jiaotong university(Science) 2017年第1期22卷 114-120页

作者：闵莉花冯灿 School of Science Nanjing University of Posts and Telecommunications Department of Beidou North Information Control Research Academy Group Co.Ltd.

Directionality of image plays a very important role in human visual system and it is important prior information of image. In this paper we propose a weighted directional total variation model to reconstruct image from its finite number of noisy compressive samples. A novel self-adaption, texture preservation method is designed to select the weight. Inspired by majorization-minimization scheme, we develop an efficient algorithm to seek the optimal solution of the proposed model by minimizing a sequence of quadratic surrogate penalties. The numerical examples are performed to compare its performance with four state-of-the-art algorithms. Experimental results clearly show that our method has better reconstruction accuracy on texture images than the existing scheme.

关键词： compressive sensing weighted directional total variation majorization-minimization algorithm TP 391.4 A

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Laplace Nonnegative Matrix Factorization with Application to Semi-supervised Audio Denoising 27

Laplace Nonnegative Matrix Factorization with Application to...

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27th European Signal Processing Conference (EUSIPCO)

作者： Tanji, Hiroki Murakami, Takahiro Kamata, Hiroyuki Meiji Univ Dept Elect & Bioinformat Sch Sci & Technol Tokyo Japan Univ Surrey Ctr Vis Speech & Signal Proc CVSSP Guildford Surrey England

ISBN: (纸本)9789082797039

This paper proposes two statistical models for the nonnegative matrix factorization (NMF) based on heavy-tailed distributions. In the NMF for acoustic signals, previous works justify the additivity of an observed spectrogram using the reproductive property of a probability density function. However, the effectiveness of these properties is not clear. Consequently, to construct a model robust to noise, statistical models based on heavy-tailed distributions are recently growing up. In this paper, as heavy-tailed models for the NMF, we introduce statistical models based on the complex Laplace distributions, and call them Laplace-NMF. Moreover, we derive convergence-guaranteed optimization algorithms to estimate parameters. From our formulation, a statistical interpretation of the Itakura-Saito (IS) divergence-based NMF is newly revealed. We confirm the effectiveness of Laplace-NMF in semi-supervised audio denoising.

关键词： complex Laplace distribution nonnegative matrix factorization majorization-minimization algorithm source separation

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Signal subspace change detection in structured covariance matrices 27

Signal subspace change detection in structured covariance ma...

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27th European Signal Processing Conference (EUSIPCO)

作者： Ben Abdallah, R. Breloy, A. Taylor, A. El Korso, M. N. Lautru, D. Univ Paris Nanterre IUT Ville dAvray LEME EA 4416 Paris France Univ Paris Saclay ONERA DEMR F-91123 Palaiseau France

ISBN: (纸本)9789082797039

Testing common properties between covariance matrices is a relevant approach in a plethora of applications. In this paper, we derive a new statistical test in the context of structured covariance matrices. Specifically, we consider low rank signal component plus white Gaussian noise structure. Our aim is to test the equality of the principal subspace, i.e., subspace spanned by the principal eigenvectors of a group of covariance matrices. A decision statistic is derived using the generalized likelihood ratio test. As the formulation of the proposed test implies a non-trivial optimization problem, we derive an appropriate majorization-minimization algorithm. Finally, numerical simulations illustrate the properties of the newly proposed detector compared to the state of the art.

关键词： Generalized likelihood ratio test subspace testing low rank structure majorization-minimization algorithm

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Two-mode three-way dominance points model for periodic dissimilarity 5

Two-mode three-way dominance points model for periodic dissi...

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5th International Conference on Applied Computing and Information Technology, 2017 4th International Conference on Computational Science/Intelligence and Applied Informatics and 2017 1st International Conference on Big Data, Cloud Computing, Data Science and Engineering, ACIT-CSII-BCD 2017

作者： Tsuchida, Jun Yadohisa, Hiroshi Graduate School of Culture and Information Science Doshisha Univesity Kyoto Japan Department of Culture and Information Science Doshisha Univesity Kyoto Japan

ISBN: (纸本)9781538633021

Asymmetric multidimensional scaling (AMDS) is important for visualizing asymmetric relationships between objects. The dominance point model involves AMDS and represents asymmetry between objects through the difference in the distances between the dominance point and objects. The advantage of this model is that the dominance point and points of objects are represented in the same space. However, there is a problem when applying the dominance point to a two-mode three-way distance model (object X object X condition). The dominance point model ignores the order of condition;that is, the estimator of the model is not changed although the order of condition is changed. To overcome this problem, we propose a two-mode three-way dominance point model using a hypersphere. Constraining the coordinate vector of objects on the hypersphere, the proposed model considers the order of condition. Moreover, the coordinate vector of objects has a periodic property. We introduce the majorizing function of the objective function of our model and obtain the estimator using the majorization-minimization algorithm. © 2017 IEEE.

关键词： Asymmetric model majorization-minimization algorithm Multidimensional scaling

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