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Inverse problems with Poisson data: statistical regularization theory, applications and algorithms

INVERSE PROBLEMS 2016年第9期32卷 1-1页

作者： Hohage, Thorsten Werner, Frank Univ Gottingen Inst Numer & Appl Math Lotzestr 16-18 D-37083 Gottingen Germany Max Planck Inst Biophys Chem Stat Inverse Problems Biophys Grp Fassberg 11 D-37077 Gottingen Germany Univ Gottingen Felix Bernstein Inst Math Stat Biosci Goldschmidtstr 7 D-37077 Gottingen Germany

Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years.

关键词： Poisson process inverse problem regularization theory positron emission tomography phase retrieval splitting algorithms

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Forward-Partial Inverse-Forward splitting for Solving Monotone Inclusions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第2期166卷 391-413页

作者： Briceno-Arias, Luis M. Univ Tecn Federico Santa Maria Dept Matemat Santiago Chile

In this paper, we provide a splitting method for finding a zero of the sum of a maximally monotone operator, a Lipschitzian monotone operator, and a normal cone to a closed vector subspace of a real Hilbert space. The problem is characterised by a simpler monotone inclusion involving only two operators: the partial inverse of the maximally monotone operator with respect to the vector subspace and a suitable Lipschitzian monotone operator. By applying the Tseng's method in this context, we obtain a fully split algorithm that exploits the whole structure of the original problem and generalises partial inverse and Tseng's methods. Connections with other methods available in the literature are provided, and the flexibility of our setting is illustrated via applications to some inclusions involving maximally monotone operators, to primal-dual composite monotone inclusions, and to zero-sum games.

关键词： Composite operator Partial inverse Monotone operator theory splitting algorithms Tseng's method

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A mobile sensor network tracking moving targets in a dynamic environment

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IFAC-PapersOnLine 2015年第5期28卷 1-6页

作者： Dang, Anh Duc Horn, Joachim Institute of Control Engineering Helmut-Schmidt-University University of the Federal Armed Forces Hamburg Holstenhofweg 85 HamburgD-22043 Germany

This paper presents a novel approach to control a mobile sensor network to track moving targets in a dynamic environment. In this approach, we solve two main issues: the sensor splitting and merging control when the number of the targets is changed. The subgroup merging into the main group is controlled by the invariable attractive force field of the virtual leader in the main swarm. In other words, under the effect of this attractive force field, free-sensors can easily reach the main group and become new members in formation of this group. In contrast, subgroups will be split from the existing group to track new targets that appear. The splitting algorithm is built based on the geometry between targets and group position. The members in a split subgroup will connect with their neighbors in order to generate a robust formation without collision while tracking their target. In addition, when a target disappears, the sensors that are tracking this target will automatically distribute into the nearest existing subgroup. The effectiveness of this proposed approach has been verified in simulations. © 2015, IFAC. Hosting by Elsevier Ltd.

关键词： Target tracking Collision avoidance Merging Sensor networks Swarm intelligence Attractive force Dynamic environments Formation control Mobile sensor networks splitting algorithms splitting and merging Tracking moving targets Vector fields

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Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2014年第1-2期59卷 135-161页

作者： Gu, Guoyong He, Bingsheng Yuan, Xiaoming Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China Nanjing Univ Int Ctr Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Hong Kong Peoples R China

This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models' structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way.

关键词： Convex minimization Saddle-point problem Proximal point algorithm Convergence rate Customized algorithms splitting algorithms

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En Masse Relay Selection algorithms for Multi-Source, Multi-Relay, Decode-and-Forward Cooperative Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第8期61卷 3170-3180页

作者： Karthik, A. Mehta, Neelesh B. Indian Inst Sci IISc Dept Elect Commun Eng Bangalore Karnataka India

Opportunistic relay selection in a multiple source-destination (MSD) cooperative system requires quickly allocating to each source-destination (SD) pair a suitable relay based on channel gains. Since the channel knowledge is available only locally at a relay and not globally, efficient relay selection algorithms are needed. For an MSD system, in which the SD pairs communicate in a time-orthogonal manner with the help of decode-and-forward relays, we propose three novel relay selection algorithms, namely, contention-free en masse assignment (CFEA), contention-based en masse assignment (CBEA), and a hybrid algorithm that combines the best features of CFEA and CBEA. En masse assignment exploits the fact that a relay can often aid not one but multiple SD pairs, and, therefore, can be assigned to multiple SD pairs. This drastically reduces the average time required to allocate an SD pair when compared to allocating the SD pairs one by one. We show that the algorithms are much faster than other selection schemes proposed in the literature and yield significantly higher net system throughputs. Interestingly, CFEA is as effective as CBEA over a wider range of system parameters than in single SD pair systems. [ABSTRACT FROM AUTHOR]

关键词： Relay selection Multiple source-destination networks splitting algorithms Cooperative communications Cross-layer design Fading channels Multiple access

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M-Ary RFID Tags splitting With Small Idle Slots

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2012年第1期9卷 177-181页

作者： Guo, Hongbo Leung, Victor C. M. Bolic, Miodrag Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada Univ Ottawa Sch Informat Technol & Engn Ottawa ON K1N 6N5 Canada

In radio frequency identifications (RFIDs), an idle slot can be interrupted by the reader and takes less time than the other slots. In this case, the widely used binary splitting (BS) protocol is not optimal. M-ary splitting (M > 2) with a carefully selected M outperforms BS, because it can take into account smaller duration of the idle slots. In this paper, we provide optimal value of M(M-opt) for varying slot sizes that yields minimum identification time. The proposed scheme is called optimal splitting (OS). We also revise OS to deal with mobile tags and propose the optimal splitting with arrival tags blocking (OS-ATB) protocol. Extensive simulations show that OS and OS-ATB consistently yield better performance than the other splitting and tree-based schemes. Note to Practitioners-An RFID reader can interrupt the slot in which no tags reply for a predefined time interval, resulting in an short idle slot. In this case, binary splitting is not the best choice but simple increase of the splitting level can yield much better performance. Since the slot sizes are usually fixed for a given system, the optimum value can be calculated offline without introducing extra computation complexity during the real-time identification.

关键词： Mobile tags optimal splitting radio frequency identification (RFID) splitting algorithms tag anticollision

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Perturbation approach to generalized Nash equilibrium problems with shared constraints

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OPTIMIZATION LETTERS 2012年第7期6卷 1379-1391页

作者： Altangerel, L. Battur, G. Natl Univ Mongolia Sch Math & Comp Sci Ulaanbaatar Mongolia

This paper aims to consider an application of conjugate duality in convex optimization to the generalized Nash equilibrium problems with shared constraints and nonsmooth cost functions. Sufficient optimality conditions for the problems regarding to players are rewritten as inclusion problems and the maximal monotonicity of set-valued mappings generated by the subdifferentials of functions from data of GNEP is proved. Moreover, some assertions dealing with solutions to GNEP are obtained and applications of splitting algorithms to the oligopolistic market equilibrium models are presented.

关键词： Generalized Nash equilibrium problem Conjugate duality Inclusion problems Maximal monotonicity Oligopolistic market equilibrium models splitting algorithms

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Performance of a Fast, Distributed Multiple Access Based Relay Selection Algorithm Under Imperfect Statistical Knowledge

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2011年第10期10卷 3516-3527页

作者： Shah, Virag Mehta, Neelesh B. Bethanabhotla, Dilip Univ Texas Austin Dept Elect Engn Austin TX 78712 USA IISc Dept Elect Commun Eng Bangalore Karnataka India Univ So Calif Dept Elect Engn Los Angeles CA 90089 USA NCC IISc Gauhati India

Cooperative wireless systems can exploit spatial diversity by opportunistically selecting the best relay to forward data to a destination. However, determining the best relay is a challenging task and requires a selection algorithm because the relays are geographically separated and only have local channel knowledge. Selecting the best relay is equivalent to finding the relay with the largest metric, where each relay computes its metric using local channel knowledge. We analyze the performance of a fast, distributed, and scalable multiple access based selection algorithm when it assumes incorrect values for two fundamental parameters that it requires to operate efficiently the number of available relays and the cumulative distribution function (CDF) of the metrics. Such imperfect knowledge will invariably arise in practice. We develop new expressions for the time required to select the best relay as a function of the assumed and actual parameters. We show that imperfect knowledge can significantly slow down the selection algorithm. Further, in a system that uses its observations to update its CDF estimate, we determine the minimum number of observations required to limit the performance degradation. We also develop a minimax formulation that makes the algorithm robust to uncertainties in the number of relays in the system.

关键词： Multiple access techniques relays cooperative communications splitting algorithms diversity selection cross-layer optimization distributed estimation

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The Relay Selection and Transmission Trade-off in Cooperative Communication Systems

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2010年第8期9卷 2505-2515页

作者： Shah, Virag Mehta, Neelesh B. Yim, Raymond Indian Inst Technol Bombay 400076 Maharashtra India Indian Inst Sci Elect Commun Eng Dept Bangalore 560012 Karnataka India MERL Cambridge MA USA

A common and practical paradigm in cooperative communication systems is the use of a dynamically selected 'best' relay to decode and forward information from a source to a destination. Such systems use two phases - a relay selection phase, in which the system uses transmission time and energy to select the best relay, and a data transmission phase, in which it uses the spatial diversity benefits of selection to transmit data. In this paper, we derive closed-form expressions for the overall throughput and energy consumption, and study the time and energy trade-off between the selection and data transmission phases. To this end, we analyze a baseline non-adaptive system and several adaptive systems that adapt the selection phase, relay transmission power, or transmission time. Our results show that while selection yields significant benefits, the selection phase's time and energy overhead can be significant. In fact, at the optimal point, the selection can be far from perfect, and depends on the number of relays and the mode of adaptation. The results also provide guidelines about the optimal system operating point for different modes of adaptation. The analysis also sheds new insights on the fast splitting-based algorithm considered in this paper for relay selection.

关键词： Cooperative communications fading channels relays relay selection splitting algorithms trade-off outage adaptation throughput energy consumption

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GENERAL PROJECTIVE splitting METHODS FOR SUMS OF MAXIMAL MONOTONE OPERATORS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2009年第2期48卷 787-811页

作者： Eckstein, Jonathan Svaiter, B. F. Rutgers State Univ Dept Management Sci & Informat Syst Piscataway NJ 08854 USA Rutgers State Univ RUTCOR Piscataway NJ 08854 USA Inst Matematica Pura & Aplicada BR-22460320 Rio De Janeiro Brazil

We describe a general projective framework for finding a zero of the sum of n maximal monotone operators over a real Hilbert space. Unlike prior methods for this problem, we neither assume n = 2 nor first reduce the problem to the case n = 2. Our analysis defines a closed convex extended solution set for which we can construct a separating hyperplane by individually evaluating the resolvent of each operator. At the cost of a single, computationally simple projection step, this framework gives rise to a family of splitting methods of unprecedented flexibility: numerous parameters, including the proximal stepsize, may vary by iteration and by operator. The order of operator evaluation may vary by iteration and may be either serial or parallel. The analysis essentially generalizes our prior results for the case n = 2. We also include a relative error criterion for approximately evaluating resolvents, which was not present in our earlier work.

关键词： monotone operators splitting algorithms proximal algorithms

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