Iterative Algorithm

We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the coefficients of such expansions, with 1 < or = p < or =2, still regularizes the problem. If p < 2, regularized solutions of such l^p-penalized problems will have sparser expansions, with respect to the basis under consideration. To compute the corresponding regularized solutions we propose an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. We also review some potential applications of this method.

Wireless communication systems have become increasingly common because of advances in radio and embedded system technologies. In recent years, a new class of applications that networks these wireless devices together is evolving. A representative of this class that has received considerable attention from the research community is the wireless sensor network. Such a sensor networks consist of numerous tetherless devices that are released into the environment and organize themselves in an adhoc fashion. The goal of the network is to perform a monitoring task, and knowledge the physical location of the individual nodes is therefore essential. Not only is this information needed for the sensor network to report the location where events take place, it also assists in group-querying or routing traffic to a designated geographic destination and provides information on physical network coverage. However, equipping every node with a GPS receiver is not always feasible due to possible obstructions in the path of the satellite signals or energy limitations in the nodes. In this paper, we present a novel location discovery approach, which we call AHLoS (Ad-Hoc Localization System), for wireless sensor networks. Only a small fraction of the nodes start with knowledge of their location and the others dynamically estimate their positions via a distributed algorithm. Furthermore, our algorithm utilizes a new iterative multi-lateration technique, such that all nodes that meet some simple connectivity requirements are eventually able to determine their position. We have analyzed the operation of AHLoS, designed a new testbed of wireless sensor nodes and verified the behavior of our distributed localization technique. The results obtained from the testbed are then incorporated in a simulation platform to perform scalability tests and evaluate the effects of error propagation.

We present a method for learning sparse representations shared across multiple tasks. This method is a generalization of the well-known singletask 1-norm regularization. It is based on a novel non-convex regularizer which controls the number of learned features common across the tasks. We prove that the method is equivalent to solving a convex optimization problem for which there is an iterative algorithm which converges to an optimal solution. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the former step it learns task-specific functions and in the latter step it learns common-across-tasks sparse representations for these functions. We also provide an extension of the algorithm which learns sparse nonlinear representations using kernels. We report experiments on simulated and real data sets which demonstrate that the proposed method can both improve the performance relative to learning each task independently and lead to a few learned features common across related tasks. Our algorithm can also be used, as a special case, to simply select -not learn -a few common variables across the tasks 3 .

Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic ( 2 ) error term added to a sparsity-inducing (usually 1 ) regularizater. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex regularizer. We propose iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian (i.e., separable in the unknowns) plus the original sparsity-inducing regularizer; our approach is suitable for cases in which this subproblem can be solved much more rapidly than the original problem. Under mild conditions (namely convexity of the regularizer), we prove convergence of the proposed iterative algorithm to a minimum of the objective function.

Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and Pthreads leave ML experts repeatedly solving the same design challenges. By targeting common patterns in ML, we developed GraphLab, which improves upon abstractions like MapReduce by compactly expressing asynchronous iterative algorithms with sparse computational dependencies while ensuring data consistency and achieving a high degree of parallel performance. We demonstrate the expressiveness of the GraphLab framework by designing and implementing parallel versions of belief propagation, Gibbs sampling, Co-EM, Lasso and Compressed Sensing. We show that using GraphLab we can achieve excellent parallel performance on large scale real-world problems.

Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory.

A maximum likelihood (ML) acoustic source location estimation method is presented for the application in a wireless ad hoc sensor network. This method uses acoustic signal energy measurements taken at individual sensors of an ad hoc wireless sensor network to estimate the locations of multiple acoustic sources. Compared to the existing acoustic energy based source localization methods, this proposed ML method delivers more accurate results and offers the enhanced capability of multiple source localization. A multiresolution search algorithm and an expectation-maximization (EM) like iterative algorithm are proposed to expedite the computation of source locations. The Cramér-Rao Bound (CRB) of the ML source location estimate has been derived. The CRB is used to analyze the impacts of sensor placement to the accuracy of location estimates for single target scenario. Extensive simulations have been conducted. It is observed that the proposed ML method consistently outperforms existing acoustic energy based source localization methods. An example applying this method to track military vehicles using real world experiment data also demonstrates the performance advantage of this proposed method over a previously proposed acoustic energy source localization method.

This paper studies the problem of finding an optimal subcarrier and power allocation strategy for downlink communication to multiple users in an orthogonal-frequency-division multiplexing-based wireless system. The problem of minimizing total power consumption with constraints on bit-error rate and transmission rate for users requiring different classes of service is formulated and simple algorithms with good performance are derived. The problem of joint allocation is divided into two steps. In the first step, the number of subcarriers that each user will get is determined based on the users' average signal-to-noise ratio. The algorithm is shown to find the distribution of subcarriers that minimizes the total power required when every user experiences a flat-fading channel. In the second stage of the algorithm, it finds the best assignment of subcarriers to users. Two different approaches are presented, the rate-craving greedy algorithm and the amplitude-craving greedy algorithm. Numerical results demonstrate that the proposed low complexity algorithms offer comparable performance with an existing iterative algorithm.

We demonstrate a hard-x-ray microscope that does not use a lens and is not limited to a small field of view or an object of finite size. The method does not suffer any of the physical constraints, convergence problems, or defocus ambiguities that often arise in conventional phase-retrieval diffractive imaging techniques. Calculation times are about a thousand times shorter than in current iterative algorithms. We need no a priori knowledge about the object, which can be a transmission function with both modulus and phase components. The technique has revolutionary implications for x-ray imaging of all classes of specimen.

Energy efficiency is becoming increasingly important for small form factor mobile devices, as battery technology has not kept up with the growing requirements stemming from ubiquitous multimedia applications. This paper addresses link adaptive transmission for maximizing energy efficiency, as measured by the "throughput per Joule" metric. In contrast to the existing water-filling power allocation schemes that maximize throughput subject to a fixed overall transmit power constraint, our scheme maximizes energy efficiency by adapting both overall transmit power and its allocation, according to the channel states and the circuit power consumed. We demonstrate the existence of a unique globally optimal link adaptation solution and develop iterative algorithms to obtain it. We further consider the special case of flat-fading channels to develop an upper bound on energy efficiency and to characterize its variation with bandwidth, channel gain and circuit power. Our results for OFDM systems demonstrate improved energy savings with energy optimal link adaptation as well as illustrate the fundamental tradeoff between energy-efficient and spectrum-efficient transmission.

This tutorial paper discusses the use of iterative restoration algorithms for the removal of linear blurs from photographic Images which may also be assumed to be degraded by pointwise nonlineariries such as film saturation and additive noise. lterative algorithms are particularly attractive for this application because they allow for the incorporation of various types of prior knowledge about the class of feasible solutions, because they can be used to remove nonstationary blurs, and because they are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms aftera finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed. Ringing artifacts are common with most image restoration methods. It is shown that these artifacts can be significantly reduced both by using constraints and also by making the algorithms spatially adaptive. Some variations on the basic iterations that accelerate the rate of convergence are discussed and numerous examples are presented.

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The "COSSO" is a method of regularization with the penalty functional being the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. The COSSO provides a unified framework for several recent proposals for model selection in linear models and smoothing spline ANOVA models. Theoretical properties, such as the existence and the rate of convergence of the COSSO estimator, are studied. In the special case of a tensor product design with periodic functions, a detailed analysis reveals that the COSSO does model selection by applying a novel soft thresholding type operation to the function components. We give an equivalent formulation of the COSSO estimator which leads naturally to an iterative algorithm. We compare the COSSO with the MARS, a popular method that builds functional ANOVA models, in simulations and real examples. The COSSO method can be extended to classification problems and we compare its performance with those of a number of machine learning algorithms on real datasets. The COSSO gives very competitive performances in these studies.

This paper describes a mel-cepstral analysis method and its adaptive algorithm. In the proposed method, we apply the criterion used in the unbiased estimation of log spectrum to the spectral model represented by the melcepstral coefficients. To solve the non-linear minimization problem involved in the method, we give an iterative algorithm whose convergence is guaranteed. Furthermore, we derive an adaptive algorithm for the mel-cepstral analysis by introducing an instantaneous estimate for gradient of the criterion. The adaptive mel-cepstral analysis system is implemented with an IIR adaptive filter which has an exponential transfer function, and whose stability is guaranteed. We also present examples of speech analysis and results of an isolated word recognition experiment.

An advanced random phase-shifting algorithm to extract phase distributions from randomly phase-shifted interferograms is proposed. The algorithm is based on a least-squares iterative procedure, but it copes with the limitation of the existing iterative algorithms by separating a frame-to-frame iteration from a pixel-to-pixel iteration. The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. The algorithm is simple, fast, and fully automatic. A computer simulation is conducted to prove the concept.

Decomposing video frames into coherent two-dimensional motion layers is a powerful method for representing videos. Such a representation provides an intermediate description that enables applications such as object tracking, video summarization and visualization, video insertion, and sprite-based video compression. Previous work on motion layer analysis has largely concentrated on two-frame or multiframe batch formulations. The temporal coherency of motion layers and the domain constraints on shapes have not been exploited. This paper introduces a complete dynamic motion layer representation in which spatial and temporal constraints on shape, motion, and layer appearance are modeled and estimated in a maximum a posteriori (MAP) framework using the generalized expectation-maximization (EM) algorithm. In order to limit the computational complexity of tracking arbitrarily shaped layer ownership, we propose a shape prior that parameterizes the representation of shape and prevents motion layers from evolving into arbitrary shapes. In this work, a Gaussian shape prior is chosen to specifically develop a near real-time tracker for vehicle tracking in aerial videos. However, the general idea of using a parametric shape representation as part of the state of a tracker is a powerful one that can be extended to other domains as well. Based on the dynamic layer representation, an iterative algorithm is developed for continuous object tracking over time. The proposed method has been successfully applied in an airborne vehicle tracking system. Its performance is compared with that of a correlation-based tracker and a motion change-based tracker to demonstrate the advantages of the new method. Examples of tracking when the backgrounds are cluttered and the vehicles undergo various rigid motions and complex interactions such as passing, turning, and stop-and-go demonstrate the strength of the complete dynamic layer representation.

Indoor positioning systems (IPSs) locate objects in 4 closed structures such as office buildings, hospitals, stores, fac-5 tories, and warehouses, where Global Positioning System devices 6 generally do not work. Most available systems apply wireless 7 concepts, optical tracking, and/or ultrasound. This paper presents 8 a standalone IPS using radio frequency identification (RFID) 9 technology. The concept is based on an object carrying an RFID 10 reader module, which reads low-cost passive tags installed next to 11 the object path. A positioning system using a Kalman filter is pro-12 posed. The inputs of the proposed algorithm are the measurements 13 of the backscattered signal power propagated from nearby RFID 14 tags and a tag-path position database. The proposed algorithm 15 first estimates the location of the reader, neglecting tag-reader 16 angle-path loss. Based on the location estimate, an iterative pro-17 cedure is implemented, targeting the estimation of the tag-reader 18 angle-path loss, where the latter is iteratively compensated from 19 the received signal strength information measurement. Experi-20 mental results are presented, illustrating the high performance of 21 the proposed positioning system. 22 Index Terms-Indoor positioning system (IPS), Kalman filter, 23 localization. 24 I. INTRODUCTION 25 R ADIO FREQUENCY IDENTIFICATION (RFID) sys-26 tems rely on two main components to fulfill their objec-27 tive. A reader coupled with an antenna that interrogates multiple 28 tags. The tags should be activated by the interrogation and reply 29 by sending a unique identification string back at the reader. The 30 generic use of RFID systems is large-scale inventory monitor-31 ing. The geographic range of the interrogation depends on the 32 types of tag used: passive, semipassive, or active. Passive tags 33 provide the least range of the three, but it is an attractive option 34 due to the minimal maintenance required. The use of RFID 35 for indoor localization has been studied extensively. Different 36 approaches have been investigated, differing in the placement 37 of tags, types of tags used, and the types of sensing systems 38 whose data have been fused with the information gained from 39 the RFID system. The following presents a discussion of 40 some RFID localization projects and presents a table summary 41 (Table I) showing the different aspects.

In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x, u, w) of the zero-sum game instead of solving for the state dependent value function V (x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) modelfree approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft. ᭧

An efficient and general multiple kernel learning (MKL) algorithm has been recently proposed by . This approach has opened new perspectives since it makes the MKL approach tractable for large-scale problems, by iteratively using existing support vector machine code. However, it turns out that this iterative algorithm needs several iterations before converging towards a reasonable solution. In this paper, we address the MKL problem through an adaptive 2-norm regularization formulation. Weights on each kernel matrix are included in the standard SVM empirical risk minimization problem with a ℓ1 constraint to encourage sparsity. We propose an algorithm for solving this problem and provide an new insight on MKL algorithms based on block 1-norm regularization by showing that the two approaches are equivalent. Experimental results show that the resulting algorithm converges rapidly and its efficiency compares favorably to other MKL algorithms.

The present paper describes a mathematical model for evaluating cooling potential of green roof and solar thermal shading in buildings. A control volume approach based on finite difference methods is used to analyze the components of green roof, viz. green canopy, soil and support layer. Further, these individual decoupled models are integrated using Newton's iterative algorithm until the convergence for continuity of interface state variables is achieved. The green roof model is incorporated in the building simulation code using fast Fourier transform (FFT) techniques in Matlab. The model is validated against the experimental data from a similar green roof-top garden in Yamuna Nagar (India), and is then used to predict variations in canopy air temperature, entering heat flux through roof and indoor air temperature. The model is found to be very accurate in predicting green canopy-air temperature and indoor-air temperature variations (error range 73.3%, 76.1%, respectively). These results are further used to study thermal performance of green roof combined with solar shading. Cooling potential of green roof is found adequate (3.02 kWh per day for LAI of 4.5) to maintain an average room air temperature of 25.7 1C. The present model can be easily coupled to different greenhouse and building simulation codes. r

Abstract—The task of reconstructing an object from its projec-tions via tomographic methods is a time-consuming process due to the vast complexity of the data. For this reason, manufacturers of equipment for medical computed tomography (CT) rely mostly on special application ...

The performance of web search engines may often deteriorate due to the diversity and noisy information contained within web pages. User click-through data can be used to introduce more accurate description (metadata) for web pages, and to improve the search performance. However, noise and incompleteness, sparseness, and the volatility of web pages and queries are three major challenges for research work on user click-through log mining. In this paper, we propose a novel iterative reinforced algorithm to utilize the user click-through data to improve search performance. The algorithm fully explores the interrelations between queries and web pages, and effectively finds "virtual queries" for web pages and overcomes the challenges discussed above. Experiment results on a large set of MSN click-through log data show a significant improvement on search performance over the naive query log mining algorithm as well as the baseline search engine.

In this paper, a new method to filter coherency matrices of polarimetric or interferometric data is presented. For each pixel, an adaptive neighborhood (AN) is determined by a region growing technique driven exclusively by the intensity image information. All the available intensity images of the polarimetric and interferometric terms are fused in the region growing process to ensure the validity of the stationarity assumption. Afterward, all the pixels within the obtained AN are used to yield the filtered values of the polarimetric and interferometric coherency matrices, which can be derived either by direct complex multilooking or from the locally linear minimum mean-squared error (LLMMSE) estimator. The entropy/alpha/anisotropy decomposition is then applied to the estimated polarimetric coherency matrices, and coherence optimization is performed on the estimated polarimetric and interferometric coherency matrices. Using this decomposition, unsupervised classification for land applications by an iterative algorithm based on a complex Wishart density function is also applied. The method has been tested on airborne high-resolution polarimetric interferometric synthetic aperture radar (POL-InSAR) images (Oberpfaffenhofen area-German Space Agency). For comparison purposes, the two estimation techniques (complex multilooking and LLMMSE) were tested using three different spatial supports: a fix-sized symmetric neighborhood (boxcar filter), directional nonsymmetric windows, and the proposed AN. Subjective and objective performance analysis, including coherence edge detection, receiver operating characteristics plots, and bias reduction tables, recommends the proposed algorithm as an effective POL-InSAR postprocessing technique.

This paper studies the robust beamforming design for a multi-antenna cognitive radio (CR) network, which transmits to multiple secondary users (SUs) and coexists with a primary network of multiple users. We aim to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINRs) of the SUs, subject to the constraints of the total SU transmit power and the received interference power at the primary users (PUs) by optimizing the beamforming vectors at the SU transmitter based on imperfect channel state information (CSI). To model the uncertainty in CSI, we consider a bounded region for both cases of channel matrices and channel covariance matrices. As such, the optimization is done while satisfying the interference constraints for all possible CSI error realizations. We shall first derive equivalent conditions for the interference constraints and then convert the problems into the form of semi-definite programming (SDP) with the aid of rank relaxation, which leads to iterative algorithms for obtaining the robust optimal beamforming solution. Results demonstrate the achieved robustness and the performance gain over conventional approaches and that the proposed algorithms can obtain the exact robust optimal solution with high probability.

AbstractÐIn an earlier work, we have introduced the problem of reconstructing a super-resolution image sequence from a given low resolution sequence. We proposed two iterative algorithms, the R-SD and the R-LMS, to generate the desired image sequence. These algorithms assume the knowledge of the blur, the down-sampling, the sequences motion, and the measurements noise characteristics, and apply a sequential reconstruction process. It has been shown that the computational complexity of these two algorithms makes both of them practically applicable. In this paper, we rederive these algorithms as approximations of the Kalman filter and then carry out a thorough analysis of their performance. For each algorithm, we calculate a bound on its deviation from the Kalman filter performance. We also show that the propagated information matrix within the R-SD algorithm remains sparse in time, thus ensuring the applicability of this algorithm. To support these analytical results we present some computer simulations on synthetic sequences, which also show the computational feasibility of these algorithms.

We propose an on-line algorithm for simultaneous localization and mapping of dynamic environments. Our algorithm is capable of differentiating static and dynamic parts of the environment and representing them appropriately on the map. Our approach is based on maintaining two occupancy grids. One grid models the static parts of the environment, and the other models the dynamic parts of the environment. The union of the two grid maps provides a complete description of the environment over time. We also maintain a third map containing information about static landmarks detected in the environment. These landmarks provide the robot with localization. Results in simulation and real robots experiments show the efficiency of our approach and also show how the differentiation of dynamic and static entities in the environment and SLAM can be mutually beneficial.

It sometimes happens, for instance in case-control studies, that a classifier is trained on a data set which does not reflect the true a priori probabilities of the target classes on real-world data. This may have a negative effect on the classification accuracy obtained on the real-world data set, especially when the classifier&#39;s decisions are based on th ea posteriori

This paper reviews a framework for numerically analyzing dynamic interactions in imperfectly competitive industries. The framework dates back to Ericson & Pakes (1995), but it is based on equilibrium notions that had been available for some time before, and it has been extended in many ways by different authors since. The frame-* We would like to thank numerous colleagues for helpful discussions. Joe Harrington, Ken Judd, Rob Porter, and Michael Riordan gave us useful feedback on an earlier draft of this chapter. Pakes would like to thank his NSF grant for financial support and acknowledge the important role of Richard Ericson and Paul McGuire in developing the techniques reported on here. This paper supercedes his NBER discussion paper with the same title (Pakes 2000).

This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical examples.

The selection of multiple regularization parameters is considered in a generalized L-curve framework. Multiple-dimensional extensions of the L-curve for selecting multiple regularization parameters are introduced, and a minimum distance function (MDF) is developed for approximating the regularization parameters corresponding to the generalized corner of the L-hypersurface. For the single-parameter (i.e. L-curve) case, it is shown through a model that the regularization parameters minimizing the MDF essentially maximize the curvature of the L-curve. Furthermore, for both the single-and multiple-parameter cases the MDF approach leads to a simple fixed-point iterative algorithm for computing regularization parameters. Examples indicate that the algorithm converges rapidly thereby making the problem of computing parameters according to the generalized corner of the L-hypersurface computationally tractable.

Component averaging (CAV) is introduced as a new iterative parallel technique suitable for large and sparse unstructured systems of linear equations. It simultaneously projects the current iterate onto all the system's hyperplanes, and is thus inherently parallel. However, instead of orthogonal projections and scalar weights (as used, for example, in Cimmino's method), it uses oblique projections and diagonal weighting matrices, with weights related to the sparsity of the system matrix. These features provide for a practical convergence rate which approaches that of algebraic reconstruction technique (ART) (Kaczmarz's row-action algorithm) ± even on a single processor. Furthermore, the new algorithm also converges in the inconsistent case. A proof of convergence is provided for unit relaxation, and the fast convergence is demonstrated on image reconstruction problems of the Herman head phantom obtained within the SNARK93 image reconstruction software package. Both reconstructed images and convergence plots are presented. The practical consequences of the new technique are far reaching for real-world problems in which iterative algorithms are used for solving large, sparse, unstructured and often inconsistent systems of linear equations. Ó

We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of oriented points, we introduce a variational definition for an oriented point that is most rotationally symmetric with respect to S . Our formulation effectively utilizes normal information to compensate for the missing data and leads to robust curve skeleton computation over regions of a shape that are generally cylindrical. We present an iterative algorithm via planar cuts to compute the ROSA of a point cloud. This is complemented by special handling of non-cylindrical joint regions to obtain a centered, topologically clean, and complete 1D skeleton. We demonstrate that quality curve skeletons can be extracted from a variety of shapes captured by incomplete point clouds. Finally, we show how our...

Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigenvalues. This paper also investigates the effects when unmatched projector/backprojector pairs are used.

New radiobiological models are used to describe tumour and normal tissue reactions and to account for their dependence on the irradiated volume and inhomogeneities o f the delivered dose distribution and cell sensitivity. The probability of accomplishing complication-free tumour control is maximized by an iterative algorithm. The algorithm is demonstrated by applying it to a one-dimensional (ID) tumour model but also to a more clinically relevant 2 0 case. The new algorithm is n-dimensional 50 it could simultaneously optimize the dose delivery in a 3 0 volume and io principle also select the ideal beam orientations, beam modalities (photons, electrons, neutrons, etc) and optimal spectral distributions of the corresponding modalities. To make calculation time reasonable, 2 0-3 0 problems are most practical, and suitable beam orientations are preselected by the choice of irradiation kernel. The energy deposition kernel should therefore be selected in order to avoid irradiation through organs at risk. Clinically established dose response parameters for the tissues of interest are used to make the optimization as relevant as possible to the clinical problems at hand. The algorithm can be used even with a poorly selected kernel because it will always, as far as passible, avoid irradiating organs at risk. The generated dose distribution will be optimal with respect to the spatial distribution and assumed radiobiological properties of the tumour and normal tisues at risk for the kernel chosen. More specifically the probability of achieving tumour control without fatal complications in normal tissues is maximized. In the clinical examples a reduced tumour dose is seen at the border to sensitive organs at risk, but instead an increased dose just inside the tumour border is generated. The increased tumour dose has the effect that the dose fall-off is as steep as possible at the border to organs at risk.

Independent component analysis (ICA) is a popular blind source separation (BSS) technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist, however the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely information maximization, maximization of non-gaussianity, joint diagonalization of cross-cumulant matrices, and second-order correlation based methods when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study the variability among different ICA algorithms and propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA, and JADE all yield reliable results; each having their strengths in specific areas. EVD, an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for the iterative ICA algorithms, it is important to investigate the variability of the estimates from different runs. We test the consistency of the iterative algorithms, Infomax and FastICA, by running the algorithm a number of times with different initializations and note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.

We consider the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. In a recent paper, Bogomolnaia and Moulin consider the case in which all agents have strict preferences, and propose the probabilistic serial (PS) mechanism; they define a new notion of efficiency, called ordinal efficiency, and prove that the probabilistic serial mechanism finds an envy-free ordinally efficient assignment. However, the restrictive assumption of strict preferences is critical to their algorithm. Our main contribution is an analogous algorithm for the full preference domain in which agents are allowed to be indifferent between objects. Our algorithm is based on a reinterpretation of the PS mechanism as an iterative algorithm to compute a "flow" in an associated network. In addition we show that on the full preference domain it is impossible for even a weak strategyproof mechanism to find a random assignment that is both ordinally efficient and envy-free. *