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Convergence and Stability of Iteratively Re-weighted Least Squares algorithms

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第1期62卷 183-195页

作者： Ba, Demba Babadi, Behtash Purdon, Patrick L. Brown, Emery N. MIT Dept Brain & Cognit Sci Cambridge MA 02139 USA Massachusetts Gen Hosp Dept Anesthesia Crit Care & Pain Med Boston MA 02114 USA MIT Harvard MIT Div Hlth Sci & Technol Cambridge MA 02139 USA

In this paper, we study the theoretical properties of iteratively re-weighted least squares (IRLS) algorithms and their utility in sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between the IRLS algorithms and a class of expectation-maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribution. The EM formalism, as well as the connection to GSMs, allow us to establish that the IRLS algorithms minimize smooth versions of the l(nu) 'norms', for 0 < nu <= 1. We leverage EM theory to show that the limit points of the sequence of IRLS iterates are stationary points of the smooth "norm" minimization problem on the constraint set. We employ techniques from Compressive Sampling (CS) theory to show that the IRLS algorithm is stable, if the limit point of the iterates coincides with the global minimizer. We further characterize the convergence rate of the IRLS algorithm, which implies global linear convergence for nu = 1 and local super-linear convergence for 0 < nu < 1. We demonstrate our results via simulation experiments. The simplicity of IRLS, along with the theoretical guarantees provided in this contribution, make a compelling case for its adoption as a standard tool for sparse signal recovery.

关键词： Compressive sampling constrained maximum likelihood estimation Gaussian scale mixtures expectation-maximization algorithms mathematical programming

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The Path Inference Filter: Model-Based Low-Latency Map Matching of Probe Vehicle Data

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2014年第2期15卷 507-529页

作者： Hunter, Timothy Abbeel, Pieter Bayen, Alexandre Univ Calif Berkeley Coll Engn Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

We consider the problem of reconstructing vehicle trajectories from sparse sequences of GPS points, for which the sampling interval is between 1 s and 2 min. We introduce a new class of algorithms, which are altogether called the path inference filter (PIF), that maps GPS data in real time, for a variety of tradeoffs and scenarios and with a high throughput. Numerous prior approaches in map matching can be shown to be special cases of the PIF presented in this paper. We present an efficient procedure for automatically training the filter on new data, with or without ground-truth observations. The framework is evaluated on a large San Francisco taxi data set and is shown to improve upon the current state of the art. This filter also provides insights about driving patterns of drivers. The PIF has been deployed at an industrial scale inside the Mobile Millennium traffic information system, and is used to map fleets of data in San Francisco and Sacramento, CA, USA;Stockholm, Sweden;and Porto, Portugal.

关键词： expectation-maximization algorithms filtering GPS data Markov random fields maximum likelihood estimation network-free data path observation generation probabilistic map matching route choice modeling

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ENHANCED RETINAL IMAGE REGISTRATION ACCURACY USING expectation MAXIMISATION AND VARIABLE BIN-SIZED MUTUAL INFORMATION

ENHANCED RETINAL IMAGE REGISTRATION ACCURACY USING EXPECTATI...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Reel, Parminder Singh Dooley, Laurence S. Wong, K. C. P. Boerner, Anko Open Univ Dept Comp & Commun Milton Keynes MK7 6AA Bucks England

ISBN: (纸本)9781479928934

While retinal images (RI) assist in the diagnosis of various eye conditions and diseases such as glaucoma and diabetic retinopathy, their innate features including low contrast homogeneous and non-uniformly illuminated regions, present a particular challenge for retinal image registration (RIR). Recently, the hybrid similarity measure, expectation maximization for Principal Component Analysis with Mutual Information (EMPCA-MI) has been proposed for RIR. This paper investigates incorporating various fixed and adaptive bin size selection strategies to estimate the probability distribution in the mutual information (MI) stage of EMPCA-MI, and analyses their corresponding effect upon RIR performance. Experimental results using a clinical mono-modal RI dataset confirms that adaptive bin size selection consistently provides both lower RIR errors and superior robustness compared to the empirically determined fixed bin sizes.

关键词： Image registration ophthalmological image processing principal component analysis mutual information expectation-maximization algorithms

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Improved Channel Estimation for Interference Cancellation in Random Access Methods for Satellite Communications 7

Improved Channel Estimation for Interference Cancellation in...

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7th Advanced Satellite Multimedia Systems Conference / 13th Signal Processing for Space Communications Workshop (ASMS/SPSC)

作者： Zidane, Karine Lacan, Jerome Boucheret, Marie-Laure Poulliat, Charly Univ Toulouse ISAE DMIA & TeSA Toulouse France Univ Toulouse IRIT ENSEEIHT Toulouse France

ISBN: (纸本)9781479958931

In the context of satellite communications, random access methods can significantly increase throughput and reduce latency over the network. The recent random access methods are based on multi-user multiple access transmission at the same time and frequency followed by iterative interference cancellation and decoding at the receiver. Generally, it is assumed that perfect knowledge of the interference is available at the receiver. In practice, the interference term has to be accurately estimated to avoid performance degradation. Several estimation techniques have been proposed lately in the case of superimposed signals. In this paper, we present an overview on existing channel estimation methods and we propose an improved channel estimation technique that combines estimation using an autocorrelation based method and the expectation-maximization algorithm, and uses pilot symbol assisted modulation to further improve the performance and achieve optimal interference cancellation.

关键词： Satellite communication Network coding Channel estimation expectation-maximization algorithms

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A Unified Approach for Representing Wireless Channels using EM-Based Finite Mixture of Gamma Distributions

A Unified Approach for Representing Wireless Channels using ...

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IEEE Global Communications Conference (GLOBECOM)

作者： Alhussein, Omar Muhaidat, Sami Liang, Jie Yoo, Paul D. Simon Fraser Univ Sch Engn Sci Burnaby BC V5A 1S6 Canada Khalifa Univ Sci Technol & Res Abu Dhabi U Arab Emirates Univ Surrey CCSR Guildford Surrey England

ISBN: (纸本)9781479974702

We present a unified framework to evaluate the error rate performance of wireless networks over generalized fading channels. In particular, we propose a new approach to represent different fading distributions by mixture of Gamma distributions. The new approach relies on the expectation-maximization (EM) algorithm in conjunction with the so-called Newton-Raphson maximization algorithm. We show that our model provides similar performance to other existing state-of-art models in both accuracy and simplicity, where accuracy is analyzed by means of mean square error (MSE). In addition, we demonstrate that this algorithm may potentially approximate any fading channel, and thus we utilize it to model both composite and non-composite fading models. We derive novel closed form expression of the raw moments of a dual-hop fixed-gain cooperative network. We also study the effective capacity of the end-to-end SNR in such networks. Numerical simulation results are provided to corroborate the analytical findings.

关键词： Mixture of gamma distributions expectation-maximization algorithms dual-hop Amplify-and-Forward (AF) semi-blind relaying

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Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第2期61卷 340-354页

作者： Ziniel, Justin Schniter, Philip Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are recovered from undersampled noisy measurements. The algorithm, AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of non-zero coefficients, and provides soft estimates of the signal vectors as well as the underlying support. Central to the proposed approach is an extension of recently developed approximate message passing techniques to the amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectation-maximization algorithm that complements AMP-MMV is described. Finally, a detailed numerical study demonstrates the power of the proposed approach and its particular suitability for application to high-dimensional problems.

关键词： Approximate message passing (AMP) belief propagation compressed sensing expectation-maximization algorithms joint sparsity Kalman filters multiple measurement vector problem statistical signal processing

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Novel Bayesian Vectorcardiographic Loop Alignment for Improved Monitoring of ECG and Fetal Movement

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 2013年第6期60卷 1580-1588页

作者： Vullings, Rik Mischi, Massimo Oei, S. Guid Bergmans, Jan W. M. Eindhoven Univ Technol Dept Elect Engn NL-5600 MB Eindhoven Netherlands Maxima Med Ctr Dept Obstet & Gynecol NL-5500 MB Veldhoven Netherlands

The continuous analysis of electrocardiographic (ECG) signals is complicated by morphological variability in the ECG due to movement of the heart. By aligning vectorcardiographic loops, movement-induced ECG variations can be partly corrected for. Existing methods for loop alignment can account for loop rotation, scaling, and time delays, but they lack the possibility to include a priori information on any of these transformations, and they are unreliable in case of low-quality signals, such as fetal ECG signals. The inclusion of a priori information might aid in the robustness of loop alignment and is, hence, proposed in this paper. We provide a generic Bayesian framework to derive our loop alignment method. In this framework, existing methods can be readily derived as well, as a simplification of our method. The loop alignment is evaluated by comparing its performance in loop alignment to two existing methods, for both adult and fetal ECG recordings. For the adult ECG recordings, a quantitative performance assessment shows that the developed method outperforms the existing method in terms of robustness. For the fetal ECG recordings, it is demonstrated that the developed method can be used to correct ECG signals for movement-induced morphology changes (enabling diagnostics) and that the method is capable of classifying recorded ECG signals to periods of fetal movement or rest (p < 0.01). This information on fetal movement can also serve as a valuable diagnostic tool.

关键词： Biomedical signal processing electrocardiography expectation-maximization algorithms fetal movement loop alignment vector cardiogram

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A Max-Product EM Algorithm for Reconstructing Markov-Tree Sparse Signals From Compressive Samples

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第23期61卷 5917-5931页

作者： Song, Zhao Dogandzic, Aleksandar Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing Markov-tree sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussian noise with an unknown variance. The signal is composed of large-and small-magnitude components identified by binary state variables whose probabilistic dependence structure is described by a Markov tree. Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys' noninformative prior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aims at maximizing the posterior distribution of the signal and its state variables given the noise variance. We construct the missing data for the EM iteration so that the complete-data posterior distribution corresponds to a hidden Marcov tree (HMT) probabilistic graphical model that contains no loops and implement its maximization (M) step via a max-product algorithm. This EM algorithm estimates the vector of state variables as well as solves iteratively a linear system of equations to obtain the corresponding signal estimate. We select the noise variance so that the corresponding estimated signal and state variables obtained upon convergence of the EM iteration have the largest marginal posterior distribution. We compare the proposed and existing state-of-the-art reconstruction methods via signal and image reconstruction experiments.

关键词： Belief propagation compressed sensing expectation-maximization algorithms hidden Markov models signal reconstruction

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Iterative Estimation of Location and Trajectory of Radioactive Sources With a Networked System of Detectors

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2013年第2期60卷 1315-1326页

作者： Deb, Budhaditya GE Global Res Adv Commun Syst Lab Niskayuna NY 12309 USA

We consider the problem of estimating the parameters (location and intensity) of multiple radioactive sources using a system of radiation detectors. The problem formulated as maximum likelihood estimation (MLE) requires the optimization of a high-dimensional objective function and presents significant computational challenges. We propose Fisher's scoring iterations approach (a special case of Newton's iterative method) for finding the MLE. While being computationally scalable, an inherent problem with this approach is finding good initial estimates specifically when multiple sources are present. We propose an expectation maximization (EM) based approach which finds the approximate distribution of the source intensity in space. Peaks in this distribution are used as initial estimates of the parameters to bootstrap the iterative MLE procedure. Next, we consider the problem of estimating the trajectory of a moving and maneuvering source. Since a priori motion model cannot be assumed, the trajectory is approximated as a set of points which again presents a high dimensional estimation problem. The trajectory estimation is posed as a constrained weighted least squares problem which is iteratively solved using the Interior Point Method (IPM). Simulation results are presented which illustrate the behavior and performance of our proposed approaches.

关键词： Estimation expectation-maximization algorithms iterative methods maximum likelihood estimation radiation imaging signal analysis-motion estimation

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Dynamic Compressive Sensing of Time-Varying Signals Via Approximate Message Passing

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第21期61卷 5270-5284页

作者： Ziniel, Justin Schniter, Philip Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.

关键词： Approximate message passing (AMP) belief propagation compressed sensing expectation-maximization algorithms time-varying sparse signals Kalman filters dynamic compressive sensing statistical signal processing

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