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 ...
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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.
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...
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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.
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) requir...
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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 expectationmaximization (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.
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-coeffici...
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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.
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...
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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.
We present a supervised learning algorithm for estimation of generic input-output relations in a real-time, online fashion. The proposed method is based on a generalized expectation-maximization approach to fit an inf...
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We present a supervised learning algorithm for estimation of generic input-output relations in a real-time, online fashion. The proposed method is based on a generalized expectation-maximization approach to fit an infinite mixture of linear experts (IMLE) to an online stream of data samples. This probabilistic model, while not fully Bayesian, can efficiently choose the number of experts that are allocated to the mixture, this way effectively controlling the complexity of the resulting model. The result is an incremental, online, and localized learning algorithm that performs nonlinear, multivariate regression on multivariate outputs by approximating the target function by a linear relation within each expert input domain and that can allocate new experts as needed. A distinctive feature of the proposed method is the ability to learn multivalued functions: one-to-many mappings that naturally arise in some robotic and computer vision learning domains, using an approach based on a Bayesian generative model for the predictions provided by each of the mixture experts. As a consequence, it is able to directly provide forward and inverse relations from the same learned mixture model. We conduct an extensive set of experiments to evaluate the proposed algorithm performance, and the results show that it can outperform state-of-the-art online function approximation algorithms in single-valued regression, while demonstrating good estimation capabilities in a multivalued function approximation context.
Retinal images (RI) are widely used to diagnose a variety of eye conditions and diseases such as myopia and diabetic retinopathy. They are inherently characterised by having non-uniform illumination and low-contrast h...
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ISBN:
(纸本)9781479903566
Retinal images (RI) are widely used to diagnose a variety of eye conditions and diseases such as myopia and diabetic retinopathy. They are inherently characterised by having non-uniform illumination and low-contrast homogeneous regions which represent a unique set of challenges for retinal image registration (RIR). This paper investigates using the expectationmaximization for principal component analysis based mutual information (EMPCA-MI) algorithm in RIR. It combines spatial features with mutual information to efficiently achieve improved registration performance. Experimental results for mono-modal RI datasets verify that EMPCA-MI together with Powell-Brent optimization affords superior robustness in comparison with existing RIR methods, including the geometrical features method.
Multimodal retinal images (RI) are extensively used for analysing various eye diseases and conditions such as myopia and diabetic retinopathy. The incorporation of either two or more RI modalities provides complementa...
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ISBN:
(纸本)9781479923410
Multimodal retinal images (RI) are extensively used for analysing various eye diseases and conditions such as myopia and diabetic retinopathy. The incorporation of either two or more RI modalities provides complementary structure information in the presence of non-uniform illumination and low-contrast homogeneous regions. It also presents significant challenges for retinal image registration (RIR). This paper investigates how the expectationmaximization for Principal Component Analysis with Mutual Information (EMPCA-MI) algorithm can effectively achieve multimodal RIR. This iterative hybrid-based similarity measure combines spatial features with mutual information to provide enhanced registration without recourse to either segmentation or feature extraction. Experimental results for clinical multimodal RI datasets comprising colour fundus and scanning laser ophthalmoscope images confirm EMPCA-MI is able to consistently afford superior numerical and qualitative registration performance compared with existing RIR techniques, such as the bifurcation structures method.
Distributed implementations of the expectation-maximization (EM) algorithm reported in literature have been proposed for applications to solve specific problems. In general, a primary requirement to derive a distribut...
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ISBN:
(纸本)9781479903566
Distributed implementations of the expectation-maximization (EM) algorithm reported in literature have been proposed for applications to solve specific problems. In general, a primary requirement to derive a distributed solution is that the structure of the centralized version enables the computation involving global information in a distributed fashion. This paper treats the problem of distributed estimation of Gaussian densities by means of the EM algorithm in wireless sensor networks using diffusion strategies, where the information is gradually diffused across the network for the computation of the global functions. The low-complexity implementation presented here is based on a two time scale operation for information averaging and diffusion. The convergence to a fixed point of the centralized solution has been studied and the appealing results motivates our choice for this model. Numerical examples provided show that the performance of the distributed EM is, in practice, equal to that of the centralized scheme.
An introduction is presented in which the editor discusses various reports within the issue on topics including areal interpolation methods, expectation-maximization algorithms and dasymetric interpolation algorithm.
An introduction is presented in which the editor discusses various reports within the issue on topics including areal interpolation methods, expectation-maximization algorithms and dasymetric interpolation algorithm.
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