Topic
Maximum a posteriori estimation
About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.
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TL;DR: The authors present an alternative method for the incorporation of anatomical information into PET image reconstruction, in which they use segmented magnetic resonance (MR) images to assign tissue composition to PET image pixels.
Abstract: The use of anatomical information to improve the quality of reconstructed images in positron emission tomography (PET) has been extensively studied. A common strategy has been to include spatial smoothing within boundaries defined from the anatomical data. The authors present an alternative method for the incorporation of anatomical information into PET image reconstruction, in which they use segmented magnetic resonance (MR) images to assign tissue composition to PET image pixels. The authors model the image as a sum of activities for each tissue type, weighted by the assigned tissue composition. The reconstruction is performed as a maximum a posteriori (MAP) estimation of the activities of each tissue type. Two prior functions, defined for tissue-type activities, are considered. The algorithm is tested in realistic simulations employing a full physical model of the PET scanner.
67 citations
23 Oct 1995
TL;DR: An approximate ML estimator for the hyperparameters of a Gibbs prior which can be computed simultaneously with a maximum a posteriori (MAP) image estimate is described.
Abstract: We describe an approximate ML estimator for the hyperparameters of a Gibbs prior which can be computed simultaneously with a maximum a posteriori (MAP) image estimate. The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one dimensional densities. We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman bound can be used to optimize the approximation for a restricted class of problems.
67 citations
14 Mar 2010
TL;DR: Algorithms for robust linear regression by leveraging the connection between the problems of robust regression and sparse signal recovery and empirical Bayesian inference based algorithms are developed.
Abstract: In this paper, we develop algorithms for robust linear regression by leveraging the connection between the problems of robust regression and sparse signal recovery. We explicitly model the measurement noise as a combination of two terms; the first term accounts for regular measurement noise modeled as zero mean Gaussian noise, and the second term captures the impact of outliers. The fact that the latter outlier component could indeed be a sparse vector provides the opportunity to leverage sparse signal reconstruction methods to solve the problem of robust regression. Maximum a posteriori (MAP) based and empirical Bayesian inference based algorithms are developed for this purpose. Experimental studies on simulated and real data sets are presented to demonstrate the effectiveness of the proposed algorithms.
66 citations
TL;DR: The segmentation results show that the proposed JMCMS improves the classification accuracy, and in particular, boundary localization and detection over the methods using a single context at comparable computational complexity.
Abstract: In this paper, a joint multicontext and multiscale (JMCMS) approach to Bayesian image segmentation is proposed. In addition to the multiscale framework, the JMCMS applies multiple context models to jointly use their distinct advantages, and we use a heuristic multistage, problem-solving technique to estimate sequential maximum a posteriori of the JMCMS. The segmentation results on both synthetic mosaics and remotely sensed images show that the proposed JMCMS improves the classification accuracy, and in particular, boundary localization and detection over the methods using a single context at comparable computational complexity.
66 citations
TL;DR: A novel conditional statistical shape model in which the condition can be relaxed instead of being treated as a hard constraint is presented and compared with three other state of the art methods shows the superior performance of the proposed algorithm.
66 citations