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.
Papers published on a yearly basis
Papers
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03 Apr 2008TL;DR: The proposed tree-search algorithm provides exact ratios of posterior probabilities for a set of high probability solutions to the sparse reconstruction problem and serves to reveal potential ambiguity among multiple candidate solutions that are ambiguous due to low signal-to-noise ratio and/or significant correlation among columns in the super-resolving regressor matrix.
Abstract: Imaging is not itself a system goal, but is rather a means to support inference tasks. For data processing with linearized signal models, we seek to report all high-probability
interpretations of the data and to report confidence labels in the form of posterior probabilities. A low-complexity recursive procedure is presented for Bayesian estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both a set of high posterior probability mixing parameters
and an approximate minimum mean squared
error (MMSE) estimate of the parameter
vector. Emphasis is given to the case of a sparse parameter vector. Numerical simulations demonstrate estimation performance and illustrate
the distinctions between MMSE estimation and maximum a posteriori probability (MAP) model selection.
The proposed tree-search algorithm provides exact ratios of posterior probabilities for a set of high probability solutions to the sparse reconstruction problem. These relative probabilities serve to reveal potential ambiguity among multiple candidate solutions that are ambiguous due to low signal-to-noise ratio and/or significant correlation among columns in the super-resolving regressor matrix.
48 citations
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TL;DR: A maximum a posteriori deconvolution framework expressly derived to improve tissue characterization is introduced and overcomes limitations associated with standard techniques by using a nonstandard prior model for the tissue response.
Abstract: Ultrasonic tissue characterization has become an area of intensive research. This procedure generally relies on the analysis of the unprocessed echo signal. Because the ultrasound echo is degraded by the non-ideal system point spread function, a deconvolution step could be employed to provide an estimate of the tissue response that could then be exploited for a more accurate characterization. In medical ultrasound, deconvolution is commonly used to increase diagnostic reliability of ultrasound images by improving their contrast and resolution. Most successful algorithms address deconvolution in a maximum a posteriori estimation framework; this typically leads to the solution of l2-norm or l1-norm constrained optimization problems, depending on the choice of the prior distribution. Although these techniques are sufficient to obtain relevant image visual quality improvements, the obtained reflectivity estimates are, however, not appropriate for classification purposes. In this context, we introduce in this paper a maximum a posteriori deconvolution framework expressly derived to improve tissue characterization. The algorithm overcomes limitations associated with standard techniques by using a nonstandard prior model for the tissue response. We present an evaluation of the algorithm performance using both computer simulations and tissue-mimicking phantoms. These studies reveal increased accuracy in the characterization of media with different properties. A comparison with state-of-the-art Wiener and l1-norm deconvolution techniques attests to the superiority of the proposed algorithm.
48 citations
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TL;DR: A novel algorithm for image segmentation via the use of the multiresolution wavelet analysis and the expectation maximization (EM) algorithm is presented, which provides an iterative and computationally simple algorithm based on the incomplete data concept.
Abstract: This article presents a novel algorithm for image seg- been developed for classification purposes. In addition, many mentation via the use of the multiresolution wavelet analysis and the authors have discovered significant advantages in the use of the expectation maximization (EM) algorithm. The development of a multiresolution concept ( 4,5 ) . Brazkovic and Neskovic presented multiresolution wavelet feature extraction scheme is based on the the Gaussian pyramid and fuzzy linking method for the adaptive Gaussian Markov random field (GMRF) assumption in mammo- detection of cancerous changes in mammograms (6). graphic image modeling. Mammographic images are hierarchically Recently, as a result of cross-fertilization of innovative ideas decomposed into different resolutions. In general, larger breast le- from image processing, spatial statistics, and statistical physics, sions are characterized by coarser resolutions, whereas higher resolu- a significant amount of research activity on image modeling and tions show finer and more detailed anatomical structures. These hier- archical variations in the anatomical features displayed by multiresolu- segmentation has also been concentrated on the two-dimensional tion decomposition are further quantified through the application of ( 2D ) Markov random field ( MRF ) . Although many of the poten- the Gaussian Markov random field. Because of its uniqueness in local- tials of MRF had been envisioned by the early works of Levy ity, adaptive features based on the nonstationary assumption of (7), McCormick and Jayaramamrhy (8), and Abend et al. (9), GMRF are defined for each pixel of the mammogram. Fibroadenomas exploitation of the powers of the MRF was not possible until are then segmented via the fuzzy C-means algorithm using these significant recent advances occurred in the appropriate mathemat- localized features. Subsequently, the segmentation results are further ical and computational tools. Chellappa and Kashyap (10 ) suc- enhanced via the introduction of a maximum a posteriori (MAP) seg- cessfully applied the noncausal autoregressive ( NCAR ) model mentation estimation scheme based on the Bayesian learning para-
48 citations
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16 Mar 2009TL;DR: A novel sparse source separation method that can estimate the number of sources and time-frequency masks simultaneously, even when the spatial aliasing problem exists is proposed, and the indeterminacy of modulus 2***k in the phase is included in the model.
Abstract: In this paper, we propose a novel sparse source separation method that can estimate the number of sources and time-frequency masks simultaneously, even when the spatial aliasing problem exists. Recently, many sparse source separation approaches with time-frequency masks have been proposed. However, most of these approaches require information on the number of sources in advance. In our proposed method, we model the phase difference of arrival (PDOA) between microphones with a Gaussian mixture model (GMM) with a Dirichlet prior. Then we estimate the model parameters by using the maximum a posteriori (MAP) estimation based on the EM algorithm. In order to avoid one cluster being modeled by two or more Gaussians, we utilize a sparse distribution modeled by the Dirichlet distributions as the prior of the GMM mixture weight. Moreover, to handle wide microphone spacing cases where the spatial aliasing problem occurs, the indeterminacy of modulus 2***k in the phase is also included in our model. Experimental results show good performance of our proposed method.
48 citations
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27 Jun 2004TL;DR: Experiments show that, Fisher boosting algorithm can generate strong classifier with less number of weaker classifiers comparing to conventional Adaboosting algorithm, that the face localization with Fisher boosting feature subspace outperforms that with PCA feature subspaces in localization accuracy and convergence rate, and that the design of hierarchical CONDENSATION framework alleviates the local minima problem which is frequently encountered by previous ASM optimization algorithms.
Abstract: We formulate face localization as a maximum a posteriori probability (MAP) problem of finding the best estimation of human face configuration in a given image. The a prior distribution for intrinsic face configuration is defined by active shape model (ASM). The likelihood model for local facial features is parameterized as mixture of Gaussians in feature space. A hierarchical CONDENSATION framework is then proposed to estimate the face configuration parameter. In order to improve the discriminative power of likelihood distribution in feature space, a new feature subspace, Fisher boosting feature space, is proposed and compared against PCA subspace and biased PCA subspace. Experiments show that, Fisher boosting algorithm can generate strong classifier with less number of weaker classifiers comparing to conventional Adaboosting algorithm as illustrated in a toy problem, that the face localization with Fisher boosting feature subspace outperforms that with PCA feature subspaces in localization accuracy and convergence rate, and that the design of hierarchical CONDENSATION framework alleviates the local minima problem which is frequently encountered by previous ASM optimization algorithms.
48 citations