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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
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Journal ArticleDOI
TL;DR: An estimation approach is described for three-dimensional reconstruction from line integral projections using incomplete and very noisy data and a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion.
Abstract: An estimation approach is described for three-dimensional reconstruction from line integral projections using incomplete and very noisy data. Generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain. The object models, a statistical measurement model, and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem. For computational feasibility, a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion. The formulation and algorithm are restricted to objects whose center axis is a single-valued function of a fixed spatial coordinate. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135 degrees sector, at an average signal-to-noise ratio of 3.3. >

62 citations

Journal ArticleDOI
TL;DR: A maximum a posteriori probability (MAP) estimation method for estimating the mixing proportions for Lambertian and specular reflectance, and also, for recovering local surface normals, which reveals not only that the method accurately estimates the proportion of specular reflection, but that it also results in good surface normal reconstruction in the proximity of Speular highlights.

62 citations

Journal ArticleDOI
TL;DR: In this paper, a maximum a posteriori (MAP) technique is developed to identify solar features in cotemporal and cospatial images of line-of-sight magnetic flux, continuum intensity, and equivalent width observed with the NASA/National Solar Observatory (NSO) Spectromagnetograph (SPM).
Abstract: A maximum a posteriori (MAP) technique is developed to identify solar features in cotemporal and cospatial images of line-of-sight magnetic flux, continuum intensity, and equivalent width observed with the NASA/National Solar Observatory (NSO) Spectromagnetograph (SPM). The technique facilitates human understanding of patterns in large data sets and enables systematic studies of feature characteristics for comparison with models and observations of long-term solar activity and variability. The method uses Bayes’ rule to compute the posterior probability of any feature segmentation of a trio of observed images from per-pixel, class-conditional probabilities derived from independently-segmented training images. Simulated annealing is used to find the most likely segmentation. New algorithms for computing class-conditional probabilities from three-dimensional Gaussian mixture models and interpolated histogram densities are described and compared. A new extension to the spatial smoothing in the Bayesian prior model is introduced, which can incorporate a spatial dependence such as center-to-limb variation. How the spatial scale of training segmentations affects the results is discussed, and a new method for statistical separation of quiet Sun and quiet network is presented.

62 citations

Journal ArticleDOI
TL;DR: A novel sensing paradigm based on expander graphs is developed and a maximum a posteriori (MAP) algorithm for recovering sparse or compressible signals from Poisson observations is proposed.
Abstract: This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a maximum a posteriori (MAP) algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. We support our results with experimental demonstrations of reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process.

62 citations

Journal ArticleDOI
TL;DR: A unified framework is proposed, based on the maximum a posteriori probability principle, by taking all these effects into account simultaneously in order to improve image segmentation performance of brain magnetic resonance (MR) images.
Abstract: Noise, partial volume (PV) effect, and image-intensity inhomogeneity render a challenging task for segmentation of brain magnetic resonance (MR) images. Most of the current MR image segmentation methods focus on only one or two of the above-mentioned effects. The objective of this paper is to propose a unified framework, based on the maximum a posteriori probability principle, by taking all these effects into account simultaneously in order to improve image segmentation performance. Instead of labeling each image voxel with a unique tissue type, the percentage of each voxel belonging to different tissues, which we call a mixture, is considered to address the PV effect. A Markov random field model is used to describe the noise effect by considering the nearby spatial information of the tissue mixture. The inhomogeneity effect is modeled as a bias field characterized by a zero mean Gaussian prior probability. The well-known fuzzy C-mean model is extended to define the likelihood function of the observed image. This framework reduces theoretically, under some assumptions, to the adaptive fuzzy C-mean (AFCM) algorithm proposed by Pham and Prince. Digital phantom and real clinical MR images were used to test the proposed framework. Improved performance over the AFCM algorithm was observed in a clinical environment where the inhomogeneity, noise level, and PV effect are commonly encountered.

62 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202364
2022125
2021211
2020244
2019250
2018236