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.

Neural network modeling and an uncertainty analysis in Bayesian framework: A case study from the KTB borehole site

Abstract: [1] A new probabilistic approach based on the concept of Bayesian neural network (BNN) learning theory is proposed for decoding litho-facies boundaries from well-log data. We show that how a multi-layer-perceptron neural network model can be employed in Bayesian framework to classify changes in litho-log successions. The method is then applied to the German Continental Deep Drilling Program (KTB) well-log data for classification and uncertainty estimation in the litho-facies boundaries. In this framework, a posteriori distribution of network parameter is estimated via the principle of Bayesian probabilistic theory, and an objective function is minimized following the scaled conjugate gradient optimization scheme. For the model development, we inflict a suitable criterion, which provides probabilistic information by emulating different combinations of synthetic data. Uncertainty in the relationship between the data and the model space is appropriately taken care by assuming a Gaussian a priori distribution of networks parameters (e.g., synaptic weights and biases). Prior to applying the new method to the real KTB data, we tested the proposed method on synthetic examples to examine the sensitivity of neural network hyperparameters in prediction. Within this framework, we examine stability and efficiency of this new probabilistic approach using different kinds of synthetic data assorted with different level of correlated noise. Our data analysis suggests that the designed network topology based on the Bayesian paradigm is steady up to nearly 40% correlated noise; however, adding more noise (∼50% or more) degrades the results. We perform uncertainty analyses on training, validation, and test data sets with and devoid of intrinsic noise by making the Gaussian approximation of the a posteriori distribution about the peak model. We present a standard deviation error-map at the network output corresponding to the three types of the litho-facies present over the entire litho-section of the KTB. The comparisons of maximum a posteriori geological sections constructed here, based on the maximum a posteriori probability distribution, with the available geological information and the existing geophysical findings suggest that the BNN results reveal some additional finer details in the KTB borehole data at certain depths, which appears to be of some geological significance. We also demonstrate that the proposed BNN approach is superior to the conventional artificial neural network in terms of both avoiding “over-fitting” and aiding uncertainty estimation, which are vital for meaningful interpretation of geophysical records. Our analyses demonstrate that the BNN-based approach renders a robust means for the classification of complex changes in the litho-facies successions and thus could provide a useful guide for understanding the crustal inhomogeneity and the structural discontinuity in many other tectonically complex regions.

Adaptive training method for pattern recognition

Abstract: Training data is LPC analyzed to obtain a feature parameter vector sequence, which is subjected to Viterbi segmentation using reference phoneme models to separate phonemes. Each piece of phoneme data is used to estimate a mean vector of the corresponding reference phoneme model by a maximum a posteriori estimation method. The adapted phoneme model and the corresponding reference phoneme model are used to estimate a mean vector for an unadapted phoneme model through interpolation by a vector field smoothing method. Alternatively, the mean vector of the adapted phoneme model is further smoothed by the vector field smoothing method. By this, an adapted model is obtained which has, as its parameters, the mean vector obtained for each phoneme and other corresponding parameters.

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Abstract: Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.

A parallel image segmentation algorithm using relaxation with varying neighborhoods and its mapping

Abstract: This paper presents a segmentation algorithm based on deterministic relaxation with varying neighborhood structures for the segmentation of noisy images. The image is modeled as a discrete-valued Markov random field (MRF), or equivalently a Gibbs random field, corrupted by additive, independent, Gaussian noise; although, additivity and Gaussian assumptions are not necessary for the algorithm. The algorithm seeks to determine the maximum a posteriori (MAP) estimate of the noiseless scene. Using varying neighborhoods during relaxation helps pick up certain directional features in the image which are otherwise smoothed out. The parallelism of the algorithm is underscored by providing its mapping to mesh-connected and systolic array processors suitable for VLSI implementation. Segmentation results are given for 2- and 4-level Gibbs distributed and geometric images corrupted by noise of different levels. A comparative study of this segmentation algorithm with other relaxation algorithms and a single-sweep dynamic programming algorithm, all seeking the MAP estimate, is also presented.