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.

Canny-VO: Visual Odometry With RGB-D Cameras Based on Geometric 3-D–2-D Edge Alignment

Abstract: This paper reviews the classical problem of free-form curve registration and applies it to an efficient RGB-D visual odometry system called Canny-VO, as it efficiently tracks all Canny edge features extracted from the images. Two replacements for the distance transformation commonly used in edge registration are proposed: approximate nearest neighbor fields and oriented nearest neighbor fields. 3-D–2-D edge alignment benefits from these alternative formulations in terms of both efficiency and accuracy. It removes the need for the more computationally demanding paradigms of data-to-model registration, bilinear interpolation, and subgradient computation. To ensure robustness of the system in the presence of outliers and sensor noise, the registration is formulated as a maximum a posteriori problem and the resulting weighted least-squares objective is solved by the iteratively reweighted least-squares method. A variety of robust weight functions are investigated and the optimal choice is made based on the statistics of the residual errors. Efficiency is furthermore boosted by an adaptively sampled definition of the nearest neighbor fields. Extensive evaluations on public SLAM benchmark sequences demonstrate state-of-the-art performance and an advantage over classical Euclidean distance fields.

Maximum a posteriori Based Decoding for CTC Acoustic Models.

Abstract: This paper presents a novel decoding framework for connectionist temporal classification (CTC)-based acoustic models (AM). Although CTC-based AM inherently has the property of a language model (LM) in itself, an external LM trained with a large text corpus is still essential to obtain the best results. In the previous literatures, a naive interpolation of the CTCbased AM score and the external LM score was used, although there is no theoretical justification for it. In this paper, we propose a theoretically more sound decoding framework derived from a maximization of the posterior probability of a word sequence given an observation. In our decoding framework, a subword LM (SLM) is newly introduced to coordinate the CTCbased AM score and the word-level LM score. In experiments with the Wall Street Journal (WSJ) corpus and Corpus of Spontaneous Japanese (CSJ), our proposed framework consistently achieved improvements of 7.4 – 15.3 % over the conventional interpolation-based framework. In the CSJ experiment, given 586 hours of training data, the CTC-based AM finally achieved a 6.7 % better word error rate than the baseline method with deep neural networks and hidden Markov models.

On the maximum likelihood estimation of the location and scale parameters of exponential distribution based on multiply Type II censored samples

Abstract: The maximum likelihood (ML) estimation of the location and scale parameters of an exponential distribution based on singly and doubly censored samples is given When the sample is multiply censored (some middle observations being censored), however, the ML method does not admit explicit solutions In this case we present a simple approximation to the likelihood equation and derive explicit estimators which are linear functions of order statistics Finally, we present some examples to illustrate this method of estimation

Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy

Abstract: We present efficient algorithms for image restoration by using the maximum a posteriori (MAP) method. Assuming Gaussian or Poisson statistics for the noise and either a Gaussian or an entropy prior distribution for the image, corresponding functionals are formulated and minimized to produce MAP estimations. Efficient algorithms are presented for finding the minimum of these functionals in the presence of nonnegativity and support constraints. Performance was tested by using simulated three-dimensional (3-D) imaging with a fluorescence confocal laser scanning microscope. Results are compared with those from two existing algorithms for superresolution in fluorescence imaging. An example is given of the restoration of a 3-D confocal image of a biological specimen.

Quantitative Susceptibility Mapping (QSM) Algorithms: Mathematical Rationale and Computational Implementations

Abstract: Quantitative susceptibility mapping (QSM) solves the magnetic field-to-magnetization (tissue susceptibility) inverse problem under conditions of noisy and incomplete field data acquired using magnetic resonance imaging. Therefore, sophisticated algorithms are necessary to treat the ill-posed nature of the problem and are reviewed here. The forward problem is typically presented as an integral form, where the field is the convolution of the dipole kernel and tissue susceptibility distribution. This integral form can be equivalently written as a partial differential equation (PDE). Algorithmic challenges are to reduce streaking and shadow artifacts characterized by the fundamental solution of the PDE. Bayesian maximum a posteriori estimation can be employed to solve the inverse problem, where morphological and relevant biomedical knowledge (specific to the imaging situation) are used as priors. As the cost functions in Bayesian QSM framework are typically convex, solutions can be robustly computed using a gradient-based optimization algorithm. Moreover, one can not only accelerate Bayesian QSM, but also increase its effectiveness at reducing shadows using prior knowledge based preconditioners. Improving the efficiency of QSM is under active development, and a rigorous analysis of preconditioning needs to be carried out for further investigation.