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.

A concave prior penalizing relative differences for maximum-a-posteriori reconstruction in emission tomography

Abstract: A well-known problem with maximum likelihood reconstruction in emission tomography is the excessive noise propagation. To prevent this, the objective function is often extended with a Gibbs prior favoring smooth solutions. We hypothesize that the following three requirements should produce a useful and conservative Gibbs prior for emission tomography: 1) the prior function should be concave to ensure that the posterior has a unique maximum; 2) the prior should penalize relative differences rather than absolute differences; 3) the prior should be tolerant for "large" differences between neighboring pixels. The second requirement should avoid tuning problems caused by the large dynamic range of activity values in the reconstructed image. A simple function has been derived that meets these three requirements. Our initial evaluations indicate that the prior behaves as intended.

Tracking deformable objects with point clouds

Abstract: We introduce an algorithm for tracking deformable objects from a sequence of point clouds. The proposed tracking algorithm is based on a probabilistic generative model that incorporates observations of the point cloud and the physical properties of the tracked object and its environment. We propose a modified expectation maximization algorithm to perform maximum a posteriori estimation to update the state estimate at each time step. Our modification makes it practical to perform the inference through calls to a physics simulation engine. This is significant because (i) it allows for the use of highly optimized physics simulation engines for the core computations of our tracking algorithm, and (ii) it makes it possible to naturally, and efficiently, account for physical constraints imposed by collisions, grasping actions, and material properties in the observation updates. Even in the presence of the relatively large occlusions that occur during manipulation tasks, our algorithm is able to robustly track a variety of types of deformable objects, including ones that are one-dimensional, such as ropes; two-dimensional, such as cloth; and three-dimensional, such as sponges. Our implementation can track these objects in real time.

Self-Calibration of Rotating and Zooming Cameras

Abstract: In this paper we describe the theory and practice of self-calibration of cameras which are fixed in location and may freely rotate while changing their internal parameters by zooming. The basis of our approach is to make use of the so-called infinite homography constraint which relates the unknown calibration matrices to the computed inter-image homographies. In order for the calibration to be possible some constraints must be placed on the internal parameters of the camera. We present various self-calibration methods. First an iterative non-linear method is described which is very versatile in terms of the constraints that may be imposed on the camera calibration: each of the camera parameters may be assumed to be known, constant throughout the sequence but unknown, or free to vary. Secondly, we describe a fast linear method which works under the minimal assumption of zero camera skew or the more restrictive conditions of square pixels (zero skew and known aspect ratio) or known principal point. We show experimental results on both synthetic and real image sequences (where ground truth data was available) to assess the accuracy and the stability of the algorithms and to compare the result of applying different constraints on the camera parameters. We also derive an optimal Maximum Likelihood estimator for the calibration and the motion parameters. Prior knowledge about the distribution of the estimated parameters (such as the location of the principal point) may also be incorporated via Maximum a Posteriori estimation. We then identify some near-ambiguities that arise under rotational motions showing that coupled changes of certain parameters are barely observable making them indistinguishable. Finally we study the negative effect of radial distortion in the self-calibration process and point out some possible solutions to it.

SAR image filtering based on the heavy-tailed Rayleigh model

Abstract: Synthetic aperture radar (SAR) images are inherently affected by a signal dependent noise known as speckle, which is due to the radar wave coherence. In this paper, we propose a novel adaptive despeckling filter and derive a maximum a posteriori (MAP) estimator for the radar cross section (RCS). We first employ a logarithmic transformation to change the multiplicative speckle into additive noise. We model the RCS using the recently introduced heavy-tailed Rayleigh density function, which was derived based on the assumption that the real and imaginary parts of the received complex signal are best described using the alpha-stable family of distribution. We estimate model parameters from noisy observations by means of second-kind statistics theory, which relies on the Mellin transform. Finally, we compare the proposed algorithm with several classical speckle filters applied on actual SAR images. Experimental results show that the homomorphic MAP filter based on the heavy-tailed Rayleigh prior for the RCS is among the best for speckle removal

Bayesian estimation and experimental design in linear regression models

Abstract: Estimation and Design as a Bayesian Decision Problem Choice of a Prior Distribution Conjugate Prior Distributions Bayes Estimation of the Regression Parameter Optimality and Robustness of the Bayes Estimator Bayesian Interpretation of Estimators Using Non-Bayesian Prior Knowledge Bayes Estimation in Case of Prior Ignorance Further Problems The Design Problem for the Linear Bayes Estimator Characterization of Optimal Designs Construction of Optimal Continuous Designs Construction of Exact Optimal Designs.