Cauchy Markov random field priors for Bayesian inversion

Gaussian Markov Random Field Priors for Inverse Problems

In this paper, our focus is on the connections between the methods of (quadratic) regularization for inverse problems and Gaussian Markov random field (GMRF) priors for problems in spatial statistics. We begin with the most standard GMRFs defined on a uniform computational grid, which correspond to the oft-used discrete negative-Laplacian regularization matrix. Next, we present a class of GMRFs...

Bayesian mapping of brain regions using compound Markov random field priors

Solutions for Bayesian Markov random field estimation problems

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . 1.1 Markov Random Field Models 1 1.2 An Overview of Optimal Estimators and Approximations . . . . . . . 2 1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Goa...

Bayesian Inference for Layer Representation with Mixed Markov Random Field

This paper presents a Bayesian inference algorithm for image layer representation [26], 2.1D sketch [6], with mixed Markov random field. 2.1D sketch is an very important problem in low-middle level vision with a synthesis of two goals: segmentation and 2.5D sketch, in other words, it is to consider 2D segmentation by incorporating occulision/depth explicitly to get the partial order of final se...

Random Projections with Bayesian Priors

The technique of random projection is one of dimension reduction, where high dimensional vectors in RD are projected down to a smaller subspace in Rk. Certain forms of distances or distance kernels such as Euclidean distances, inner products [10], and lp distances [12] between high dimensional vectors are approximately preserved in this smaller dimensional subspace. Word vectors which are repre...