An Efficient Gaussian Filter Based on Gaussian Symmetric Markov Random Field

Circularly-Symmetric Gaussian random vectors

A number of basic properties about circularly-symmetric Gaussian random vectors are stated and proved here. These properties are each probably well known to most researchers who work with Gaussian noise, but I have not found them stated together with simple proofs in the literature. They are usually viewed as too advanced or too detailed for elementary texts but are used (correctly or incorrect...

An Efficient Constrained Gaussian Particle Filter

The paper deals with a state estimation of nonlinear stochastic dynamic systems subject to a nonlinear inequality constraint. A special focus is paid to particle filters, which provide an estimate of the whole probability density as opposed to the local filters, such as the extended Kalman filter or the unscented Kalman filter, which provide a point estimate only. Within the particle filtering ...

Autoregressive Gaussian Random Vectors of First Order

Ground-Glass-Opacity Nodule Detection and Segmentation Based on Dot Filter and Gaussian Mixture Model Hidden Markov Random Field

Aiming at solving the problem that ground-glass-opacity (GGO) nodules cannot be detected directly by “dot” filter, a method based on vessel elimination and “dot” filter was used to detect them. Because of spatial properties consideration, it is proposed to use hidden Markov random field based on Gaussian Mixture Model (GMMHMRF) and Expectation-Maximization (EM) algorithm to segment GGO nodule i...

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...