In this paper we develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gau...

Face images from the Feret database [3] were convolved with a Gaussian filter and inputed to the CSU Face Identification Evaluation System (FES) [1]. Both the gallery and probe images were convolved with the Gaussian filter before being inputed to the FES. The probe images were convolved with the Gaussian filter to simulate optical defocus. The gallery images were convolved with the Gaussian fi...

This work investigates the information loss in a decimation system, i.e., in a downsampler preceded by an antialiasing filter. It is shown that, without a specific signal model in mind, the anti-aliasing filter cannot reduce information loss, while, e.g., for a simple signal-plus-noise model it can. For the Gaussian case, the optimal anti-aliasing filter is shown to coincide with the one obtain...

This article presents a new image denoising algorithm that uses Gaussian Symmetric Markov random fields based on maximum posteriori estimation. First, an model is built, and the problem was converted to estimation problem. The prior probability of can be estimated using Gibbs distribution, which equivalent fields. Second, calculated expectation-maximization conjugate gradient method, where used...

The Probability Hypothesis Density (PHD) filter is a multipletarget filter for recursively estimating the number of targets and their state vectors from sets of observations. The filter is able to operate in environments with false alarms and missed detections. Two distinct algorithmic implementations of this technique have been developed. The first of which, called the Particle PHD filter, req...

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable c...