相关论文: Convergence Theorems for the Non-Local Means Filte…

In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…

In this paper, we propose a so-called probabilistic non-local means (PNLM) method for image denoising. Our main contributions are: 1) we point out defects of the weight function used in the classic NLM; 2) we successfully derive all…

A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$…

The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the…

In this work, we present a new perspective on the origin and interpretation of adaptive filters. By applying Bayesian principles of recursive inference from the state-space model and using a series of simplifications regarding the structure…

Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…

This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…

In this paper we show that the knowledge of noise statistics contaminating a signal can be effectively used to choose an optimal Gaussian filter to eliminate noise. Very specifically, we show that the additive white Gaussian noise (AWGN)…

In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…

The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…

We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…

An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…

Elongated anisotropic Gaussian filters are used for the orientation estimation of fibers. In cases where computed tomography images are noisy, roughly resolved, and of low contrast, they are the method of choice even if being efficient only…

This paper considers the problem of compact source detection on a Gaussian background in 1D. Two aspects of this problem are considered: the design of the detector and the filtering of the data. Our detection scheme is based on local maxima…

A distributed adaptive algorithm for estimation of sparse unknown parameters in the presence of nonGaussian noise is proposed in this paper based on normalized least mean fourth (NLMF) criterion. At the first step, local adaptive NLMF…