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The Gaussian Free Field (GFF) is a canonical random surface in probability theory generalizing Brownian motion to higher dimensions. In two dimensions, it is critical in several senses, and is expected to be the universal scaling limit of a…
The performance of a particle filter (PF) in nonlinear and non-Gaussian environments is often affected by particle degeneracy and impoverishment problems. In this paper, these two problems are re-assessed using the concepts of importance…
Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…
This paper proposes new algorithms for attitude estimation and control based on fused inertial vector measurements using linear complementary filters principle. First, n-order direct and passive complementary filters combined with TRIAD…
Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…
Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…
Matched filters (MFs) are elegant and widely used tools to detect and measure signals that resemble a known template in noisy data. However, they can perform poorly in the presence of contaminating sources of similar or smaller spatial…
In this paper it is shown that the nonfeedback capacity of multiple-input multiple-output (MIMO) additive Gaussian noise (AGN) channels, when the noise is nonstationary and unstable, is characterized by an asymptotic optimization problem…
Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended…
Level set methods underpin modern safety techniques such as control barrier functions (CBFs), while also serving as implicit surface representations for geometric shapes via distance fields. Inspired by these two paradigms, we propose a…
The spline adaptive filtering (SAF) algorithm-based information-theoretic learning has exhibited strong convergence performance in nonlinear system identification (NSI), establishing SAF as a promising framework for adaptive filtering.…
Geometrical acoustics is well suited for simulating room reverberation in interactive real-time applications. While the image source model (ISM) is exceptionally fast, the restriction to specular reflections impacts its perceptual…
A simple procedure for the design of recursive digital filters with an infinite impulse response (IIR) and non-recursive digital filters with a finite impulse response (FIR) is described. The fixed-lag smoothing filters are designed to…
Collaborative filtering is a critical technique in recommender systems. It has been increasingly viewed as a conditional generative task for user feedback data, where newly developed diffusion model shows great potential. However, existing…
Over the last few decades, image-based building surface reconstruction has garnered substantial research interest and has been applied across various fields, such as heritage preservation, architectural planning, etc. Compared to the…
Relative Fisher information, also known as score matching, is a recently introduced learning method for parameter estimation. Fundamental relations between relative entropy and score matching have been established in the literature for…
In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) =…
Gaussian noise is an irreducible component of the background in gravitational wave (GW) detectors. Although stationary Gaussian noise is uncorrelated in frequencies, we show that there is an important correlation in time when looking at the…
Context. The Galactic magnetic field (GMF) has a huge impact on the evolution of the Milky Way. Yet currently there exists no standard model for it, as its structure is not fully understood. In the past many parametric GMF models of varying…
The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task.…