Related papers: Density reconstruction from schlieren images throu…
We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
In compressive sensing, it is challenging to reconstruct image of high quality from very few noisy linear projections. Existing methods mostly work well on piecewise constant images but not so well on piecewise smooth images such as natural…
We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work…
This paper presents DENSER, an efficient and effective approach leveraging 3D Gaussian splatting (3DGS) for the reconstruction of dynamic urban environments. While several methods for photorealistic scene representations, both implicitly…
For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…
A method for the recovery of the real space line-of-sight mass density field from Lyman absorption in QSO spectra is presented. The method makes use of a Lucy-type algorithm for the recovery of the HI density. The matter density is inferred…
In this paper, we propose a dense depth estimation pipeline for multiview 360{\deg} images. The proposed pipeline leverages a spherical camera model that compensates for radial distortion in 360{\deg} images. The key contribution of this…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…
Free-surface synthetic Schlieren (FS-SS) is a high-resolution, refraction-based optical technique for measuring the instantaneous elevation of a liquid interface. Under the assumptions of small amplitude, small slope, and small paraxial…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer…
We investigated the use of the Bayesian inference to restore noise-degraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
The standard approach to inference from cosmic large-scale structure data employs summary statistics that are compared to analytic models in a Gaussian likelihood with pre-computed covariance. To overcome the idealising assumptions about…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…