Related papers: Adaptive local density estimation in tomography
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z,…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2 < \eta \leq 1$, we propose a novel estimator of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $Ce^{-B(m+n)^{r/ 2}}$, for fixed…
We study the problem of semi-supervised anomaly detection with domain adaptation. Given a set of normal data from a source domain and a limited amount of normal examples from a target domain, the goal is to have a well-performing anomaly…
Given an i.i.d. sample $X_1,...,X_n$ with common bounded density $f_0$ belonging to a Sobolev space of order $\alpha$ over the real line, estimation of the quadratic functional $\int_{\mathbb{R}}f_0^2(x) \mathrm{d}x$ is considered. It is…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree…
We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence…
In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized…
The ability to remove unwanted dependencies from data is crucial in various domains, including fairness, robust learning, and privacy protection. In this work, we propose an encoder-based approach that learns a representation independent of…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…
We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…