Related papers: Utilizing Bochners Theorem for Constrained Evaluat…

Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the…

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…

Signal processing of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Besides randomly and independently occurring outliers also correlated data gaps are investigated. Non-parametric…

Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common…

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…

The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…

In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems. Given measurement variables and parameters, the Buckingham Pi theorem provides a procedure…

In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also…

When using the K-nearest neighbors method, one often ignores uncertainty in the choice of K. To account for such uncertainty, Holmes and Adams (2002) proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN (BKNN)…

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This…

The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also…

A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…

Bayesian image analysis has played a large role over the last 40+ years in solving problems in image noise-reduction, de-blurring, feature enhancement, and object detection. However, these problems can be complex and lead to computational…

In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a…

The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive…

Comparing composite models for multi-component observational data is a prevalent scientific challenge. When fitting composite models, there exists the potential for systematics from a poor fit of one model component to be absorbed by…