Related papers: Multivariate Spectral Estimation based on the conc…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…
In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito…
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing…
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for…
For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises…
Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in…
Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple…
We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…
We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints…
We define the min-min expectation selection problem (resp. max-min expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
This paper deals with M$^2$-signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random…