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We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…
We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues…
We introduce a novel application of the Hartmann sensor, traditionally designed for wavefront sensing, to measure the coherence properties of optical signals. By drawing an analogy between the coherence matrix and the density matrix of a…
Consider a bound state (an eigenfunction) $\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\gamma$ and of the one-particle kinetic energy density matrix $\tau$ associated with $\psi$. The paper…
A scheme for the detection of low-intensity optical coherent signals was studied which uses a probabilistic amplifier operated in the non-heralded version, as the underlying non-linear operation to improve the detection efficiency. This…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols.…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
Spectrum sensing is a key technology for cognitive radios. We present spectrum sensing as a classification problem and propose a sensing method based on deep learning classification. We normalize the received signal power to overcome the…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions. By reducing algorithmic complexity through the elimination of non-essential…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
In this paper three different scenarios in wide band spectrum sensing have been studied. While the signal and noise statistics are supposed to be unspecified, random matrixes have been utilized in order to estimate the noise variance. These…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
In this paper, a new cooperation structure for spectrum sensing in cognitive radio networks is proposed which outperforms the existing commonly-used ones in terms of energy efficiency. The efficiency is achieved in the proposed design by…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…