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The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…
Second-order variational properties have been shown to play important theoretical and numerical roles for different classes of optimization problems. Among such properties, twice epi-differentiability has a special place because of its…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Dimensional reduction of high dimensional data can be achieved by keeping only the relevant eigenmodes after principal component analysis. However, differentiating relevant eigenmodes from the random noise eigenmodes is problematic. A new…
We propose the eigenvalue problem of an anisotropic diffusion operator for image segmentation. The diffusion matrix is defined based on the input image. The eigenfunctions and the projection of the input image in some eigenspace capture key…
The probability density function (pdf) of the received signal of an ambient backscatter communication system is derived, assuming that on-off keying (OOK) is performed at the tag, and that the ambient radio frequency (RF) signal is white…
We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the…
This report describes the computation of gradients by algorithmic differentiation for statistically optimum beamforming operations. Especially the derivation of complex-valued functions is a key component of this approach. Therefore the…
Spectral density estimation is a core problem of system identification, which is an important research area of system control and signal processing. There have been numerous results on the design of spectral density estimators. However to…
The problem of estimating the spectrum of a density matrix is considered. Other problems, such as bipartite pure state entanglement, can be reduced to spectrum estimation. A local operations and classical communication (LOCC) measurement…
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…
In the context of distributed estimation, we consider the problem of sensor collaboration, which refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. While incorporating the cost of…
Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
Rapid growth in the field of quantitative digital image analysis is paving the way for researchers to make precise measurements about objects in an image. To compute quantities from the image such as the density of compressed materials or…
Cooperative spectrum sensing is a robust strategy that enhances the detection probability of primary licensed users. However, a large number of detectors reporting to a fusion center for a final decision causes significant delay and also…
Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab…
In this paper, we investigate the performance of cooperative spectrum sensing (CSS) with multiple antenna nodes over composite and generalized fading channels. We model the probability density function (PDF) of the signal-to-noise ratio…
We study the problem of joint estimation of real squeezing and amplitude of the radiation field, deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters. More generally, we…