Related papers: Spectral deconvolution of unitarily invariant matr…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
In this paper, we study a nonlinear spiked random matrix model where a nonlinear function is applied element-wise to a noise matrix perturbed by a rank-one signal. We establish a signal-plus-noise decomposition for this model and identify…
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions…
We revisit the classic Wigner semi-circle from two different angles. One consists in studying the Stieltjes transform directly on the real axis, which does not converge to a fixed value but follows a Cauchy distribution that depends on the…
In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse…
This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…
Quantum entanglement, a fundamental property ensuring security of key distribution and efficiency of quantum computing, is extremely sensitive to decoherence. Different procedures have been developed in order to recover entanglement after…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a…
A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…
The perturbation of the Sturm-Liouville operator on a finite interval with Dirichlet boundary conditions by a convolution operator is considered. Local stability and global unique solvability of the inverse problem of recovering the…
In this paper, we propose a Bayesian spectral deconvolution method for absorption spectra. In conventional analysis, the noise mechanism of absorption spectral data is never considered appropriately. In that analysis, the least-squares…
We consider the limiting spectral distribution of matrices of the form $\frac{1}{2b_{n}+1} (R + X)(R + X)^{*}$, where $X$ is an $n\times n$ band matrix of bandwidth $b_{n}$ and $R$ is a non random band matrix of bandwidth $b_{n}$. We show…