Related papers: On the Well-Posedness of a Parametric Spectral Est…
A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously…
Many materials have distinct spectral profiles. This facilitates estimation of the material composition of a scene at each pixel by first acquiring its hyperspectral image, and subsequently filtering it using a bank of spectral profiles.…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…
Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
We address the problem of causal effect estimation in the presence of hidden confounders, using nonparametric instrumental variable (IV) regression. A leading strategy employs spectral features - that is, learned features spanning the top…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
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…