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This paper introduces two key contributions aimed at improving the speed and quality of images generated through inverse diffusion processes. The first contribution involves reparameterizing the diffusion process in terms of the angle on a…

A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…

Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…

We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

Sub-diffraction-limit resolution, or super-resolution, had been successfully demonstrated by recent theoretical and experimental studies for two-point sources with ideal equal-brightness and strict incoherenceness. Unfortunately, practical…

Recently a blind source separation model was suggested for spatial data together with an estimator based on the simultaneous diagonalisation of two scatter matrices. The asymptotic properties of this estimator are derived here and a new…

For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…

Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…

Many practical problems are related to the pointwise estimation of dis- tribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control,…

Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point…

We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…

Long baseline diffraction-limited optical aperture synthesis technology by interferometry plays an important role in scientific study and practical application. In contrast to amplitude (phase) interferometry, intensity interferometry --…

In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…

Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…

The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article we present two new…

We present a novel algorithm for high resolution coherent imaging of sound sources in random scattering media using time resolved measurements of the acoustic pressure at an array of receivers. The sound waves travel a long distance between…

Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced through the use of mode sorting. Here we theoretically and experimentally investigate…

The localisation of fluorophores is an important aspect of the determination of the biological function of cellular systems. Quantum correlation microscopy (QCM) is a promising technique for providing diffraction unlimited emitter…

An interferometric technique is proposed for determining the spatial forms of the individual degrees of freedom through which a many body system can absorb energy from its environment. The method separates out the coherent excitations…