Related papers: Fault-tolerant and finite-error localization for p…
We solve the general problem of determining, through imaging, the three-dimensional positions of $N$ weak incoherent point-like emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a linear…
Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially…
The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…
Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods…
Interferometers are widely used in imaging technologies to achieve enhanced spatial resolution, but require that the incoming photons be indistinguishable. In previous work, we built and analyzed color erasure detectors which expand the…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
Imaging using interferometer arrays based on the Van Cittert-Zernike theorem has been widely used in astronomical observation. Recently it was shown that superresolution can be achieved in this system for imaging two weak thermal point…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
We present a method to determine the static aberrations in a nearly diffraction-limited spectrograph introduced, for example, by alignment or manufacturing errors. We consider an instrument with two stages separated by a slit or image…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to…
Sub-nanometer and nanometer-sized tips provide high coherence electron sources. Conventionally, the effective source size is estimated from the extent of the experimental biprism interference pattern created on the detector by applying the…
The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…