Related papers: Superresolution in separation estimation between t…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
The spatial resolution of astronomical images is limited by atmospheric turbulence and diffraction in the telescope optics, resulting in blurred images. This makes it difficult to accurately measure the brightness of blended objects because…
We propose and examine the use of biphoton pairs, such as those created in parametric down conversion or four-wave mixing, to enhance the precision and the resolution of measuring optical displacements by position-sensitive detection. We…
The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are…
This paper studies sensor calibration in spectral estimation where the true frequencies are located on a continuous domain. We consider a uniform array of sensors that collects measurements whose spectrum is composed of a finite number of…
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…
Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optical methods. By…
We proposed a method to achieve superresolved optical imaging without beating the diffraction limit of light. This is achieved by magnifying the ideal optical image of the object through higher-order spatial frequency generation while…
Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization…
We introduce spatial deformations to an array of light sources and study how the estimation precision of the interspacing distance, d, changes with the sources of light used. The quantum Fisher information (QFI) is used as the figure of…
Waveform decomposition is needed as a first step in the extraction of various types of geometric and spectral information from hyperspectral full-waveform LiDAR echoes. We present a new approach to deal with the "Pseudo-monopulse" waveform…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
No imaging apparatus can produce perfect images: spatial resolution is limited by the Rayleigh diffraction bound that is a consequence of the imager's finite spatial extent. We show some N-photon strategies that permit resolution of details…
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
The quantum Cram\'er-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same…
In this paper we establish accuracy bounds of Prony's method (PM) for recovery of sparse measures from incomplete and noisy frequency measurements, or the so-called problem of super-resolution, when the minimal separation between the points…
Optimal error estimation is key to achieve accurate photometry and astrometry. Stellar fluxes and positions in high angular resolution images are typically measured with PSF fitting routines, such as StarFinder. However, the formal…
We demonstrate super-resolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…