English
Related papers

Related papers: Mathematical Theory of Computational Resolution Li…

200 papers

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…

Numerical Analysis · Mathematics 2017-09-12 Clarice Poon , Gabriel Peyré

Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies…

Quantum Physics · Physics 2022-02-08 Mateusz Mazelanik , Adam Leszczyński , Michał Parniak

We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes…

Numerical Analysis · Mathematics 2025-02-11 Nuha Diab

Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…

Information Theory · Computer Science 2024-03-07 Netanel Raviv

Conventional incoherent imaging based on measuring the spatial intensity distribution in the image plane faces the resolution hurdle described by the Rayleigh diffraction criterion. Here, we demonstrate theoretically using the concept of…

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate resolution enhancement beyond the Rayleigh bound using random scanning of a…

It has been recently shown that an interferometric measurement may allow for sub-wavelength resolution of incoherent light. Whereas this holds for noiseless detectors, one could expect that the resolution is in practice limited by…

Quantum Physics · Physics 2020-02-24 Cosmo Lupo

In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper…

Information Theory · Computer Science 2015-04-06 Veniamin I. Morgenshtern , Emmanuel J. Candes

The PhaseLift algorithm is an effective convex method for solving the phase retrieval problem from Fourier measurements with coded diffraction patterns (CDP). While exact reconstruction guarantees are well-established in the noiseless case,…

Numerical Analysis · Mathematics 2025-10-14 Meng Huang , Jinming Wen , Ran Zhang

The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. An important figure of merit for sensing time dependent signals is the spectral…

Quantum Physics · Physics 2019-12-05 Tuvia Gefen , Amit Rotem , Alex Retzker

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…

Information Theory · Computer Science 2020-05-15 Veniamin I. Morgenshtern

Spatial mode demultiplexing was proved to be a successful tool for estimation of the separation between incoherent sources, allowing for sensitivity much below the Rayleigh limit. However, with the presence of measurement's noise,…

Quantum Physics · Physics 2024-07-23 Fattah Sakuldee , Łukasz Rudnicki

Noisy supervision refers to supervising image restoration learning with noisy targets. It can alleviate the data collection burden and enhance the practical applicability of deep learning techniques. However, existing methods suffer from…

Image and Video Processing · Electrical Eng. & Systems 2025-06-03 Haosen Liu , Jiahao Liu , Shan Tan , Edmund Y. Lam

The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…

Information Theory · Computer Science 2020-09-29 Lan V. Truong , Jonathan Scarlett

We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable…

Information Theory · Computer Science 2022-10-17 Weilin Li , Wenjing Liao

Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate…

Quantum Physics · Physics 2026-02-13 Joseph T. Iosue , Paraj Titum , Taohan Lin , Clare Lau , Leigh M. Norris

We investigate theoretically coherent detection implemented simultaneously on a set of mutually orthogonal spatial modes in the image plane as a method to characterize properties of a composite thermal source below the Rayleigh limit. A…

Motivated by the X-ray crystallography technology to determine the atomic structure of biological molecules, we study the crystallographic phase retrieval problem, arguably the leading and hardest phase retrieval setup. This problem entails…

Information Theory · Computer Science 2020-07-06 Tamir Bendory , Dan Edidin

We establish fundamental bounds on subwavelength resolution for the radar ranging problem, ``super radar''. Information theoretical metrics are applied to probe the resolution limits for the case of both direct electric field measurement…

Optics · Physics 2024-06-04 Andrew N. Jordan , John C. Howell

The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…

Functional Analysis · Mathematics 2019-07-12 H. N. Mhaskar