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Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture.…

Instrumentation and Methods for Astrophysics · Physics 2020-04-22 Frantz Martinache , Alban Ceau , Romain Laugier , Jens Kammerer , Mamadou N'Diaye , David Mary , Nick Cvetojevic , Coline Lopez

Far-field characterization of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

Superresolution fluorescence microscopy techniques beat the diffraction limit, enabling ultra-high resolution imaging in biological physics and nanoscience. In all cases that have been studied experimentally, the resolution scales inversely…

Optics · Physics 2012-10-10 Alexander Small

Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…

Image and Video Processing · Electrical Eng. & Systems 2019-05-31 Muhammad Aminul Islam , Derek T. Anderson , John E. Ball , Nicolas H. Younan

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…

By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Veit Elser

Fourier optics is a powerful and efficient tool for solving many diffraction problems, but relies on the assumption of scalar diffraction theory and ignores the three-dimensional structure and material properties of the diffracting element.…

Optics · Physics 2021-06-10 Anthony Harness

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

Machine Learning · Statistics 2023-03-20 Christian Fiedler , Michael Herty , Michael Rom , Chiara Segala , Sebastian Trimpe

Convolutional neural networks are paramount in image and signal processing including the relevant classification and training tasks alike and constitute for the majority of machine learning compute demand today. With convolution operations…

We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…

Numerical Analysis · Mathematics 2025-05-21 Anna Volpara , Alessandro Lupoli , Emma Perracchione

We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…

Statistics Theory · Mathematics 2025-10-31 Grigorios A. Pavliotis , Andrea Zanoni

Fluorescence microscopy is an important and extensively utilised tool for imaging biological systems. However, the image resolution that can be obtained has a limit as defined through the laws of diffraction. Demand for improved resolution…

Biological Physics · Physics 2007-08-27 James H. Rice

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to…

Machine Learning · Computer Science 2019-10-08 Jiaxuan Xie , Fanghui Liu , Kaijie Wang , Xiaolin Huang

Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…

Numerical Analysis · Mathematics 2025-05-19 Toni Karvonen , Gabriele Santin , Tizian Wenzel

A reproducing kernel can define an embedding of a data point into an infinite dimensional reproducing kernel Hilbert space (RKHS). The norm in this space describes a distance, which we call the kernel distance. The random Fourier features…

Machine Learning · Computer Science 2026-03-24 Di Chen , Jeff M. Phillips

The Differential Fourier Holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [1] the Differential Fourier Holography was successfully applied in…

Optics · Physics 2016-04-20 Sergey G. Podorov , Eckhart Förster

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

Kernel phase interferometry is an approach to high angular resolution imaging which enhances the performance of speckle imaging with adaptive optics. Kernel phases are self-calibrating observables that generalize the idea of closure phases…

Instrumentation and Methods for Astrophysics · Physics 2016-09-21 Benjamin J. S. Pope

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…

Signal Processing · Electrical Eng. & Systems 2021-03-16 Vincent Schellekens , Laurent Jacques