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We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we…

Machine Learning · Statistics 2026-04-10 Jonah Botvinick-Greenhouse , Yunan Yang

Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion…

Computational Physics · Physics 2025-08-15 Haoran Sun , Daoqi Liu , Hongyu Zhou , Maokun Li , Shenheng Xu , Fan Yang

We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…

Differential Geometry · Mathematics 2025-05-01 Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas , Anthony Várilly-Alvarado

Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…

Machine Learning · Statistics 2021-11-05 Venkata Gandikota , Arya Mazumdar , Soumyabrata Pal

Polarized X-rays allow for imaging birefringent or dichroic properties of materials with nanometric resolution. To disentangle these properties from the electronic density, either a polarization analyzer or several measurements with…

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…

Numerical Analysis · Mathematics 2017-08-08 Qin Li , Ruiwen Shu , Li Wang

Based on the recently introduced homogenization theory developed in [Phys. Rev. B 84, 075153 (2011)], we propose a generalized retrieval method that allows extracting physically meaningful bulk effective parameters from conventional…

Mesoscale and Nanoscale Physics · Physics 2015-06-15 Xing-Xiang Liu , Andrea Alu

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing…

Machine Learning · Computer Science 2020-10-28 Ren Wang , Meng Wang , Jinjun Xiong

We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises naturally when multiple measurements are taken over time, e.g., and…

Information Theory · Computer Science 2012-10-09 Reinhard Heckel , Helmut Bölcskei

Gravitational wave astronomy is just beginning, after the recent success of the four direct detections of binary black hole (BBH) mergers, the first observation from a binary neutron star inspiral and with the expectation of many more…

Instrumentation and Methods for Astrophysics · Physics 2018-01-23 I. Di Palma , M. Drago

Accurate segmentation of floating debris on water is often compromised by surface glare and changing outdoor illumination. Polarimetric imaging offers a single-sensor route to mitigate water-surface glare that disrupts semantic segmentation…

Computer Vision and Pattern Recognition · Computer Science 2025-09-30 Luis F. W. Batista , Tom Bourbon , Cedric Pradalier

In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…

Signal Processing · Electrical Eng. & Systems 2021-08-09 Mehmet Yamac , Ugur Akpinar , Erdem Sahin , Serkan Kiranyaz , Moncef Gabbouj

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

Analysis of PDEs · Mathematics 2021-11-10 Giovanni S. Alberti , Matteo Santacesaria

This paper aims at studying how finitely many generalized polarization tensors of an algebraic domain can be used to determine its shape. Precisely, given a planar set with real algebraic boundary, it is shown that the minimal polynomial…

Analysis of PDEs · Mathematics 2018-07-03 Habib Ammari , Mihai Putinar , Andries Steenkamp , Faouzi Triki

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

Signal Processing · Electrical Eng. & Systems 2021-10-15 Michael Koller , Wolfgang Utschick

In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…

Differential Geometry · Mathematics 2025-07-22 Fernando Etayo , Pablo Gómez-Nicolás , Rafael Santamaría

A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…

Mathematical Physics · Physics 2007-05-23 Tuncay Aktosun , Vassilis G. Papanicolaou , Vassilis Zisis

We define a multiparty entanglement measure, called generalized geometric measure, that can detect and quantify genuine multiparty entanglement for any number of parties. The quantum phase transitions in exactly solvable models like the…

Quantum Physics · Physics 2010-02-08 Aditi Sen De , Ujjwal Sen

Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…

Analysis of PDEs · Mathematics 2026-04-15 Huaian Diao , Hongyu Liu , Longyue Tao

A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…

Mathematical Physics · Physics 2016-09-07 Semion Gutman