#inverse problems
19 resultsOn ErdÅs-Ginzburg-Ziv inverse theorems for Dihedral and Dicyclic groups
Jun Seok Oh, Qinghai Zhong
The paper determines the exact values of the Erdős‑Ginzburg‑Ziv constants s(G) and E(G) for dihedral and dicyclic groups and characterizes the extremal sequences that avoid the req…
Applications of microlocal analysis to inverse problems
Mikko Salo
The paper provides lecture notes that introduce and illustrate how microlocal analysis methods are applied to solve various inverse problems.
Local marked boundary rigidity under hyperbolic trapping assumptions
Thibault Lefeuvre
The paper shows that, assuming the X‑ray transform is injective on symmetric solenoidal 2‑tensors, smooth compact manifolds with strictly convex boundaries, no conjugate points, an…
On the s-injectivity of the X-ray transform on manifolds with hyperbolic trapped set
Thibault Lefeuvre
The paper proves that for smooth compact manifolds with strictly convex boundary, no conjugate points, and a hyperbolic trapped set, the X-ray transform on symmetric solenoidal ten…
Model Learning: Primal Dual Networks for Fast MR imaging
Jing Cheng, Haifeng Wang, Leslie Ying +1
The paper proposes a deep network that unrolls the primal‑dual hybrid gradient algorithm to reconstruct MR images from highly undersampled k‑space data, combining optimization conv…
On the Well-Posedness of a Parametric Spectral Estimation Problem and Its Numerical Solution
Bin Zhu
The paper studies a parametric formulation of a spectral estimation inverse problem, proving it is well‑posed and that the solution depends continuously on a prior, and proposes a…
Optoacoustic Model-Based Inversion Using Anisotropic Adaptive Total-Variation Regularization
Shai Biton, Nadav Arbel, Gilad Drozdov +2
The paper proposes an adaptive anisotropic total‑variation regularization method for optoacoustic tomography that better preserves complex boundaries and improves image contrast co…
On the identification of source term in the heat equation from sparse data
William Rundell, Zhidong Zhang
The paper studies how to uniquely recover a separable source term in the heat equation from a very small number of boundary measurements, proving uniqueness with just two points an…
Sparse synthesis regularization with deep neural networks
Daniel Obmann, Johannes Schwab, Markus Haltmeier
The paper introduces a sparse reconstruction framework for inverse problems that trains an encoder‑decoder network with an ℓ¹ penalty, enabling sparse signal recovery via threshold…
A Projectional Ansatz to Reconstruction
Sören Dittmer, Peter Maass
The paper proposes a projectional framework for solving inverse problems that integrates learned and hand‑crafted priors while preserving data consistency, implemented via plug‑and…
Reconstruction of the magnetic field for a Schrödinger operator in a cylindrical setting
Daniel Campos
The paper develops a method to reconstruct the magnetic field of a Schrödinger operator on a cylindrical domain using boundary measurements and Carleman estimates.
Monotonicity-based inversion of the fractional Schrödinger equation I. Positive potentials
Bastian Harrach, Yi-Hsuan Lin
The paper develops monotonicity-based techniques to uniquely determine positive potentials and reconstruct obstacles in the fractional Schrödinger equation using Dirichlet-to-Neuma…
Direct and inverse results on restricted signed sumsets in integers
Jagannath Bhanja, Takao Komatsu, Ram Krishna Pandey
The paper investigates the smallest possible size of restricted signed sumsets of integer sets and characterizes the sets that achieve this minimum, providing direct and inverse re…
Monotonicity and local uniqueness for the Helmholtz equation
Bastian Harrach, Valter Pohjola, Mikko Salo
The paper extends monotonicity-based techniques to the Helmholtz equation, establishing a relation between the scattering coefficient and the Neumann‑Dirichlet map and using it to…
A learning-based method for solving ill-posed nonlinear inverse problems: a simulation study of Lung EIT
Jin Keun Seo, Kang Cheol Kim, Ariungerel Jargal +2
The paper introduces a learning-based technique that uses variational autoencoders to create a low‑dimensional representation of lung electrical impedance tomography data, turning…
An ensemble Kalman filter approach based on level set parameterization for acoustic source identification using multiple frequency information
Zhiliang Deng, Xiaomei Yang
The paper proposes a statistical inversion method that combines an ensemble Kalman filter with level set parameterization to reconstruct spatially varying acoustic sources from noi…
Inverse quantum measurement problem
D. Sokolovski, S. MartÃnez-Garaot, M. Pons
The paper investigates when and how the complex phases of quantum probability amplitudes can be reconstructed from measured probability distributions and expectation values, effect…
Deep Neural Network Approach to Forward-Inverse Problems
Hyeontae Jo, Hwijae Son, Hyung Ju Hwang +1
The paper introduces a feed‑forward deep neural network framework that simultaneously approximates solutions of differential equations and identifies model parameters from data, pr…
Learning to Synthesize: Robust Phase Retrieval at Low Photon counts
Mo Deng, Shuai Li, Alexandre Goy +2
The paper introduces a "learning to synthesize" deep‑learning framework that separately processes low‑ and high‑frequency components and then combines them to achieve high‑resoluti…