Inverse Problems

Follow this topic Ask about this topic

Momentum

20 papers in the last four weeks, up 186% on the four weeks before. 0.2% of all new papers.

Jul 13Week of Sep 28

Latest papers 161

All topics

Robustness to Sparse Adversarial Corruption in Arbitrary Linear Measurements: Beyond Exact Recovery
Oct 28, 2025Vishal Halder, Alexandre Reiffers-Masson, Abdeldjalil Aïssa-El-Bey +1Sparse Recovery Adversarial Robustness
IMT Atlantique, Lab-STICC, CNRS UMR 6285, Brest, France · Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India
Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions
Oct 6, 2025Akira KitaokaMixed-Integer Linear Programming Learning to Optimize
MACS: Measurement-Aware Consistency Sampling for Inverse Problems
Oct 2, 2025Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Seyed Mohammad Eshtehardian +2Diffusion Model Sampling Inverse Problems
Department of Electrical Engineering Sharif University of Technology Tehran, Iran · Electronics Research Institute Sharif University of Technology Tehran, Iran
Patch Rebirth: Fast and Transferable Model Inversion of Vision Transformers
Sep 27, 2025Seongsoo Heo, Dong-Wan ChoiVision Transformer Inverse Problems
Inha University
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
Sep 23, 2025Tim Y. J. Wang, O. Deniz AkyildizWasserstein Gradient Flows Bayesian Inverse Problems
Department of Mathematics Imperial College London
Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments
May 30, 2025Abhijeet Vishwasrao, Sai Bharath Chandra Gutha, Andres Cremades +8Diffusion-Based Inverse Problems Inverse Problems
Department of Aerospace Engineering, University of Michigan, Ann Arbor, USA · FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden · Division of Robotics, Perception and Learning, School of EECS, KTH Royal Institute of Technology, Stockholm, Sweden +7
Learning from samples: inverse problems over measures
May 11, 2025Francisco Andrade, Gabriel Peyré, Clarice PoonInverse Optimal Transport Inverse Problems
INRIA (PreMeDICaL & HeKA) · CNRS and ENS, PSL Universit´e · Mathematics Institute, University of Warwick
Superstate Quantum Mechanics
Jan 25, 2025Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov +3Inverse Problems
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, GSP-1, Moscow, Vorob’evy Gory, 119991, Russia · Autretech Group, Skolkovo Innovation Center, Nobel Street, Building 7, Moscow, 121205, Russia · Peter the Great St. Petersburg Polytechnic University, 195251, Russia +1
An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations
Jul 1, 2024Weimin Bai, Yifei Wang, Wenzheng Chen +1Expectation-Maximization Diffusion-Based Inverse Problems
Academy for Advanced Interdisciplinary Studies, Peking University · College of Future Technology, Peking University · National Biomedical Imaging Center, Peking University +3
Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations
Date pendingOluwatosin Akande, Gabriel P. Langlois, Akwum OnwuntaInverse Problems
Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA 18015, USA · Department of Mathematics, University of Illinois Urbana-Champaign, Chicago, IL, USA
Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems
Date pendingSean Gunn, Jorio Cocola, Oliver De Candido +2Generative Modeling Compressed Sensing
Northeastern University · Harvard University · Technical University of Munich +1

Oct 28, 2025, cs.ITJ/K move · Enter open · S save

Robustness to Sparse Adversarial Corruption in Arbitrary Linear Measurements: Beyond Exact Recovery

Vishal Halder, Alexandre Reiffers-Masson, Abdeldjalil Aïssa-El-Bey, Gugan Thoppe

IMT Atlantique, Lab-STICC, CNRS UMR 6285, Brest, France · Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India

Sparse Recovery Adversarial Robustness Corruption Robustness Inverse Problems

Open paper AskPDF arXiv

Recovery from linear measurements under sparse adversarial corruption is typically formulated as an exact-recovery problem: one seeks structural conditions on

\mathbf{A}

(e.g., restricted isometry property) guaranteeing unique recovery of

\mathbf{x}^\star

from

\mathbf{y} = \mathbf{A}\mathbf{x}^\star + \mathbf{e}

with

\|\mathbf{e}\|_0 \leq q

. However, these guarantees provide no guidance once exact recovery fails. This limitation obscures simple robustness phenomena -- for instance, repeated rows in

\mathbf{A}

can preserve nontrivial information about

\mathbf{x}^\star

under sparse corruption. In this paper, we study what information about

\mathbf{x}^\star

can be \emph{uniformly} recovered from

\mathbf{y} = \mathbf{A}\mathbf{x}^\star + \mathbf{e}

for arbitrary

\mathbf{A}\in\mathbb{R}^{m\times n}

and \emph{any}

q

-sparse

\mathbf{e}

. We show that the robust information is precisely

\mathbf{x}^\star + \ker(\mathbf{U})

, where

\mathbf{U}

is the orthogonal projection onto the intersection of rowspaces of all submatrices of

\mathbf{A}

obtained by deleting

2q

rows. This clarifies how the row structure of

\mathbf{A}

governs whether a

q

-sparse corruption allows exact, partial, or only trivial recovery. We further prove every

\mathbf{x}

minimizing

\|\mathbf{y} - \mathbf{A} \mathbf{x}\|_0

belongs to

\mathbf{x}^\star + \ker(\mathbf{U})

, yielding a constructive approach to recover this set. For i.i.d. Gaussian matrices, we establish a sharp phase transition between exact and trivial recovery. We sketch two applications: robust network tomography and signal reconstruction from oversampled DCT.

Momentum

Related topics

Latest papers 161