On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods
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Abstract (arXiv)
Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic-looking but incorrect details, undermining their reliability, especially when ground truth data is unavailable. We develop a theoretical framework showing that such hallucinations are not merely artifacts of particular models, but can arise from the ill-posed nature of the inverse problem itself. We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that depend only on the forward model. Building on this theory, we introduce algorithms to: (1) estimate the minimum hallucination magnitude achievable by any reconstruction model for a given input; (2) assess the faithfulness of reconstructed details by a given reconstruction model. Experiments across three imaging tasks demonstrate that our approach applies broadly, including to modern generative models, and provides a principled way to quantify and evaluate AI hallucinations.
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References · 27
- 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
- 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,287
- 2015Accurate Image Super-Resolution Using Very Deep Convolutional Networkscited by 903
- 2017The Perception-Distortion Tradeoffcited by 587
- 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 470
- 2019Scaling Out-of-Distribution Detection for Real-World Settingscited by 465
- 2019Algorithms for Verifying Deep Neural Networkscited by 221
- 2019On instabilities of deep learning in image reconstruction - Does AI come at a cost?cited by 212
- 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
- 2020On hallucinations in tomographic image reconstructioncited by 68
- 2020Solving Inverse Problems With Deep Neural Networks -- Robustness Included?cited by 58
- 2021Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problemcited by 53
15 more
- 2020The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problemscited by 40
- 2021How I failed machine learning in medical imaging -- shortcomings and recommendationscited by 37
- 2024Hallucination Index: An Image Quality Metric for Generative Reconstruction Modelscited by 26
- 2020Uncertainty Estimation in Medical Image Denoising with Bayesian Deep Image Priorcited by 18
- 2021A review and experimental evaluation of deep learning methods for MRI reconstructioncited by 13
- 2022Adversarial Robustness of MR Image Reconstruction under Realistic Perturbationscited by 11
- 2025Tackling Hallucination from Conditional Models for Medical Image Reconstruction with DynamicDPScited by 11
- 2024On the Learnability of Out-of-distribution Detectioncited by 8
- 2024A robust and scalable framework for hallucination detection in virtual tissue staining and digital pathologycited by 6
- 2024Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problemscited by 5
- 2022Mining the manifolds of deep generative models for multiple data-consistent solutions of ill-posed tomographic imaging problemscited by 3
- 2024Ground-based image deconvolution with Swin Transformer UNetcited by 2
- 2024DARDA: Domain-Aware Real-Time Dynamic Neural Network Adaptationcited by 1
- 2025Average Kernel Sizes -- Computable Sharp Accuracy Bounds for Inverse Problemscited by 1
- 2025CHEM: Estimating and Understanding Hallucinations in Deep Learning for Image Processingcited by 1
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