On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods
For practitioners of AI-based imaging (e.g., medical diagnostics, Earth observation), this work provides a theoretical and algorithmic framework to quantify and evaluate hallucinations, enhancing reliability when ground truth is unavailable.
The paper establishes fundamental limits on hallucinations in inverse problems, showing they are inherent due to ill-posedness, and provides provable methods to estimate minimum hallucination magnitude and assess faithfulness of reconstructions, validated across three imaging tasks.
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.