AI summaryⓘ
The authors explore how generative models, which create realistic images, can sometimes produce results that look good but aren’t fully based on actual measurements, especially in medical scans. They focus on understanding whether the way measurements are taken can uniquely identify images that the generative model thinks are likely. By introducing a way to measure how well measurements capture important details from the model, they show this helps control errors and reduce guessing. Their approach also guides smarter ways to collect data during imaging, improving results in settings like MRI scans without needing extra training. Overall, the authors provide a framework to predict when reconstructions might go wrong and suggest better sampling methods.
Generative modelsInverse problemsMeasurement operatorMedical imagingMRI acquisitionSampling designReconstruction errorMeasurement geometryLocal manifoldTomographic imaging
Abstract
Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study generative inverse problems from a measurement-geometry perspective. The central question is whether a fixed measurement operator can distinguish nearby images that are plausible under the generative prior, and whether this relationship can guide better measurements. We introduce a local measurement-manifold compatibility measure that quantifies how well the operator observes prior-relevant tangent directions. Under local regularity assumptions, we prove that this quantity controls the stable part of the reconstruction error, while the generative prior controls off-manifold drift. This worst-direction certificate motivates practical fixed and sequential acquisition rules based on overall local volume preservation, including a posterior-cloud design that adapts measurements at test time without training a sampling policy. Across row-sampling, tomographic, and MR acquisition settings, the proposed scores predict failure modes, explain measurement-induced hallucinations, and guide better sampling. In fastMRI Cartesian sampling, posterior-cloud measurement design improves over strong non-learned ACS-preserving baselines, including variable-density and Poisson-like masks.