# Hypothesis Testing in Imaging Inverse Problems

arXiv: https://arxiv.org/abs/2505.22481 · HTML: https://mlsanity.com/paper/2505.22481/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 30 of 30)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [MedCLIP: Contrastive Learning from Unpaired Medical Images and Text](https://mlsanity.com/paper/2210.10163/) (2022)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [RemoteCLIP: A Vision Language Foundation Model for Remote Sensing](https://mlsanity.com/paper/2306.11029/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Imaging with Equivariant Deep Learning](https://mlsanity.com/paper/2209.01725/) (2022)
- [Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning](https://mlsanity.com/paper/2409.06219/) (2024)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Know "No" Better: A Data-Driven Approach for Enhancing Negation Awareness in CLIP](https://mlsanity.com/paper/2501.10913/) (2025)
- [Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms](https://mlsanity.com/paper/2103.10182/) (2021)
- [Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization](https://mlsanity.com/paper/1803.00889/) (2018)
- [Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems](https://mlsanity.com/paper/2310.11838/) (2023)
- [LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization](https://mlsanity.com/paper/2503.12615/) (2025)
- [Generalized Recorrupted-to-Recorrupted: Self-Supervised Learning Beyond Gaussian Noise](https://mlsanity.com/paper/2412.04648/) (2024)
- [Maximum-a-posteriori estimation with Bayesian confidence regions](https://mlsanity.com/paper/1602.08590/) (2016)
- [Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging](https://mlsanity.com/paper/2312.00125/) (2023)
- [Do Bayesian imaging methods report trustworthy probabilities?](https://mlsanity.com/paper/2405.08179/) (2024)
- [Uncertainty quantification for radio interferometric imaging: II. MAP estimation](https://mlsanity.com/paper/1711.04819/) (2017)
- [Self-supervised Conformal Prediction for Uncertainty Quantification in Imaging Problems](https://mlsanity.com/paper/2502.05127/) (2025)
- [Self-supervised conformal prediction for uncertainty quantification in Poisson imaging problems](https://mlsanity.com/paper/2502.19194/) (2025)

## Abstract (arXiv)

This paper proposes a framework for semantic hypothesis testing tailored to imaging inverse problems. Modern imaging methods struggle to support hypothesis testing, a core component of the scientific method that is essential for the rigorous interpretation of experiments and robust interfacing with decision-making processes. There are three main reasons why image-based hypothesis testing is challenging. First, the difficulty of using a single observation to simultaneously reconstruct an image, formulate hypotheses, and quantify their statistical significance. Second, the hypotheses encountered in imaging are mostly of semantic nature, rather than quantitative statements about pixel values. Third, it is challenging to control test error probabilities because the null and alternative distributions are often unknown. Our proposed approach addresses these difficulties by leveraging concepts from self-supervised computational imaging, vision-language models, and non-parametric hypothesis testing with e-values. We demonstrate our proposed framework through numerical experiments related to image-based phenotyping, where we achieve excellent power while robustly controlling Type I errors.