Hypothesis Testing in Imaging Inverse Problems

TL;DR

This paper introduces a novel framework for semantic hypothesis testing in imaging inverse problems, addressing key challenges in statistical inference for image-based scientific analysis.

Contribution

It presents a new approach combining self-supervised imaging, vision-language models, and non-parametric testing to enable robust hypothesis testing in complex imaging scenarios.

Findings

Achieves high statistical power in image-based phenotyping

Effectively controls Type I error rates

Demonstrates practical applicability through numerical experiments

Abstract

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.