Beyond point estimates: learning and validating posterior distributions for uncertainty-aware photoacoustic oximetry

Functional biomedical imaging seeks to recover physiologically meaningful parameters that provide insight beyond anatomical structure. In particular, quantitative estimation of sO₂ is of high clinical relevance due to its association with tumor hypoxia, vascular pathology, and other disease processes.

Multispectral photoacoustic imaging (PAI) has emerged as a promising modality for this purpose, as it combines optical contrast with ultrasonic detection to probe tissue composition at depth. However, quantitative photoacoustic oximetry remains challenging because measured spectra are shaped not only by optical absorption but also by spatially varying light fluence, resulting in a nonlinear and nonunique mapping from measurements to tissue properties. Consequently, distinct physiological states can produce similar photoacoustic (PA) signals, rendering sO₂ estimation an ill-posed inverse problem.

This thesis addresses these challenges by adopting a probabilistic approach to photoacoustic oximetry and by developing methodological tools for uncertainty-aware inference and validation.

First, conditional invertible neural networks (cINNs) are introduced for probabilistic sO₂ estimation from multispectral PA measurements. Unlike conventional learning-based approaches that provide point estimates, these models learn full posterior distributions conditioned on the measured spectra, enabling explicit representation of uncertainty and multimodality. Simulation-based experiments demonstrate that posterior inference from single-pixel spectral measurements often results in multimodal posterior distributions, reflecting inherent ambiguities and indicating that unique sO₂ estimates cannot always be supported by the data.

Second, the influence of imaging conditions and neural network input design on posterior uncertainty is analyzed systematically. By combining posterior inference with statistical modeling, the work examines the impact of spatial location, acquisition noise, spectral sampling, and spatial context on posterior distributions. The results show that ambiguity is structured and condition-dependent: certain imaging scenarios yield well-constrained estimates, while others remain intrinsically ambiguous. These findings highlight the importance of uncertainty-aware analysis for understanding the limits of quantitative performance.

Finally, the thesis introduces an application-aware framework for validating posterior-based methods in inverse problems. The framework accounts for the structure of the inverse problem and the nature of the available reference data, enabling principled selection of validation metrics. By formalizing key properties that guide metric selection and adopting a mode-centric perspective, it provides a coherent basis for validating posterior distributions in settings where multiple solutions may exist and reference information is incomplete. Although motivated by PAI, the framework is applicable to a wide range of inverse problems in medical image analysis.

Together, these contributions establish a coherent approach to uncertainty-aware photoacoustic oximetry and advance the methodological foundations for posterior-based inference and validation in inverse problems. By making ambiguity explicit and quantifiable, this work supports the development of more transparent and reliable data-driven imaging pipelines.