Bridging MRI and PET physiology: Untangling complementarity through orthogonal representations

TL;DR

This paper introduces a novel subspace decomposition framework for multimodal MRI and PET imaging, separating shared and modality-specific information to better understand their complementarity in prostate cancer analysis.

Contribution

It proposes a geometric orthogonal subspace separation method for multimodal fusion, moving beyond traditional joint latent representations.

Findings

Residual PET components not captured by MRI are largest in tumor regions.

The model effectively separates MRI-explainable and orthogonal PET signal components.

Decomposition clarifies modality complementarity in physiological imaging.

Abstract

Multimodal imaging analysis often relies on joint latent representations, yet these approaches rarely define what information is shared versus modality-specific. Clarifying this distinction is clinically relevant, as it delineates the irreducible contribution of each modality and informs rational acquisition strategies. We propose a subspace decomposition framework that reframes multimodal fusion as a problem of orthogonal subspace separation rather than translation. We decompose Prostate-Specific Membrane Antigen (PSMA) PET uptake into an MRI-explainable physiological envelope and an orthogonal residual reflecting signal components not expressible within the MRI feature manifold. Using multiparametric MRI, we train an intensity-based, non-spatial implicit neural representation (INR) to map MRI feature vectors to PET uptake. We introduce a projection-based regularization using singular value decomposition to penalize residual components lying within the span of the MRI feature manifold. This enforces mathematical orthogonality between tissue-level physiological properties (structure, diffusion, perfusion) and intracellular PSMA expression. Tested on 13 prostate cancer patients, the model demonstrates that residual components spanned by MRI features are absorbed into the learned envelope, while the orthogonal residual is largest in tumour regions. This indicates that PSMA PET contains signal components not recoverable from MRI-derived physiological descriptors. The resulting decomposition provides a structured characterization of modality complementarity grounded in representation geometry rather than image translation.