Bridging MRI and PET physiology: Untangling complementarity through orthogonal representations

2026-04-08

AI Summary

This work addresses the challenge of disentangling shared and modality-specific information in multimodal medical image fusion, particularly the difficulty in attributing distinct physiological contributions from MRI and PET. The authors propose a novel subspace decomposition framework that formulates fusion as an orthogonal subspace separation problem: implicit neural representations (INRs) are employed to predict PSMA PET uptake from multiparametric MRI, while singular value decomposition (SVD)-based projection regularization enforces orthogonality between the residual signal and the MRI feature manifold. This approach achieves, for the first time, a geometrically principled decoupling of an interpretable MRI-derived physiological envelope and PET-specific signals, thereby rigorously defining inter-modality complementarity. Validation on data from 13 prostate cancer patients demonstrates significantly enhanced orthogonal residuals within tumor regions, confirming that PET captures critical biological information not recoverable from MRI alone.

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.

Problem

• multimodal imaging
• modality-specific information
• shared information
• MRI-PET complementarity
• orthogonal representations

Innovation

• orthogonal subspace decomposition
• implicit neural representation
• multimodal fusion
• projection-based regularization
• modality complementarity