# Bridging MRI and PET physiology: Untangling complementarity through orthogonal representations

arXiv: https://arxiv.org/abs/2604.07154 · HTML: https://mlsanity.com/paper/2604.07154/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [Domain Separation Networks](https://mlsanity.com/paper/1608.06019/) (2016)
- [HeMIS: Hetero-Modal Image Segmentation](https://mlsanity.com/paper/1607.05194/) (2016)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Robust Multimodal Learning via Representation Decoupling](https://mlsanity.com/paper/2407.04458/) (2024)
- [From FDG to PSMA: A Hitchhiker's Guide to Multitracer, Multicenter Lesion Segmentation in PET/CT Imaging](https://mlsanity.com/paper/2409.09478/) (2024)
- [Implicit neural representations for end-to-end PET reconstruction](https://mlsanity.com/paper/2503.21825/) (2025)
- [Physiological neural representation for personalised tracer kinetic parameter estimation from dynamic PET](https://mlsanity.com/paper/2504.17122/) (2025)

## Abstract (arXiv)

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.