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.

翻译：多模态成像分析常依赖联合潜在表征，但这类方法极少明确定义信息共享与模态特异性之间的界限。阐明这种区别具有临床相关性，因为它能明确每种模态的不可约贡献，并指导合理的采集策略。我们提出一种子空间分解框架，将多模态融合重构为正交子空间分离问题而非翻译问题。我们将前列腺特异性膜抗原（PSMA）PET摄取值分解为两个成分：可通过MRI解释的生理包络，以及反映磁共振特征流形内无法表达信号成分的正交残差。利用多参数MRI，我们训练基于强度而非空间位置的隐式神经表征（INR），将MRI特征向量映射为PET摄取值。我们引入基于奇异值分解的投影正则化方法，对处于MRI特征流形张成空间内的残差成分进行惩罚。这实现了组织级生理特性（结构、弥散、灌注）与细胞内PSMA表达之间的数学正交性。在13例前列腺癌患者上的测试表明，由MRI特征张成的残差成分被纳入学习到的包络中，而正交残差在肿瘤区域最大。这表明PSMA PET包含无法从MRI衍生生理描述符中恢复的信号成分。所得分解基于表征几何而非图像翻译，提供了模态互补性的结构化描述。