Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal geometric structure induced by the normalised singular spectra of imaging operators. By identifying spectral equivalence classes with points on a probability simplex, and equipping this space with the Fisher--Rao information metric, a well-defined Riemannian geometry can be obtained that is invariant under unitary transformations and global rescaling. The resulting geometry admits closed-form expressions for distances and geodesics, and has constant positive curvature. Under explicit restrictions, composition enforces boundary faces through rank constraints and, in an aligned model with stated idealisations, induces a non-linear re-weighting of spectral states. Fisher--Rao distances are preserved only in the spectrally uniform case. The construction is abstract and operator-level, introducing no optimisation principles, stochastic models, or modality-specific assumptions. It is intended to provide a fixed geometric background for subsequent analysis of information flow and constraints in imaging pipelines.

翻译：成像系统被表示为线性算子，其奇异值谱描述了在算子层面可恢复的结构。基于算子化的信息论框架，本文引入了由成像算子的归一化奇异谱所诱导的最小几何结构。通过将谱等价类识别为概率单纯形上的点，并为此空间配备Fisher-Rao信息度量，可以获得一个在酉变换和全局缩放下不变、定义良好的黎曼几何。所得几何具有闭式距离与测地线表达式，且具有恒定正曲率。在显式限制下，复合运算通过秩约束强制边界面的形成，并在具有既定理想化条件的对齐模型中诱导出谱态的非线性重加权。仅当谱分布均匀时，Fisher-Rao距离得以保持。该构造是抽象且基于算子层面的，未引入任何优化原理、随机模型或特定模态假设，旨在为后续分析成像流程中的信息流与约束提供一个固定的几何背景。