Information Geometry of Imaging Operators

Abstract

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.