Operator-Based Information Theory for Imaging: Entropy, Capacity, and Irreversibility in Physical Measurement Systems

Imaging systems are commonly described using resolution, contrast, and signal-to-noiseratio, but these quantities do not provide a general account of how physicaltransformations affect the flow of information. This paper introduces an operator-basedformulation of information theory for imaging. The approach models the imaging chain asa composition of bounded operators acting on functions, and characterises informationredistribution using the spectral properties of these operators. Three measures aredeveloped. Operator entropy quantifies how an operator distributes energy across itssingular spectrum. Operator information capacity describes the number of modes thatremain recoverable above a noise-dependent threshold. An irreversibility index measuresthe information lost through suppression or elimination of modes and captures theaccumulation of information loss under operator composition. The framework applies tolinear, nonlinear, and stochastic operators and does not depend on the specific imagingmodality. Analytical examples show how attenuation, blur, and sampling affect entropy,capacity, and irreversibility in different ways. The results provide a general structure foranalysing the physical limits of imaging and form the basis for subsequent work oninformation geometry, spatiotemporal budgets, nonlinear channels, and reconstructionalgorithms.