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

TL;DR

This paper develops an operator-based information theory framework for imaging systems, analyzing how physical transformations affect information flow, capacity, and irreversibility across various modalities.

Contribution

It introduces a novel operator-based formulation of information theory for imaging, applicable to linear, nonlinear, and stochastic systems, with new measures for entropy, capacity, and irreversibility.

Findings

Attenuation, blur, and sampling impact entropy, capacity, and irreversibility differently.

The framework applies broadly to different imaging modalities and operator types.

Provides a basis for analyzing physical limits and reconstruction in imaging systems.

Abstract

Imaging systems are commonly described using resolution, contrast, and signal-to-noise ratio, but these quantities do not provide a general account of how physical transformations affect the flow of information. This paper introduces an operator-based formulation of information theory for imaging. The approach models the imaging chain as a composition of bounded operators acting on functions, and characterises information redistribution using the spectral properties of these operators. Three measures are developed. Operator entropy quantifies how an operator distributes energy across its singular spectrum. Operator information capacity describes the number of modes that remain recoverable above a noise-dependent threshold. An irreversibility index measures the information lost through suppression or elimination of modes and captures the accumulation of information loss under operator composition. The framework applies to linear, nonlinear, and stochastic operators and does not depend on the specific imaging modality. Analytical examples show how attenuation, blur, and sampling affect entropy, capacity, and irreversibility in different ways. The results provide a general structure for analysing the physical limits of imaging and form the basis for subsequent work on information geometry, spatiotemporal budgets, nonlinear channels, and reconstruction algorithms.