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Information Theory: An X-ray Microscopy Perspective

Charles Wood

TL;DR

This work reframes X-ray microscopy as an information-processing system and develops an applied information-theoretic framework using entropy, mutual information, and KL divergence to quantify how acquisition, denoising, alignment, sparse sampling, and reconstruction reshape the data's statistical structure. Through Walnut 1 case studies and cross-dataset validation with LoDoPaB-CT, it demonstrates that information loss is dominated by upstream steps and that reconstruction saturates once the information budget is fixed, with mutual information serving as a reconstruction-agnostic fidelity indicator. The findings provide actionable guidance for protocol design, emphasizing acquisition optimization under low-dose or time-constrained conditions and highlighting the limits of reconstruction-improved quality beyond information budget constraints. The work also introduces an empirical information budget and dose–information relationships to compare protocols and illuminate the information-theoretic trade-offs inherent in XRM, offering a principled basis for extending the framework to other modalities and advanced reconstruction paradigms.

Abstract

X-ray microscopy (XRM) is commonly used to obtain three-dimensional information on internal microstructure, but the imaging pipeline introduces noise, redundancy and information loss at multiple stages. This paper treats the XRM workflow as an information-processing system acting on a finite information budget. Using entropy, mutual information and Kullback-Leibler divergence, we quantify how acquisition, denoising, alignment, sparse-angle sampling, dose variation and reconstruction reshape the statistical structure of projection data and reconstructed volumes. Case studies based on the Walnut 1 dataset illustrate how these processes redistribute information and impose bottlenecks. We summarise the workflow using a unified information budget and show that mutual information provides a reconstruction-agnostic indicator of fidelity, supporting quantitative comparison and optimisation of XRM protocols, particularly under low-dose or time-constrained conditions

Information Theory: An X-ray Microscopy Perspective

TL;DR

This work reframes X-ray microscopy as an information-processing system and develops an applied information-theoretic framework using entropy, mutual information, and KL divergence to quantify how acquisition, denoising, alignment, sparse sampling, and reconstruction reshape the data's statistical structure. Through Walnut 1 case studies and cross-dataset validation with LoDoPaB-CT, it demonstrates that information loss is dominated by upstream steps and that reconstruction saturates once the information budget is fixed, with mutual information serving as a reconstruction-agnostic fidelity indicator. The findings provide actionable guidance for protocol design, emphasizing acquisition optimization under low-dose or time-constrained conditions and highlighting the limits of reconstruction-improved quality beyond information budget constraints. The work also introduces an empirical information budget and dose–information relationships to compare protocols and illuminate the information-theoretic trade-offs inherent in XRM, offering a principled basis for extending the framework to other modalities and advanced reconstruction paradigms.

Abstract

X-ray microscopy (XRM) is commonly used to obtain three-dimensional information on internal microstructure, but the imaging pipeline introduces noise, redundancy and information loss at multiple stages. This paper treats the XRM workflow as an information-processing system acting on a finite information budget. Using entropy, mutual information and Kullback-Leibler divergence, we quantify how acquisition, denoising, alignment, sparse-angle sampling, dose variation and reconstruction reshape the statistical structure of projection data and reconstructed volumes. Case studies based on the Walnut 1 dataset illustrate how these processes redistribute information and impose bottlenecks. We summarise the workflow using a unified information budget and show that mutual information provides a reconstruction-agnostic indicator of fidelity, supporting quantitative comparison and optimisation of XRM protocols, particularly under low-dose or time-constrained conditions
Paper Structure (39 sections, 16 equations, 13 figures, 4 tables)

This paper contains 39 sections, 16 equations, 13 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Information Metrics for X-ray Microscopy
  3. Entropy and Noise in Projection Data
  4. Mutual Information and Reconstruction Fidelity
  5. Kullback--Leibler Divergence and Distributional Change
  6. Channel Capacity and Information Limits in Imaging Systems
  7. Information Flow and Entropy Across the X-ray Microscopy Pipeline
  8. Data Acquisition
  9. Image Formation
  10. Image Reconstruction
  11. Post-Processing and Enhancement
  12. Noise Characterisation and Its Impact on Information Metrics
  13. Different Noise Types in X-ray Microscopy
  14. How Noise Influences Entropy and Mutual Information
  15. Methods to Estimate, Separate, and Quantify Noise Using Information Metrics
  16. ...and 24 more sections

Figures (13)

  • Figure 1: Unified information budget for the X-ray microscopy pipeline.
  • Figure 2: Projection 600 from the Walnut 1 dataset and its denoised counterparts. Left to right: raw, Gaussian smoothing, NLM, and TV regularisation. The visual differences correspond to the quantitative entropy and KL divergence values reported in Table \ref{['tab:entropy_kl']}.
  • Figure 3: Information--theoretic comparison of denoising methods for projection 600. Top: Shannon entropy. Bottom: Kullback--Leibler divergence relative to the raw projection. The trend reflects increasing distortion of the original intensity distribution from Gaussian to NLM to TV.
  • Figure 4: Structural similarity index (SSIM) and mutual information (MI) between the raw projection and its denoised counterparts. Both SSIM and MI decrease monotonically from Gaussian smoothing to NLM to TV regularisation, consistent with progressively stronger regularisation removing high-frequency structure while preserving the dominant attenuation features under typical laboratory XRM noise conditions.
  • Figure 5: Effect of misalignment and registration for projection 580. Left to right: reference projection 600, original projection 580, misaligned version with synthetic shift $(5,-3)$ pixels, and registered reconstruction using subpixel phase correlation.
  • ...and 8 more figures