Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Automatic regularization parameter choice for tomography using a double model approach

Chuyang Wu, Samuli Siltanen

TL;DR

This work addresses automatic regularization parameter selection for CT by reframing it as a closed-loop control problem using a double-model (two-grid) reconstruction to create a consistency-based feedback signal. The method computes reconstructions on grids with forward operators $A$ and $A_\theta$, defines $S(\alpha)$ via SSIM, and updates $\alpha$ in the $\log_{10}$ domain toward a user-specified target $S_{\mathrm{ref}}$. Key contributions include the double-model consistency framework, a monotonicity-based control premise, and solver-agnostic performance that preserves texture while controlling noise, demonstrated on Walnut and Pine Cone datasets with TV and Tikhonov regularizers. The approach offers a transparent, domain-informed alternative to heuristic parameter selection and has practical implications for robust, automated CT reconstructions without ground-truth data or explicit noise knowledge.

Abstract

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances data fidelity against a priori information. We present a novel method for automatic parameter selection based on the use of two distinct computational discretizations of the same problem. A feedback control algorithm dynamically adjusts the regularization strength, driving an iterative reconstruction toward the smallest parameter that yields sufficient similarity between reconstructions on the two grids. The effectiveness of the proposed approach is demonstrated using real tomographic data.

Automatic regularization parameter choice for tomography using a double model approach

TL;DR

This work addresses automatic regularization parameter selection for CT by reframing it as a closed-loop control problem using a double-model (two-grid) reconstruction to create a consistency-based feedback signal. The method computes reconstructions on grids with forward operators and , defines via SSIM, and updates in the domain toward a user-specified target . Key contributions include the double-model consistency framework, a monotonicity-based control premise, and solver-agnostic performance that preserves texture while controlling noise, demonstrated on Walnut and Pine Cone datasets with TV and Tikhonov regularizers. The approach offers a transparent, domain-informed alternative to heuristic parameter selection and has practical implications for robust, automated CT reconstructions without ground-truth data or explicit noise knowledge.

Abstract

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances data fidelity against a priori information. We present a novel method for automatic parameter selection based on the use of two distinct computational discretizations of the same problem. A feedback control algorithm dynamically adjusts the regularization strength, driving an iterative reconstruction toward the smallest parameter that yields sufficient similarity between reconstructions on the two grids. The effectiveness of the proposed approach is demonstrated using real tomographic data.
Paper Structure (17 sections, 3 equations, 6 figures, 1 algorithm)

This paper contains 17 sections, 3 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Discrete Inverse Problem
  4. Double Model Reconstruction
  5. Monotonicity Assumption
  6. Closed-Loop Control Formulation
  7. Experimental Setup
  8. Codes and Datasets
  9. Control Parameters and Execution
  10. Results
  11. Experiment 1 (Walnut / TV)
  12. Experiment 2 (Walnut / Tikhonov)
  13. Experiments 3 and 4 (Pine Cone)
  14. Comparative Analysis
  15. Baselines
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Feedback loop using double-model consistency sensing; update $\alpha$ until $S$ matches the user target.
  • Figure 2: Walnut / TV. (a) Initial noise-dominated state. (b) The converged result at target SSIM 0.95. (c) Over-regularized reference showing loss of detail. (d) The recorded monotonic SSIM vs. $\alpha$ curve. The controller halts in the target band.
  • Figure 3: Walnut / Tikhonov. The monotonic SSIM trajectories demonstrate that the control method is solver-agnostic.
  • Figure 4: Pine Cone / TV. The controller preserves the sharp scale structures while removing noise.
  • Figure 5: Pine Cone /Tikhonov. The loop stabilizes effectively even with the smoothing $L_2$ prior.
  • ...and 1 more figures