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Accelerated Optimization of Implicit Neural Representations for CT Reconstruction

Mahrokh Najaf, Gregory Ongie

TL;DR

This work tackles the slow optimization of implicit neural representations (INRs) for CT reconstruction by introducing two acceleration strategies: a filtered least squares (FLS) loss that preconditions the problem with a FBPreconditioning matrix ${m{F}}$, and an ADMM-based training scheme that alternates between updating the image estimate and INR parameters. The authors show that FLS improves conditioning and speeds convergence, while ADMM provides a robust, inexact-solve framework that yields superior final image quality in synthetic sparse-view breast CT across multiple INR architectures. Experiments demonstrate substantial improvements in convergence speed and final mean-squared error (MSE) compared to the standard least-squares loss, suggesting practical INR-based CT reconstruction with limited-view data. The approaches offer a pathway to faster, regularized INR reconstructions and can potentially be combined with ordered-subsets or meta-optimization in future work to further enhance performance.

Abstract

Inspired by their success in solving challenging inverse problems in computer vision, implicit neural representations (INRs) have been recently proposed for reconstruction in low-dose/sparse-view X-ray computed tomography (CT). An INR represents a CT image as a small-scale neural network that takes spatial coordinates as inputs and outputs attenuation values. Fitting an INR to sinogram data is similar to classical model-based iterative reconstruction methods. However, training INRs with losses and gradient-based algorithms can be prohibitively slow, taking many thousands of iterations to converge. This paper investigates strategies to accelerate the optimization of INRs for CT reconstruction. In particular, we propose two approaches: (1) using a modified loss function with improved conditioning, and (2) an algorithm based on the alternating direction method of multipliers. We illustrate that both of these approaches significantly accelerate INR-based reconstruction of a synthetic breast CT phantom in a sparse-view setting.

Accelerated Optimization of Implicit Neural Representations for CT Reconstruction

TL;DR

This work tackles the slow optimization of implicit neural representations (INRs) for CT reconstruction by introducing two acceleration strategies: a filtered least squares (FLS) loss that preconditions the problem with a FBPreconditioning matrix , and an ADMM-based training scheme that alternates between updating the image estimate and INR parameters. The authors show that FLS improves conditioning and speeds convergence, while ADMM provides a robust, inexact-solve framework that yields superior final image quality in synthetic sparse-view breast CT across multiple INR architectures. Experiments demonstrate substantial improvements in convergence speed and final mean-squared error (MSE) compared to the standard least-squares loss, suggesting practical INR-based CT reconstruction with limited-view data. The approaches offer a pathway to faster, regularized INR reconstructions and can potentially be combined with ordered-subsets or meta-optimization in future work to further enhance performance.

Abstract

Inspired by their success in solving challenging inverse problems in computer vision, implicit neural representations (INRs) have been recently proposed for reconstruction in low-dose/sparse-view X-ray computed tomography (CT). An INR represents a CT image as a small-scale neural network that takes spatial coordinates as inputs and outputs attenuation values. Fitting an INR to sinogram data is similar to classical model-based iterative reconstruction methods. However, training INRs with losses and gradient-based algorithms can be prohibitively slow, taking many thousands of iterations to converge. This paper investigates strategies to accelerate the optimization of INRs for CT reconstruction. In particular, we propose two approaches: (1) using a modified loss function with improved conditioning, and (2) an algorithm based on the alternating direction method of multipliers. We illustrate that both of these approaches significantly accelerate INR-based reconstruction of a synthetic breast CT phantom in a sparse-view setting.

Paper Structure

This paper contains 10 sections, 12 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Proposed Approaches
  4. Filtered Least Squares Loss Function
  5. Linearized analysis
  6. ADMM Algorithm
  7. Experiments
  8. Discussion and Conclusion
  9. Compliance with ethical standards
  10. Acknowledgments

Figures (2)

  • Figure 1: Reconstruction of simulated sparse-view breast CT data with various INR architectures (ReLU, SIREN, Hash Encoding) using a standard least squares (LS) loss, the proposed filtered least squares (FLS) loss, and the proposed ADMM algorithm. The left panel shows a baseline filtered back-projection (FBP) and total variation (TV) regularized reconstruction.
  • Figure 2: Reconstruction MSE vs iterations for the different INR architectures optimized using a standard least squares (LS) loss, the proposed filtered least squares (FLS) loss, and the proposed ADMM algorithm.