Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning Wavelet-Sparse FDK for 3D Cone-Beam CT Reconstruction

Yipeng Sun, Linda-Sophie Schneider, Chengze Ye, Mingxuan Gu, Siyuan Mei, Siming Bayer, Andreas Maier

TL;DR

This work tackles noise and artifacts in cone-beam CT reconstructions by enhancing the efficient FDK algorithm with a neural network that selectively learns cosine weighting and filtering. It leverages 2D wavelet transforms to sparsify these components, achieving a substantial parameter reduction of $93.75\%$ without increasing inference cost and while preserving the interpretability of the classical method. Empirical results on simulated data show improved PSNR and SSIM across views, with robust performance under noise. The approach is designed to be plug-and-play for integration into existing CT pipelines, offering a practical path toward higher-quality CBCT reconstructions in resource-constrained clinical environments.

Abstract

Cone-Beam Computed Tomography (CBCT) is essential in medical imaging, and the Feldkamp-Davis-Kress (FDK) algorithm is a popular choice for reconstruction due to its efficiency. However, FDK is susceptible to noise and artifacts. While recent deep learning methods offer improved image quality, they often increase computational complexity and lack the interpretability of traditional methods. In this paper, we introduce an enhanced FDK-based neural network that maintains the classical algorithm's interpretability by selectively integrating trainable elements into the cosine weighting and filtering stages. Recognizing the challenge of a large parameter space inherent in 3D CBCT data, we leverage wavelet transformations to create sparse representations of the cosine weights and filters. This strategic sparsification reduces the parameter count by $93.75\%$ without compromising performance, accelerates convergence, and importantly, maintains the inference computational cost equivalent to the classical FDK algorithm. Our method not only ensures volumetric consistency and boosts robustness to noise, but is also designed for straightforward integration into existing CT reconstruction pipelines. This presents a pragmatic enhancement that can benefit clinical applications, particularly in environments with computational limitations.

Learning Wavelet-Sparse FDK for 3D Cone-Beam CT Reconstruction

TL;DR

This work tackles noise and artifacts in cone-beam CT reconstructions by enhancing the efficient FDK algorithm with a neural network that selectively learns cosine weighting and filtering. It leverages 2D wavelet transforms to sparsify these components, achieving a substantial parameter reduction of without increasing inference cost and while preserving the interpretability of the classical method. Empirical results on simulated data show improved PSNR and SSIM across views, with robust performance under noise. The approach is designed to be plug-and-play for integration into existing CT pipelines, offering a practical path toward higher-quality CBCT reconstructions in resource-constrained clinical environments.

Abstract

Cone-Beam Computed Tomography (CBCT) is essential in medical imaging, and the Feldkamp-Davis-Kress (FDK) algorithm is a popular choice for reconstruction due to its efficiency. However, FDK is susceptible to noise and artifacts. While recent deep learning methods offer improved image quality, they often increase computational complexity and lack the interpretability of traditional methods. In this paper, we introduce an enhanced FDK-based neural network that maintains the classical algorithm's interpretability by selectively integrating trainable elements into the cosine weighting and filtering stages. Recognizing the challenge of a large parameter space inherent in 3D CBCT data, we leverage wavelet transformations to create sparse representations of the cosine weights and filters. This strategic sparsification reduces the parameter count by without compromising performance, accelerates convergence, and importantly, maintains the inference computational cost equivalent to the classical FDK algorithm. Our method not only ensures volumetric consistency and boosts robustness to noise, but is also designed for straightforward integration into existing CT reconstruction pipelines. This presents a pragmatic enhancement that can benefit clinical applications, particularly in environments with computational limitations.
Paper Structure (9 sections, 11 equations, 2 figures, 2 tables)

This paper contains 9 sections, 11 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Choice of Wavelet Basis
  4. Trainable Cosine Weighting
  5. Trainable Filtering
  6. Integration into a Neural Network
  7. Experiments
  8. Results
  9. Discussion and Conclusion

Figures (2)

  • Figure 1: Network for $I_{\text{rec}} = \text{ReLU}( A^{-1} {F}^{-1}H_{rec}{F} W_{rec}P )$ from projections $P$ to reconstruction ${I}_{rec}$.
  • Figure 2: Comparison of visualization results between our proposed method and FDK reconstruction (Ram-Lak filter). The figure shows axial, sagittal, and coronal views with their corresponding difference maps (Patient ID: 07).