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Frequency-regularized Neural Representation Method for Sparse-view Tomographic Reconstruction

Jingmou Xian, Jian Zhu, Haolin Liao, Si Li

TL;DR

Sparse-view tomography seeks to reconstruct attenuation or activity fields from few projections, but the problem is ill-posed and prone to high-frequency artifacts. The authors propose Freq-NAF, a self-supervised method using hash-based positional encoding and a neural attenuation/activity field, with a frequency-regularization schedule that gradually reveals higher-frequency components. They validate on CBCT and SPECT datasets, showing state-of-the-art PSNR/SSIM/LPIPS and improved edge preservation via a Beer-Lambert-based projection synthesis, $I = I_0 \exp(-\sum_i v_i \delta_i)$. The approach mitigates overfitting, reduces artifacts, and enables high-quality, low-dose sparse-view reconstructions with potential for broad clinical impact.

Abstract

Sparse-view tomographic reconstruction is a pivotal direction for reducing radiation dose and augmenting clinical applicability. While many research works have proposed the reconstruction of tomographic images from sparse 2D projections, existing models tend to excessively focus on high-frequency information while overlooking low-frequency components within the sparse input images. This bias towards high-frequency information often leads to overfitting, particularly intense at edges and boundaries in the reconstructed slices. In this paper, we introduce the Frequency Regularized Neural Attenuation/Activity Field (Freq-NAF) for self-supervised sparse-view tomographic reconstruction. Freq-NAF mitigates overfitting by incorporating frequency regularization, directly controlling the visible frequency bands in the neural network input. This approach effectively balances high-frequency and low-frequency information. We conducted numerical experiments on CBCT and SPECT datasets, and our method demonstrates state-of-the-art accuracy.

Frequency-regularized Neural Representation Method for Sparse-view Tomographic Reconstruction

TL;DR

Sparse-view tomography seeks to reconstruct attenuation or activity fields from few projections, but the problem is ill-posed and prone to high-frequency artifacts. The authors propose Freq-NAF, a self-supervised method using hash-based positional encoding and a neural attenuation/activity field, with a frequency-regularization schedule that gradually reveals higher-frequency components. They validate on CBCT and SPECT datasets, showing state-of-the-art PSNR/SSIM/LPIPS and improved edge preservation via a Beer-Lambert-based projection synthesis, . The approach mitigates overfitting, reduces artifacts, and enables high-quality, low-dose sparse-view reconstructions with potential for broad clinical impact.

Abstract

Sparse-view tomographic reconstruction is a pivotal direction for reducing radiation dose and augmenting clinical applicability. While many research works have proposed the reconstruction of tomographic images from sparse 2D projections, existing models tend to excessively focus on high-frequency information while overlooking low-frequency components within the sparse input images. This bias towards high-frequency information often leads to overfitting, particularly intense at edges and boundaries in the reconstructed slices. In this paper, we introduce the Frequency Regularized Neural Attenuation/Activity Field (Freq-NAF) for self-supervised sparse-view tomographic reconstruction. Freq-NAF mitigates overfitting by incorporating frequency regularization, directly controlling the visible frequency bands in the neural network input. This approach effectively balances high-frequency and low-frequency information. We conducted numerical experiments on CBCT and SPECT datasets, and our method demonstrates state-of-the-art accuracy.
Paper Structure (11 sections, 5 equations, 5 figures, 3 tables)

This paper contains 11 sections, 5 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Proposed Method
  3. Positional encoding
  4. Attenuation coefficient/Activity estimation
  5. Attenuation coefficient/Activity synthesis
  6. Frequency regularization
  7. Experiments
  8. Experimental Setups
  9. Experimental Results
  10. Ablation Study
  11. Conclusion

Figures (5)

  • Figure 1: The motivation of frequency regularization in sparse-view tomographic reconstruction. The left and middle columns display the results of NAF and Freq-NAF, respectively, and the right column presents the ground truth.
  • Figure 2: Overview of Freq-NAF for sparse-view tomographic reconstruction. Given input views, we synthesized projections along X- or gamma-rays with uniformly-sampled points. Subsequently, we employed the proposed frequency regularization method to regulate the available frequency bands of positional encoding during training of neural attenuation/activity field. In reconstruction stage, different strategies were employed for CBCT and SPECT modalities.
  • Figure 3: Qualitative results of four methods. From left to right: examples of Xray projections, slices of 3D CT models reconstructed by four methods, and the ground truth CT slices. Please zoom in for a better view.
  • Figure 4: Qualitative result of SPECT reconstruction. Please zoom in for a better view.
  • Figure 5: Effects of frequency regularization duration on CT and SPECT datasets. We set the end iteration for frequency regularization as $T = \lfloor x\% \times \text{total\_iters} \rfloor$. Freq-NAF achieves good performance across a wide range of duration choices, which uniformly outperform "w/o. frequency regularization".