UnWave-Net: Unrolled Wavelet Network for Compton Tomography Image Reconstruction

TL;DR

This work addresses the ill-posed problem of Compton scatter tomography (CST) image reconstruction for a non-collimated circular CST geometry, where no analytic inversion is known for the double circular-arc forward model. It introduces UnWave-Net, a wavelet-based unrolled network that regularizes iterative reconstructions by applying a discrete wavelet transform (LL band) processed with a Swin Transformer to capture long-range dependencies, while maintaining efficiency through subband dimensionality reduction. The network takes the data y and a pseudo-inverse term Ay and performs 16 unrolled iterations to produce high-quality reconstructions, achieving state-of-the-art PSNR/SSIM and faster inference compared with existing unrolling and post-processing methods on the AAPM CT dataset. The approach demonstrates robust performance in the presence of noise and offers a practical CST reconstruction framework with potential extensions to other imaging modalities, albeit with the caveat of longer training times typical of deep unrolling methods.

Abstract

Computed tomography (CT) is a widely used medical imaging technique to scan internal structures of a body, typically involving collimation and mechanical rotation. Compton scatter tomography (CST) presents an interesting alternative to conventional CT by leveraging Compton physics instead of collimation to gather information from multiple directions. While CST introduces new imaging opportunities with several advantages such as high sensitivity, compactness, and entirely fixed systems, image reconstruction remains an open problem due to the mathematical challenges of CST modeling. In contrast, deep unrolling networks have demonstrated potential in CT image reconstruction, despite their computationally intensive nature. In this study, we investigate the efficiency of unrolling networks for CST image reconstruction. To address the important computational cost required for training, we propose UnWave-Net, a novel unrolled wavelet-based reconstruction network. This architecture includes a non-local regularization term based on wavelets, which captures long-range dependencies within images and emphasizes the multi-scale components of the wavelet transform. We evaluate our approach using a CST of circular geometry which stays completely static during data acquisition, where UnWave-Net facilitates image reconstruction in the absence of a specific reconstruction formula. Our method outperforms existing approaches and achieves state-of-the-art performance in terms of SSIM and PSNR, and offers an improved computational efficiency compared to traditional unrolling networks.

Figures (4)

• Figure 1: NCCCST setup. Left: the dotted circle represents the ring containing point-like blue detectors $D_{k}$, with the red source $S$. Center: measured data. Right: reconstruction using pseudo-inversion of the data exhibits severe artifacts.
• Figure 2: Overall structure of the proposed UnWave-Net for NCCCST reconstruction. The method utilizes wavelet transform to reduce computational complexity.
• Figure 3: Visual comparison with noisy data and $K = 100$. The cropped region highlights the superior artifact supression of our UnWave-Net compared to RegFormer.
• Figure 4: Ablation on the number of unrolling iterations. Quantitative and efficiency comparisons of our UnWave-Net against RegFormer and LEARN.