  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.
