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.

使用 UnWave-Net 网络进行计算机斯康特引弹散射层析成像的图像重建，达到了优于现有方法的性能并提供了改善的计算效率。

UnWave-Net：无卷积扩展小波网络用于康普顿层析图像重建

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

Combining the strengths of model-based iterative algorithms and data-driven
deep learning solutions, deep unrolling networks (DuNets) have become a popular
tool to solve inverse imaging problems. While DuNets have been successfully
applied to many linear inverse problems, nonlinear problems tend to impair the
performance of the method. Inspired by momentum acceleration techniques that
are often used in optimization algorithms, we propose a recurrent momentum
acceleration (RMA) framework that uses a long short-term memory recurrent
neural network (LSTM-RNN) to simulate the momentum acceleration process. The
RMA module leverages the ability of the LSTM-RNN to learn and retain knowledge
from the previous gradients. We apply RMA to two popular DuNets -- the learned
proximal gradient descent (LPGD) and the learned primal-dual (LPD) methods,
resulting in LPGD-RMA and LPD-RMA respectively. We provide experimental results
on two nonlinear inverse problems: a nonlinear deconvolution problem, and an
electrical impedance tomography problem with limited boundary measurements. In
the first experiment we have observed that the improvement due to RMA largely
increases with respect to the nonlinearity of the problem. The results of the
second example further demonstrate that the RMA schemes can significantly
improve the performance of DuNets in strongly ill-posed problems.

结合模型驱动的迭代算法和数据驱动的深度学习解决方案，我们提出了一种循环动量加速（RMA）框架，使用长短期记忆循环神经网络（LSTM-RNN）来模拟动量加速过程，通过应用 RMA 到两种流行的 DuNets 方法（LPGD-RMA 和 LPD-RMA），在非线性逆问题上取得了显著的性能提升。

深度展开网络与循环动量加速在非线性逆问题中的应用

Deep Unrolling Networks with Recurrent Momentum Acceleration for  Nonlinear Inverse Problems

Deep unrolling networks that utilize sparsity priors have achieved great
success in dynamic magnetic resonance (MR) imaging. The convolutional neural
network (CNN) is usually utilized to extract the transformed domain, and then
the soft thresholding (ST) operator is applied to the CNN-transformed data to
enforce the sparsity priors. However, the ST operator is usually constrained to
be the same across all channels of the CNN-transformed data. In this paper, we
propose a novel operator, called soft thresholding with channel attention
(AST), that learns the threshold for each channel. In particular, we put
forward a novel deep unrolling shrinkage network (DUS-Net) by unrolling the
alternating direction method of multipliers (ADMM) for optimizing the
transformed $l_1$ norm dynamic MR reconstruction model. Experimental results on
an open-access dynamic cine MR dataset demonstrate that the proposed DUS-Net
outperforms the state-of-the-art methods. The source code is available at
https://github.com/yhao-z/DUS-Net.

通过使用一种称为带通道注意力的软阈值算子 (AST)，我们提出了一种用于动态磁共振成像的新型深度展开收缩网络 (DUS-Net)，通过展开交替方向乘法因子方法 (ADMM) 对转换后的 $l_1$ 范数动态 MR 重建模型进行优化，实验证明 DUS-Net 优于现有的方法。