IEEE Trans Med Imaging. 2022 Aug;41(8):2048-2066. doi: 10.1109/TMI.2022.3154011. Epub 2022 Aug 1.
Encoding-decoding (ED) CNNs have demonstrated state-of-the-art performance for noise reduction over the past years. This has triggered the pursuit of better understanding the inner workings of such architectures, which has led to the theory of deep convolutional framelets (TDCF), revealing important links between signal processing and CNNs. Specifically, the TDCF demonstrates that ReLU CNNs induce low-rankness, since these models often do not satisfy the necessary redundancy to achieve perfect reconstruction (PR). In contrast, this paper explores CNNs that do meet the PR conditions. We demonstrate that in these type of CNNs soft shrinkage and PR can be assumed. Furthermore, based on our explorations we propose the learned wavelet-frame shrinkage network, or LWFSN and its residual counterpart, the rLWFSN. The ED path of the (r)LWFSN complies with the PR conditions, while the shrinkage stage is based on the linear expansion of thresholds proposed Blu and Luisier. In addition, the LWFSN has only a fraction of the training parameters (<1%) of conventional CNNs, very small inference times, low memory footprint, while still achieving performance close to state-of-the-art alternatives, such as the tight frame (TF) U-Net and FBPConvNet, in low-dose CT denoising.
在过去的几年中，编码-解码 (ED) CNN 在降噪方面表现出了最先进的性能。这引发了人们对更好地理解这些架构内部工作原理的追求，从而催生了深度卷积框架理论 (TDCF)，揭示了信号处理和 CNN 之间的重要联系。具体来说，TDCF 表明 ReLU CNN 诱导了低秩性，因为这些模型通常不满足实现完美重建 (PR) 的必要冗余。相比之下，本文探讨了满足 PR 条件的 CNN。我们证明了在这些类型的 CNN 中可以假设软收缩和 PR。此外，基于我们的探索，我们提出了学习的小波-帧收缩网络或 LWFSN 及其残差对应物 rLWFSN。(r)LWFSN 的 ED 路径符合 PR 条件，而收缩阶段基于 Blu 和 Luisier 提出的阈值的线性扩展。此外，LWFSN 的训练参数（<1%）仅为传统 CNN 的一小部分，推理时间非常短，内存占用低，同时在低剂量 CT 降噪方面仍能实现接近最先进替代方案（如紧框架 (TF) U-Net 和 FBPConvNet）的性能。
