Encoding-decoding convolutional neural networks (CNNs) play a central role in data-driven noise reduction and can be found within numerous deep learning algorithms. However, the development of these CNN architectures is often done in an ad hoc fashion and theoretical underpinnings for important design choices are generally lacking. Up to now, there have been different existing relevant works that have striven to explain the internal operation of these CNNs. Still, these ideas are either scattered and/or may require significant expertise to be accessible for a bigger audience. To open up this exciting field, this article builds intuition on the theory of deep convolutional framelets (TDCFs) and explains diverse encoding-decoding (ED) CNN architectures in a unified theoretical framework. By connecting basic principles from signal processing to the field of deep learning, this self-contained material offers significant guidance for designing robust and efficient novel CNN architectures.

中文翻译：

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降噪卷积神经网络的信号处理解读：探索编码-解码 CNN 的数学公式

编码-解码卷积神经网络 (CNN) 在数据驱动的降噪中发挥着核心作用，并且可以在许多深度学习算法中找到。然而，这些 CNN 架构的开发通常是以临时方式完成的，并且通常缺乏重要设计选择的理论基础。到目前为止，已经有不同的现有相关工作致力于解释这些 CNN 的内部运作。尽管如此，这些想法要么是分散的，要么可能需要大量的专业知识才能为更多的受众所接受。为了开拓这个令人兴奋的领域，本文建立了深度卷积框架 (TDCF) 理论的直觉，并在统一的理论框架中解释了不同的编码-解码 (ED) CNN 架构。通过将信号处理的基本原理与深度学习领域联系起来，这种独立的材料为设计稳健且高效的新型 CNN 架构提供了重要指导。