Signal decomposition (analysis) and reconstruction (synthesis) are cornerstones in signal processing and feature recognition tasks. Signal decomposition is traditionally achieved by projecting data onto predefined basis functions, often known as atoms. Coefficient manipulation (e.g., thresholding) combined with signal reconstruction then either provides signals with enhanced quality or permits extraction of desired features only. More recently dictionary learning and deep learning have also been actively used for similar tasks. The purpose of dictionary learning is to derive the most appropriate basis functions directly from the observed data. In deep learning, neural networks or other transfer functions are taught to perform either feature classification or data enhancement directly, provided solely some training data. This review shows first how popular signal processing methods, such as basis pursuit and sparse coding, are related to analysis and synthesis. We then explain how dictionary learning and deep learning using neural networks can also be interpreted as generalized analysis and synthesis methods. We introduce the underlying principles of all techniques and then show their inherent strengths and weaknesses using various examples, including two toy examples, a moonscape image, a magnetic resonance image, and geophysical data.

中文翻译：

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使用字典、原子和深度学习的信号处理：通用分析-综合框架

信号分解（分析）和重构（合成）是信号处理和特征识别任务的基石。信号分解传统上是通过将数据投影到预定义的基函数（通常称为原子）上来实现的。然后，与信号重构相结合的系数操作（例如，阈值处理）或者提供具有增强质量的信号，或者只允许提取期望的特征。最近，字典学习和深度学习也被积极用于类似的任务。字典学习的目的是直接从观察到的数据中推导出最合适的基函数。在深度学习中，神经网络或其他传递函数被教导直接执行特征分类或数据增强，只提供一些训练数据。这篇综述首先展示了流行的信号处理方法，如基追踪和稀疏编码，是如何与分析和综合相关的。然后我们解释了字典学习和使用神经网络的深度学习如何也可以解释为广义的分析和综合方法。我们介绍了所有技术的基本原理，然后使用各种示例展示了它们的内在优势和劣势，包括两个玩具示例、月球景观图像、磁共振图像和地球物理数据。