  Signal processing, communications, and control have traditionally relied on
classical statistical modeling techniques. Such model-based methods utilize
mathematical formulations that represent the underlying physics, prior
information and additional domain knowledge. Simple classical models are useful
but sensitive to inaccuracies and may lead to poor performance when real
systems display complex or dynamic behavior. On the other hand, purely
data-driven approaches that are model-agnostic are becoming increasingly
popular as datasets become abundant and the power of modern deep learning
pipelines increases. Deep neural networks (DNNs) use generic architectures
which learn to operate from data, and demonstrate excellent performance,
especially for supervised problems. However, DNNs typically require massive
amounts of data and immense computational resources, limiting their
applicability for some signal processing scenarios. We are interested in hybrid
techniques that combine principled mathematical models with data-driven systems
to benefit from the advantages of both approaches. Such model-based deep
learning methods exploit both partial domain knowledge, via mathematical
structures designed for specific problems, as well as learning from limited
data. In this article we survey the leading approaches for studying and
designing model-based deep learning systems. We divide hybrid
model-based/data-driven systems into categories based on their inference
mechanism. We provide a comprehensive review of the leading approaches for
combining model-based algorithms with deep learning in a systematic manner,
along with concrete guidelines and detailed signal processing oriented examples
from recent literature. Our aim is to facilitate the design and study of future
systems on the intersection of signal processing and machine learning that
incorporate the advantages of both domains.
