Model-Based Deep Learning

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilizemathematical 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 ordynamic behavior. More recently, deep learning approaches that use highly parametric deep neural networks (DNNs) are becoming increasingly popular. Deep learning systems do not rely on mathematical modeling, and learn their mapping from data, which allows them to operate in complex environments. However, they lack the interpretability and reliability of model-based methods, typically require large training sets to obtain good performance,and tend to be computationally complex. Model-based signal processing methods and data-centric deep learning each have their pros and cons. These paradigms can be characterized as edges of a continuous spectrum varying in specificity and parameterization. The methodologies that lie in the middle ground of this spectrum, thus integrating model-based signal processing with deep learning, are referred to asmodel-based deep learning, and are the focushere. This monograph provides a tutorial style presentation ofmodel-based deep learning methodologies. These are familiesof algorithms that combine principled mathematicalmodels with data-driven systems to benefit from the advantagesof both approaches. Such model-based deep learningmethods exploit both partial domain knowledge, via mathematicalstructures designed for specific problems, as well aslearning from limited data. We accompany our presentationwith running signal processing examples, in super-resolution,tracking of dynamic systems, and array processing. We showhow they are expressed using the provided characterizationand specialized in each of the detailed methodologies. Ouraim is to facilitate the design and study of future systemsat the intersection of signal processing and machine learningthat incorporate the advantages of both domains. Thesource code of our numerical examples are available andreproducible as Python notebooks.