Medical ultrasound imaging relies heavily on high-quality signal processing
algorithms to provide reliable and interpretable image reconstructions.
Hand-crafted reconstruction methods, often based on approximations of the
underlying measurement model, are useful in practice, but notoriously fall
behind in terms of image quality. More sophisticated solutions, based on
statistical modelling, careful parameter tuning, or through increased model
complexity, can be sensitive to different environments. Recently, deep learning
based methods have gained popularity, which are optimized in a data-driven
fashion. These model-agnostic methods often rely on generic model structures,
and require vast training data to converge to a robust solution. A relatively
new paradigm combines the power of the two: leveraging data-driven deep
learning, as well as exploiting domain knowledge. These model-based solutions
yield high robustness, and require less trainable parameters and training data
than conventional neural networks. In this work we provide an overview of these
methods from the recent literature, and discuss a wide variety of ultrasound
applications. We aim to inspire the reader to further research in this area,
and to address the opportunities within the field of ultrasound signal
processing. We conclude with a future perspective on these model-based deep
learning techniques for medical ultrasound applications