Deep neural networks provide unprecedented performance gains in many real-world problems in signal and image processing. Despite these gains, the future development and practical deployment of deep networks are hindered by their black-box nature, i.e., a lack of interpretability and the need for very large training sets.
On the other hand, signal processing has traditionally relied on classical statistical modeling techniques that utilize mathematical formulations representing 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. Here we introduce various approaches to model based learning which merge parametric models with optimization tools and classical algorithms leading to efficient, interpretable networks from reasonably sized training sets. We then consider application of these ideas to super resolution microscopy and show that we can obtain super-resolution imaging from a small number of high emitter density frames without knowledge of the optical system and across different test sets using the proposed network.
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