  The use of fluorescent molecules to create long sequences of low-density,
diffraction-limited images enables highly-precise molecule localization.
However, this methodology requires lengthy imaging times, which limits the
ability to view dynamic interactions of live cells on short time scales. Many
techniques have been developed to reduce the number of frames needed for
localization, from classic iterative optimization to deep neural networks.
Particularly, deep algorithm unrolling utilizes both the structure of iterative
sparse recovery algorithms and the performance gains of supervised deep
learning. However, the robustness of this approach is highly dependant on
having sufficient training data. In this paper we introduce deep unrolled
self-supervised learning, which alleviates the need for such data by training a
sequence-specific, model-based autoencoder that learns only from given
measurements. Our proposed method exceeds the performance of its supervised
counterparts, thus allowing for robust, dynamic imaging well below the
diffraction limit without any labeled training samples. Furthermore, the
suggested model-based autoencoder scheme can be utilized to enhance
generalization in any sparse recovery framework, without the need for external
training data.
