Title: Fast Two-photon Microscopy by Neuroimaging with Oblong Random Acquisition (NORA)
Primary area: applications to neuroscience & cognitive science
Keywords: Low-Rank, Computational Imaging, multi-photon imaging, matrix completion, two-photon imaging, nuclear-minimization, neuroimaging

Abstract: Advances in neural imaging have enabled neuroscientists to study how the activity of large neural populations produce perception, behavior and cognition. Despite many developments in optical methods, there exists a fundamental tradeoff between imaging speed, field of view, and resolution that limits the scope of neural imaging, especially for the raster-scanning multi-photon imaging needed for imaging deeper into the brain. One approach to overcoming this trade-off is computational imaging, in which an imaging system efficiently encodes the target image through its optical design and then recovers the acquired information through inverting the encoded measurements algorithmically. Computational imaging thus fundamentally depends on the reliability of recovery. While such approaches are emerging for recovery of optical neural imaging from encoded measurements, they lack a core theoretical sampling theory that will guarantee reliable and accurate recovery. We present here such a theory, based on the widely used model of functional optical imaging videos being low-rank. We show that under simple blurring and randomized line-subsampling conditions, full videos can be recovered from a small fraction of the lines, providing the opportunity for an order-of-magnitude speedup. We use this theory to develop a practical design for fast imaging: Neuroimaging with Oblong Random Acquisition (NORA). NORA, guided by our theory, can be implemented through simple-to-implement changes to widely available systems. Moreover, following our theory, NORA reconstructs the entire video together via nuclear-norm minimization on the pixels-by-time matrix, rather than more common frame-by-frame recovery. We simulated NORA imaging using the Neural Anatomy and Optical Microscopy (NAOMi) biophysical simulator, showing that NORA can accurately recover 400~$\mu$m~X~400~$\mu$m fields of view at subsampling rates up to 20X despite realistic noise and motion conditions, thereby demonstrating that our theory holds. These speeds open up the capability of future systems to extend into imaging faster processes in neural systems, such as voltage and glutamate.

TL;DR: Theory-grounded method for fast multi-photon microscopy using simple optical design and matrix completion