Compressed Hadamard microscopy for high-speed optically sectioned neuronal activity recordings

Structured illumination microscopies achieve optical sectioning via differential modulation of in-focus and out-of-focus contributions to an image. Multiple wide-field camera images are analyzed to recreate an optical section. The requirement for multiple camera frames per image entails a loss of temporal resolution compared to conventional wide-field imaging. Here we describe a computational structured illumination imaging scheme, compressed Hadamard imaging, which achieves simultaneously high spatial and temporal resolution for optical sectioning of 3D samples with low-rank dynamics (e.g. neurons labeled with fluorescent activity reporters). We validate the technique with numerical simulations, and then illustrate with wide-area optically sectioned recordings of membrane voltage dynamics in mouse neurons in an acute brain slice and of calcium dynamics in zebrafish brain in vivo.