Generalized temporal sampling with active illumination in optical microscopy

Generalized sampling is a flexible framework for signal acquisition, which relaxes the need for ideal pre-filters. Nevertheless, implementation remains challenging for dynamic imaging applications because it requires simultaneously measuring multiple overlapping inner-products and because only positive signals (intensities) can be measured by cameras. We present a method to collect videos of monochromatic objects by projecting the incoming signal at each pixel in a temporal B-spline space of degree 0, 1, or 2 by using a conventional RGB camera and a modulated three-color light source for illumination. Specifically, we solve the basis function overlap problem by multiplexing the acquisition in different color ranges and use B-spline pieces (which are positive) as projection kernels of a biorthogonal projection-expansion bases pair. The steps to recover signal samples include spectral unmixing and inverse filtering. Reconstructions we obtained from simulated and experimentally-acquired microscopy data demonstrate the feasibility of our approach.