  The mathematical theory of compressed sensing (CS) asserts that one can
acquire signals from measurements whose rate is much lower than the total
bandwidth. Whereas the CS theory is now well developed, challenges concerning
hardware implementations of CS-based acquisition devices-especially in
optics-have only started being addressed. This paper presents an implementation
of compressive sensing in fluorescence microscopy and its applications to
biomedical imaging. Our CS microscope combines a dynamic structured wide-field
illumination and a fast and sensitive single-point fluorescence detection to
enable reconstructions of images of fluorescent beads, cells, and tissues with
undersampling ratios (between the number of pixels and number of measurements)
up to 32. We further demonstrate a hyperspectral mode and record images with
128 spectral channels and undersampling ratios up to 64, illustrating the
potential benefits of CS acquisition for higher-dimensional signals, which
typically exhibits extreme redundancy. Altogether, our results emphasize the
interest of CS schemes for acquisition at a significantly reduced rate and
point to some remaining challenges for CS fluorescence microscopy.
