  This work reveals an experimental microscopy acquisition scheme successfully
combining Compressed Sensing (CS) and digital holography in off-axis and
frequency-shifting conditions. CS is a recent data acquisition theory involving
signal reconstruction from randomly undersampled measurements, exploiting the
fact that most images present some compact structure and redundancy. We propose
a genuine CS-based imaging scheme for sparse gradient images, acquiring a
diffraction map of the optical field with holographic microscopy and recovering
the signal from as little as 7% of random measurements. We report experimental
results demonstrating how CS can lead to an elegant and effective way to
reconstruct images, opening the door for new microscopy applications.
