  We propose a novel method that records a single compressive hologram in a
short time and extracts the depth of a scene from that hologram using a stereo
disparity technique. The method is verified with numerical simulations, but
there is no restriction on adapting this into an optical experiment. In the
simulations, a computer-generated hologram is first sampled with random binary
patterns, and measurements are utilized in a recovery algorithm to form a
compressive hologram. The compressive hologram is then divided into two parts
(two apertures), and these parts are separately reconstructed to form a stereo
image pair. The pair is eventually utilized in stereo disparity method for
depth map extraction. The depth maps of the compressive holograms with the
sampling rates of 2, 25, and 50 percent are compared with the depth map
extracted from the original hologram, on which compressed sensing is not
applied. It is demonstrated that the depth profiles obtained from the
compressive holograms are in very good agreement with the depth profile
obtained from the original hologram despite the data reduction.
