Sectional image reconstruction in optical scanning holography using compressed sensing

Optical scanning holography is a form of digital holographic system, which allows us to capture a three-dimensional (3D) object in the two-dimensional (2D) hologram. A post-processing step known as sectional image reconstruction can then be applied to reconstruct a 2D plane of the object. In this paper, we show that the Fourier transform of the hologram corresponds to samples along a semi-spherical surface of the Fourier transform of the 3D object. Since the Fourier basis satisfies the uniform uncertainty principle, we can view the hologram capture as a form of compressed sensing, and reconstruction of the sectional images can then be accomplished by solving a total variation minimization problem.