Three-dimensional (3D) object tomography from a two-dimensional recorded hologram is a process of high-dimensional data inference from undersampled data. As such, recently, techniques developed in the field of compressive sensing and sparse representation have been applied for this task. While many applications of compressive sensing for tomography from digital holograms have been demonstrated in the past few years, the fundamental limits involved have not yet been addressed. We formulate the guarantees for compressive sensing-based recovery of 3D objects and show their relation to the physical attributes of the recording setup.
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