Compressed sensing and differential measurements in interferometry

摘要

In this paper, we propose and analyze a new compressive Fourier phase retrieval (PR) technique based on differential measurement, that can provably recover sparse signals with O(s polylog N) phase-less measurements. This measurement technique is easily implementable using intcrferometric techniques like Holography and Frequency Domain Optical Coherence Tomography. The proposed l_1 minimization based recovery is able to achieve the same reconstruction quality as some of the popular PR algorithms with far fewer measurements.