Denoised Wigner distribution deconvolution via low-rank matrix completion

Wigner distribution deconvolution (WDD) is a decades-old method for recovering phase from intensity measurements. Although the technique offers an elegant linear solution to the quadratic phase retrieval problem, it has seen limited adoption due to its high computational/memory requirements and the fact that the technique often exhibits high noise sensitivity. Here, we propose a method for noise suppression in WDD via low-rank noisy matrix completion. Our technique exploits the redundancy of an object's phase space to denoise its WDD reconstruction. We show in model calculations that our technique outperforms other WDD algorithms as well as modern iterative methods for phase retrieval such as ptychography. Our results suggest that a class of phase retrieval techniques relying on regularized direct inversion of ptychographic datasets (instead of iterative reconstruction techniques) can provide accurate quantitative phase information in the presence of high levels of noise.