Speaker：Song Li (Zhejiang University) 

Time：2020-11-06, 15:00

Location：Tencent Meeting  ID：722 980 579 (Pwd：1106)

Abstract:

In my talk, I shall consider the problem of phase retrieval from Fourier measurements. E. Candés, X. Li and M. Soltanolkotabi have researched this problem with random diffraction patterns. By using the Phase Lift approach, they originally proved that O(log4 n) coded different patterns suffice for perfect recovery of complex-valued signals. Moreover, they expected to reduce this measurement number as pointed out in their paper. Subsequently, D. Gross, F. Krahmer and R. Kueng provided different coded diffraction patterns with real masks. Then they demonstrated that the phase information can be exactly recovered from O(log2 n) coded diffraction patterns for complex-valued signals of odd dimensions. By establishing a modified key lemma, combined with PhaseLift method and the works of D. Gross, F. Krahmer and R. Kueng, we prove that O(log2 n) coded diffraction patterns are sufficient to recover real-valued signals of even dimensions. Furthermore, two kinds of Riemannian optimization algorithms, namely, Riemannian gradient descent algorithm (RGrad) and Riemannian conjugate gradient descent algorithm (RCG), are presented to solve such problem. The measurements number are only O(n log n) which is optimal.