Phase retrieval by linear algebra

The null vector method, based on a simple linear algebraic concept, is proposed as an initialization method for nonconvex approaches to the phase retrieval problem. For the stylized measurement with random complex Gaussian matrices, a nonasymptotic error bound is derived, stronger than that of the spectral vector method. Numerical experiments show that the null vector method also has a superior performance for the realistic measurement of coded diffraction patterns in coherent diffractive imaging.