1-D and 2-D minimum and non-minimum phase retrieval by solving linear systems of equations

The discrete phase retrieval problem is to reconstruct a discrete-time signal whose support is known and compact from the magnitude of its discrete Fourier transform. We assume knowledge of some values of the signal, e.g. bands of zeros or known values, and solve the problem by solving linear systems of equations. No rooting of polynomials or tracking zero curves of algebraic functions (both very expensive computationally and unstable numerically) is required. Not only is our method much simpler computationally than previous methods, but it also allows the use of total least squares type techniques to be applied to the linear systems of equations, so that noisy data can be handled