Discrete phase retrieval by solving linear systems of equations: performance under noisy conditions

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 presented new solutions to the discrete phase retrieval problem of Yagle and Bell (see Proc. ICIP, Santa Barbara, CA, 1997) which formulate the problem as a linear system of equations. These methods are computationally simpler and more stable than previous iterative and exact phase retrieval methods. Moreover, our new solutions are able to explicitly address noisy magnitude information through total least squares type techniques. We present examples of our algorithms´ performance under various noise conditions for two approaches, one based on the singular value decomposition and the other based on preserving the structure in the system matrix