2-D phase retrieval by partitioning into coupled 1-D problems using discrete Radon transforms

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 solve the 2-D discrete phase retrieval problem by partitioning it into a mostly-decoupled set of 1-D phase retrieval problems. The discrete and modulated Radon transforms are used to formulate two coupled 1-D problems, the solution to which then specifies solutions to the other decoupled 1-D problems. The latter may in turn be solved in parallel; however, using the solution to one problem as the input to a neighboring problem reduces the computation significantly for serial computers. Unlike other exact 2-D phase retrieval methods which rely on tracking zero curves of algebraic functions or equivalent operations, no continuous-function-based methods are used here. This makes the procedure more robust numerically