A Study of the Performance of Nonlinear Least-square Optimization Methods in the Problem of Phase Retrieval

The efficiency of an important class of Newton methods (the Levenberg-Marquardt algorithm) for solving overdetermined sets of nonlinear equations is tested in finding the solution to the two-dimensional phase problem. It is seen that the nonlinearity and number of local minima of the cost function increases dramatically with the size of the object array, making these methods of little practical use for sizes greater than 6 2 6.

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