Phase retrieval is an important optimization problem that arises in di raction imaging, where the original structure of an object needs to be... Show morePhase retrieval is an important optimization problem that arises in di raction imaging, where the original structure of an object needs to be reconstructed from its measured di raction data that does not have information concerning the phase of the object. Multilevel algorithms can be used to compute solutions to the standard phase retrieval optimization problem by constructing a hierarchy of problems using a series of restriction and prolongation operations. The coarser problems have a quarter of the variables as the ner problems, and hence, there are much less linear algebra requirements for solving the coarser problems. Further, the prolongation of the solutions computed for the coarser problems yield good starting points for the ner problems. We can also use an approach that alternates between solving the coarse and ne problem. Parameters for these methods include the number of levels, prolongation and restriction operations, and the number of iterations to perform at each level. We study the solutions to the standard phase retrieval optimization problem that result from exploring these parameters and compare them to the results obtained from using single-level methods. M.S. in Applied Mathematics, December 2014 Show less
