STOCHASTIC PROJECTION METHODS FOR SOLVING INVERSE PROBLEMS OF PHASE RETRIEVING AND X-RAY DIFFRACTION ANALYSIS

We suggest a stochastic simulation techniques for solving the inverse problem of recovering the phase of a complex-valued function provided its absolute value is known, under some additional information, and apply this method for retrieving the step structure of the epitaxial films from the x-ray diffraction analysis. To solve these problems we develop a new stochastic version of the Kaczmarz method with a new strategy of row sampling, and present some comparative simulations with a stochastic genetic algorithm and a simple version of a randomized projections method.