Information retrieval in coherent diffraction imaging

D.E. Galli (1), E. Carlino (2), L. De Caro (3), A. Colombo (1), F. Scattarella (2) 1. Dipartimento di Fisica, Università degli Studi di Milano, Milano, Italy 2. Istituto Officina dei Materiali (IOM CNR), Laboratorio TASC, Trieste, Italy 3. Istituto di Cristallografia (IC CNR), Bari, Italy

Coherent diffractive imaging (CDI) is a promising technique for visualizing objects down to atomic resolution using X-rays or to sub-atomic resolution using electrons. Quite often, the weakest link in the CDI reconstruction procedure is the difficulty of the numerical phase retrieval from experimental diffraction patterns. Standard algorithms are based on deterministic iterative procedures, which update an estimate of the spatial density iteratively applying constraints in direct and reciprocal spaces. It is well known that such iterative procedure easily gets into stagnation issues, and this drawback is stimulating search for better numerical phase retrieval algorithms. Standard and novel approaches to address the so called “phase problem” will be discussed. In particular, I will present a new approach which mixes stochastic optimization and deterministic methods trying to exploit both the ability of iterative algorithms (such as Error Reduction and Hybrid Input Output) to quickly find a “local” optimal solution and the ability of stochastic optimization methods (in particular genetic algorithms) to smartly gather the information provided by parallel recovering processes with different initial conditions.