CPM Seminar

Phase problem and iterative algorithms

Pierre Thibault

Paul Scherrer Institut

How to compute a Fourier transform when only a part of the information (the amplitude) is available, and the rest (the phase) is irremediably lost? This “phase problem”, although it is probably a hundred years old, is still a problem to which many scientists are commonly confronted. In this talk, I will describe the development of new microscopy methods grouped under the name of “coherent diffractive imaging” and which rely on the possibility of solving the phase problem. Emphasis will be put on one particular reconstruction method developed in this field and expressed in terms of constraint sets and projection onto them. In addition to the microscopy applications, I will quickly show recent results that demonstrate the broader range of applications of the formalism, going from quasicrystals to folding proteins and solving Sudoku puzzles.