NCKU Math Colloquium / RCTS Seminar

DATE2016-01-07 16:10-17:00



TITLETitle Phase Retrieval with Random Illumination

ABSTRACT Abstract: In many areas of imaging science, it is difficult to determine the phase of linear measurements. For example, in the X-ray imaging, the detector can only measure the Fourier magnitude of the received optical wave. In this setting, the goal of the phase retrieval is to reconstruct the unknown image from its Fourier magnitude data. Due to the absence of the phase information, the phase retrieval does not have a unique solution. In 2012, Albert Fannjiang proved that randomly modifying the phases of the unknown image by a mask can lead to a unique solution up to a global phase factor. Apart from considering the uniqueness of the phase retrieval problem, the simulation results show that random illuminations also significantly improve the numerical performance of the Error-Reduction (ER) algorithm, which is the most popular phase-retrieval algorithm. This talk describes the mathematical formulation of the phase retrieval problem, why the random illumination can improve the performance of the ER algorithm, and what breakthroughs about the convergence of the ER algorithm have been made compared with related works.