Alternating Direction Methods for Classical and Ptychographic Phase Retrieval

Stefano just sent me the following:

Hi Igor,

I'd like to bring your attention to some references on phase retrieval, I hope you enjoy the links:

http://math.sjtu.edu.cn/faculty/zw2109/paper/PRADM.pdf

http://arxiv.org/abs/1209.4924

a presentation by Filipe Maia on Multi-GPU Real-Time Ptychographic X-ray Image Reconstruction at http://nvidia.fullviewmedia.com/gtc2012/0516-A8-S0131.html

some diffraction data is available here :http://cxidb.org/

see also this (By Filipe Maia):

http://www.nature.com/nmeth/journal/v9/n9/full/nmeth.2110.html

cheers,

Stefano

Thanks Stefano .Here are the two papers:

Alternating Direction Methods for Classical and Ptychographic Phase Retrieval by Zaiwen Wen, Chao Yang, Xin Liu, Stefano Marchesini

Abstract. In this paper, we show how augmented Lagrangian alternating direction method (ADM) can be used to solve both the classical and ptychographic phase retrieval problems. We point out the connection between ADM and projection algorithms such as the hybrid input-output (HIO) algorithm, and compare its performance against standard algorithms for phase retrieval on a number of test images. Our computational experiments show that ADM appears to be less sensitive to the choice of relaxation parameters, and it usually outperforms the existing techniques for both the classical and ptychographic phase retrieval problems.

Augmented projections for ptychographic imaging by Stefano Marchesini, Andre Schirotzek, Filipe Maia, Chao Yang. The abstract reads:

Ptychography is a popular technique to achieve diffraction limited resolution images of a two or three dimensional sample using high frame rate detectors. We introduce a relaxation of common projection algorithms to account for instabilities given by intensity and background fluctuations, position errors, or poor calibration using multiplexing illumination. This relaxation introduces an additional phasing optimization at every step that enhances the convergence rate of common projection algorithms. Numerical tests exhibit the exact recovery of the object and the noise when there is high redundancy in the data.

Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.