Simultaneous deconvolution and phase retrieval from noisy data

In this work we present a new method for image reconstruction from the magnitude of its Fourier transform assuming availability of a blurred (low-resolution) version of the sought image. The method is based on convex optimization techniques that were previously considered impractical for the phase retrieval problem. However, experiments demonstrate that in case of noisy measurements, our method significantly outperforms classical method both in terms of reconstruction quality and number of iterations required. c © 2010

[1]  J. Miao,et al.  An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[2]  M. Nieto-Vesperinas.  A Study of the Performance of Nonlinear Least-square Optimization Methods in the Problem of Phase Retrieval , 1986 .

[3]  J. Zuo,et al.  Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities , 2003, Science.

[4]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[5]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[6]  S. Marchesini,et al.  X-ray image reconstruction from a diffraction pattern alone , 2003, physics/0306174.

[7]  I. Yavneh,et al.  Signal Reconstruction From The Modulus of its Fourier Transform , 2009 .

[8]  Irad Yavneh,et al.  Fast Reconstruction Method for Diffraction Imaging , 2009, ISVC.

[9]  M. Zibulevsky,et al.  Sequential Subspace Optimization Method for Large-Scale Unconstrained Problems , 2005 .

[10]  J. Miao,et al.  Quantitative imaging of single, unstained viruses with coherent x rays. , 2008, Physical review letters.

[11]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[12]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[13]  J. Kirz,et al.  Biological imaging by soft x-ray diffraction microscopy , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[14]  J R Fienup,et al.  Reconstruction of an object from the modulus of its Fourier transform. , 1978, Optics letters.