Abstract
We present a fast image reconstruction method for two- and three-dimensional diffraction imaging. Provided that very little information about the phase is available, the method demonstrates convergence rates that are several orders of magnitude faster than current reconstruction techniques. Unlike current methods, our approach is based on convex optimization. Besides fast convergence, our method allows great deal of flexibility in choosing most appropriate objective function as well as introducing additional information about the sought signal, e.g., smoothness. Benefits of good choice of the objective function are demonstrated by reconstructing an image from noisy data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Neutze, R., Wouts, R., van der Spoel, D., Weckert, E., Hajdu, J.: Potential for biomolecular imaging with femtosecond x-ray pulses. Nature 406(6797), 752–757 (2000)
Marchesini, S., He, H., Chapman, H.N., Hau-Riege, S.P., Noy, A., Howells, M.R., Weierstall, U., Spence, J.C.H.: X-ray image reconstruction from a diffraction pattern alone. Physical Review B 68(14) (October 2003); 140101 Copyright (C) 2009 The American Physical Society; Please report any problems to prola@aps.org
Hayes, M.: The reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform. IEEE Transactions on Acoustics, Speech, and Signal Processing [IEEE Transactions on Signal Processing] 30(2), 140–154 (1982)
Hove, P.V., Hayes, M., Lim, J., Oppenheim, A.: Signal reconstruction from signed fourier transform magnitude. IEEE Transactions on Acoustics, Speech and Signal Processing 31(5), 1286–1293 (1983)
Gerchberg, R.W., Saxton, W.O.: A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237–246 (1972)
Fienup, J.R.: Phase retrieval algorithms: a comparison. Applied Optics 21(15), 2758–2769 (1982)
Osherovich, E., Zibulevsky, M., Yavneh, I.: Signal reconstruction from the modulus of its fourier transform. Technical Report CS-2009-09, Technion (December 2008)
Nieto-Vesperinas, M.: A study of the performance of nonlinear least-square optimization methods in the problem of phase retrieval. Journal of Modern Optics 33, 713–722 (1986)
Narkiss, G., Zibulevsky, M.: Sequential subspace optimization method for Large-Scale unconstrained problems. CCIT 559, Technion, EE Department (2005)
Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Mathematical Programming 45(1), 503–528 (1989)
Miao, J., Hodgson, K.O., Sayre, D.: An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images. Proceedings of the National Academy of Sciences of the United States of America 98(12), 6641–6645 (2001)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1-4), 259–268 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Osherovich, E., Zibulevsky, M., Yavneh, I. (2009). Fast Reconstruction Method for Diffraction Imaging. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2009. Lecture Notes in Computer Science, vol 5876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10520-3_102
Download citation
DOI: https://doi.org/10.1007/978-3-642-10520-3_102
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10519-7
Online ISBN: 978-3-642-10520-3
eBook Packages: Computer ScienceComputer Science (R0)