Geodesic
The use of connected masks for reconstructing the single particle image from X-ray diffraction data
Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015), pp. t1-t19.

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The problem of reconstructing the image of a single macromolecular object from X-ray diffraction data can be formulated as a problem of the reconstruction of the 3D electron density distribution from the magnitudes of its Fourier transform. This problem can be reduced to a series of standard X-ray crystallography tasks, namely, the recovery of a periodic function from its Fourier coefficients (structure factors) magnitudes, which are determined in an X-ray diffraction experiment. In this work, a new approach to the solution of these tasks is suggested which is based on the use of connected binary masks as an approximation of the required electron density distribution. The approach includes the random generation of a great number of connected masks, the selection of the masks that are in agreement with an experimental and a priori information about the object, and the alignment and the averaging of the phase sets of the structure factors that correspond to the selected masks. The averaged phase values together with the experimentally determined magnitudes are used for the calculation of the Fourier synthesis, which is applied for the visualization of the object under study. The approach can be used in studies of both single particles and crystalline species; however, it holds the greatest promise for investigations of single objects. The results of testing the approach are presented. 
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     author = {V. Y. Lunin and N. L. Lunina and T. E. Petrova},
     title = {The use of connected masks for reconstructing the single particle image from {X-ray} diffraction data},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
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V. Y. Lunin; N. L. Lunina; T. E. Petrova. The use of connected masks for reconstructing the single particle image from X-ray diffraction data. Matematičeskaâ biologiâ i bioinformatika, Tome 10 (2015), pp. t1-t19. http://geodesic.mathdoc.fr/item/MBB_2015_10_a0/

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