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Non-uniqueness and instability of ‘ankylography’

Abstract

Arising from K. S. Raines et al. Nature 463, 214–217 (2010)10.1038/nature08705

Raines et al.1 have proposed ‘ankylography’ as a three-dimensional tomographic modality with a single monochromatic beam1. They believe that the three-dimensional structure of an object is “in principle determined by the 2D spherical pattern” that “is sampled at a sufficiently fine scale on the Ewald sphere.” Although they restricted their approach to unspecified “certain circumstances”, they claim potential “broad applications in the physical and life sciences”. Nevertheless, the imaging principles and proposed methodology of ankylography are flawed, bringing into question its applications, which was also pointed out by others, such as in ref. 2.

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Figure 1: Numerical studies of ‘ankylography’ and ‘one-view divergent tomography’.

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Contributions

G.W. conceptualized and wrote the manuscript. G.W., H.Y. and W.C. identified non-uniqueness of ankylography in simple cases, and A.K. constructed the general argument. H.Y., W.C. and G.W. analysed stability of ankylography and simulated spectrography.

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Wang, G., Yu, H., Cong, W. et al. Non-uniqueness and instability of ‘ankylography’. Nature 480, E2–E3 (2011). https://doi.org/10.1038/nature10635

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