NDLI: Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines

Content Provider	PubMed Central
Author	Press, William H.
Copyright Year	2006
Abstract	Götz, Druckmüller, and, independently, Brady have defined a discrete Radon transform (DRT) that sums an image's pixel values along a set of aptly chosen discrete lines, complete in slope and intercept. The transform is fast, O(N 2log N) for an N × N image; it uses only addition, not multiplication or interpolation, and it admits a fast, exact algorithm for the adjoint operation, namely backprojection. This paper shows that the transform additionally has a fast, exact (although iterative) inverse. The inverse reproduces to machine accuracy the pixel-by-pixel values of the original image from its DRT, without artifacts or a finite point-spread function. Fourier or fast Fourier transform methods are not used. The inverse can also be calculated from sampled sinograms and is well conditioned in the presence of noise. Also introduced are generalizations of the DRT that combine pixel values along lines by operations other than addition. For example, there is a fast transform that calculates median values along all discrete lines and is able to detect linear features at low signal-to-noise ratios in the presence of pointlike clutter features of arbitrarily large amplitude.
Related Links	http://dx.doi.org/10.1073/pnas.0609228103
Ending Page	19254
Page Count	6
Starting Page	19249
File Format	PDF
ISSN	00278424
e-ISSN	10916490
Journal	Proceedings of the National Academy of Sciences of the United States of America
Issue Number	51
Volume Number	103
Language	English
Publisher	National Academy of Sciences
Publisher Date	2006-12-19
Access Restriction	Open
Rights Holder	National Academy of Sciences
Subject Keyword	General Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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