TY - JOUR

T1 - Exact image representation via a number-theoretic Radon transform

AU - Chandra, Shekhar

AU - Svalbe, Imants

PY - 2014/1/1

Y1 - 2014/1/1

N2 - This study presents an integer-only algorithm to exactly recover an image from its discrete projected views that can be computed with the same computational complexity as the fast Fourier transform (FFT). Most discrete transforms for image reconstruction rely on the FFT, via the Fourier slice theorem (FST), in order to compute reconstructions with lowcomputational complexity. Consequently, complex arithmetic and floating point representations are needed, the latter of which is susceptible to round-off errors. This study shows that the slice theorem is valid within integer fields, via modulo arithmetic, using a circulant theory of the Radon transform (RT). The resulting number-theoretic RT (NRT) provides a representation of images as discrete projections that is always exact and real-valued. The NRT is ideally suited as part of a discrete tomographic algorithm, an encryption scheme or for when numerical overflow is likely, such as when computing a large number of convolutions on the projections. The low-computational complexity of the NRT algorithm also provides an efficient method to generate discrete projected views of image data.

AB - This study presents an integer-only algorithm to exactly recover an image from its discrete projected views that can be computed with the same computational complexity as the fast Fourier transform (FFT). Most discrete transforms for image reconstruction rely on the FFT, via the Fourier slice theorem (FST), in order to compute reconstructions with lowcomputational complexity. Consequently, complex arithmetic and floating point representations are needed, the latter of which is susceptible to round-off errors. This study shows that the slice theorem is valid within integer fields, via modulo arithmetic, using a circulant theory of the Radon transform (RT). The resulting number-theoretic RT (NRT) provides a representation of images as discrete projections that is always exact and real-valued. The NRT is ideally suited as part of a discrete tomographic algorithm, an encryption scheme or for when numerical overflow is likely, such as when computing a large number of convolutions on the projections. The low-computational complexity of the NRT algorithm also provides an efficient method to generate discrete projected views of image data.

UR - http://www.scopus.com/inward/record.url?scp=84928334309&partnerID=8YFLogxK

U2 - 10.1049/iet-cvi.2013.0101

DO - 10.1049/iet-cvi.2013.0101

M3 - Article

AN - SCOPUS:84928334309

VL - 8

SP - 338

EP - 346

JO - IET Computer Vision

JF - IET Computer Vision

SN - 1751-9632

IS - 4

ER -