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Unitary rotations in two-, three-, and D-dimensional Cartesian data arrays

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Abstract

Using a previous technique to rotate two-dimensional images on an N×N square pixellated screen unitarily, we can rotate three-dimensional pixellated cubes of side N, and also generally D-dimensional Cartesian data arrays, also unitarily. Although the number of operations inevitably grows as N2D (because each rotated pixel depends on all others), and Gibbs-like oscillations are inevitable, the result is a strictly unitary and real transformation (thus orthogonal) that is invertible (thus no loss of information) and could be used as a standard.

© 2014 Optical Society of America

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