Methods for performing fast discrete curvelet transforms of data
First Claim
1. A method for transforming an image for use with a data processor comprising:
- converting said image to a plurality of image pixel data; and
performing a discrete curvelet transformation on the plurality of image pixel data,wherein the performing of the discrete curvelet transform comprises;
representing the plurality of image pixel data in the frequency space or Fourier domain by means of a Fourier transform; and
dividing the Fourier transform of the plurality of image pixel data into dyadic annuli based on concentric squares for two-dimensional data or concentric cubes for three-dimensional data and each annulus is subdivided into trapezoidal regions for two-dimensional data or prismoids for three-dimensional data.
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Abstract
Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while another is based on the wrapping of specially selected Fourier samples. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Both implementations are fast in the sense that they run in about O(n2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.
52 Citations
26 Claims
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1. A method for transforming an image for use with a data processor comprising:
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converting said image to a plurality of image pixel data; and performing a discrete curvelet transformation on the plurality of image pixel data, wherein the performing of the discrete curvelet transform comprises; representing the plurality of image pixel data in the frequency space or Fourier domain by means of a Fourier transform; and dividing the Fourier transform of the plurality of image pixel data into dyadic annuli based on concentric squares for two-dimensional data or concentric cubes for three-dimensional data and each annulus is subdivided into trapezoidal regions for two-dimensional data or prismoids for three-dimensional data. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)
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Specification