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Methods for performing fast discrete curvelet transforms of data

United States Patent

November 23, 2010
View the Complete Patent at the US Patent & Trademark Office
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(n.sup.2 log n) flops for n by n Cartesian arrays or about O(N log N) flops for Cartesian arrays of size N=n.sup.3; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.
Candes; Emmanuel (Los Angeles, CA), Donoho; David (Setauket, NY), Demanet; Laurent (Pasadena, CA)
California Institute of Technology (Pasadena, CA), Stanford University (Palo Alto, CA)
11/ 400,048
April 7, 2006
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT Subject matter disclosed in this specification was supported at least in part through governmental grants no. DE-FG02-02ER25529 awarded by the Department of Energy and no. DMS-0140540 awarded by the National Science Foundation, and is subject to certain governmental rights and interests.