Transcription of Fast Discrete Curvelet Transforms
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Fast Discrete Curvelet Transforms
Fast Discrete Curvelet TransformsEmmanuel Cand`es , Laurent Demanet , David Donoho]and Lexing Ying Applied and Computational Mathematics, Caltech, Pasadena, CA 91125]Department of Statistics, Stanford University, Stanford, CA 94305 July 2005, revised March 2006 AbstractThis paper describes two digital implementations of a new mathematical transform, namely,the second generationcurvelet transform[12, 10] in two and three dimensions. The first digitaltransformation is based on unequally-spaced fast Fourier Transforms (USFFT) while the second isbased on the wrapping of specially selected Fourier samples. The two implementations essentiallydiffer by the choice of spatial grid used to translate curvelets at each scale and angle. Both digitaltransformations return a table of digital Curvelet coefficients indexed by a scale parameter, anorientation parameter, and a spatial location parameter.
1 Introduction 1.1 Classical Multiscale Analysis The last two decades have seen tremendous activity in the development of new mathematical and computational tools based on multiscale ideas.
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