This paper describes two digital implementations of a new mathematical transform, namely,

the second generation curvelet transform [12, 10] in two and three dimensions. The first digital

transformation is based on unequally-spaced fast Fourier transforms (USFFT) while the second is

based on the wrapping of specially selected Fourier samples. The two implementations essentially

differ 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. And both implementations are



fast in

the sense that they run in O(n2 log n) flops for n by n Cartesian arrays in addition, they are

also invertible, with rapid inversion algorithms of about the same complexity.-This paper describes two digital implementations of a new mathematical transform, namely,

the second generation curvelet transform [12, 10] in two and three dimensions. The first digital

transformation is based on unequally-spaced fast Fourier transforms (USFFT) while the second is

based on the wrapping of specially selected Fourier samples. The two implementations essentially

differ 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. And both implementations are



fast in

the sense that they run in O(n2 log n) flops for n by n Cartesian arrays　in addition, they are

also invertible, with rapid inversion algorithms of about the same complexity.