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SPARSE FOURIER TRANSFORM VIA BUTTERFLY ALGORITHM
Fourier transform butterfly algorithm multiscale methods far field pattern
2015/7/14
This paper introduces a fast algorithm for computing sparse Fourier transforms with spatial and Fourier data supported on curves or surfaces. This problem appears naturally in several important applic...
A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
Fourier integral operators butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/7/14
This paper is concerned with the fast computation of Fourier integral operators of the general form Rd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
A Butterfly Algorithm for Synthetic Aperture Radar Imaging
fast algorithms low-rank expansions backprojection synthetic aperture radar
2015/7/14
In spite of an extensive literature on fast algorithms for synthetic aperture radar (SAR) imaging, it is not currently known if it is possible to accurately form an image from N data points in provabl...
A fast butterfly algorithm for generalized Radon transforms
fast butterfly algorithm generalized Radon transforms
2015/7/14
Generalized Radon transforms, such as the hyperbolic Radon transform, cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. ...
A PARALLEL BUTTERFLY ALGORITHM
butterfly algorithm Egorov operator Radon transform parallel Blue Gene/Q
2015/7/14
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform Rd K(x, y)g(y)dy at large numbers of target points when the kernel, K(x, y), is...
A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTEGRAL OPERATORS
Fourier integral operators the butterfly algorithm hierarchical decomposition separated representation
2015/7/14
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = Rd a(x, ξ)e2πıΦ(x,ξ)f (ξ)dξ, where Φ(x, ξ) is a phase funct...