Results 11  20
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35
Using NFFT 3  a software library for various nonequispaced fast Fourier transforms
, 2008
"... NFFT 3 is a software library that implements the nonequispaced fast Fourier transform (NFFT) and a number of related algorithms, e.g. nonequispaced fast Fourier transforms on the sphere and iterative schemes for inversion. This is to provide a survey on the mathematical concepts behind the NFFT and ..."
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Cited by 12 (8 self)
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NFFT 3 is a software library that implements the nonequispaced fast Fourier transform (NFFT) and a number of related algorithms, e.g. nonequispaced fast Fourier transforms on the sphere and iterative schemes for inversion. This is to provide a survey on the mathematical concepts behind the NFFT and its variants, as well as a general guideline for using the library. Numerical examples for a number of applications are given.
A FAST BUTTERFLY ALGORITHM FOR THE COMPUTATION OF FOURIER INTEGRAL OPERATORS
, 2009
"... This paper is concerned with the fast computation of Fourier integral operators of the general form ∫ Rd e2πıΦ(x,k) f(k)dk, wherekisafrequency variable, Φ(x, k) is a phase function obeying a standard homogeneity condition, and f is a given input. This is of interest, for such fundamental computation ..."
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Cited by 6 (2 self)
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This paper is concerned with the fast computation of Fourier integral operators of the general form ∫ Rd e2πıΦ(x,k) f(k)dk, wherekisafrequency variable, Φ(x, k) is a phase function obeying a standard homogeneity condition, and f is a given input. This is of interest, for such fundamental computations are connected with the problem of finding numerical solutions to wave equations and also frequently arise in many applications including reflection seismology, curvilinear tomography, and others. In two dimensions, when the input and output are sampled on N × N Cartesian grids, a direct evaluation requires O(N 4) operations, which is often times prohibitively expensive. This paper introduces a novel algorithm running in O(N 2 log N) time, i.e., with nearoptimal computational complexity, and whose overall structure follows that of the butterfly algorithm. Underlying this algorithm is a mathematical insight concerning the restriction of the kernel e2πıΦ(x,k) to subsets of the time and frequency domains. Whenever these subsets obey a simple geometric condition, the restricted kernel is approximately lowrank; we propose constructing such lowrank approximations using a special interpolation scheme, which prefactors the oscillatory component, interpolates the remaining nonoscillatory part, and finally remodulates the outcome. A byproduct of this scheme is that the whole algorithm is highly efficient in terms of memory requirement. Numerical results demonstrate the performance and illustrate the empirical properties of this algorithm.
Sparse Fourier transform via butterfly algorithm
, 2008
"... We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is that the interaction between a frequency region and a spatia ..."
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Cited by 4 (4 self)
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We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is that the interaction between a frequency region and a spatial region is approximately low rank if the product of their radii are bounded by the maximum frequency. Based on this property, equivalent sources located at Cartesian grids are used to speed up the computation of the interaction between these two regions. The overall structure of our algorithm follows the recentlyintroduced butterfly algorithm. The computation is further accelerated by exploiting the tensorproduct property of the Fourier kernel in two and three dimensions. The proposed algorithm is accurate and has an O(N log N) complexity. Finally, we present numerical results in both two and three dimensions.
Accurate and Fast Discrete Polar Fourier Transform
 in Proc. 37th Asilomar Conf. Signals, Systems & Computers
, 2003
"... In this article we develop a fast high accuracy Polar FFT. For a given twodimensional signal of size N N , the proposed algorithm's complexity is O(N log N), just like in a Cartesian 2DFFT. A special feature of our approach is that it involves only 1D equispaced FFT's and 1D inter ..."
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Cited by 2 (0 self)
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In this article we develop a fast high accuracy Polar FFT. For a given twodimensional signal of size N N , the proposed algorithm's complexity is O(N log N), just like in a Cartesian 2DFFT. A special feature of our approach is that it involves only 1D equispaced FFT's and 1D interpolations. A central tool in our approach is the pseudopolar FFT, an FFT where the evaluation frequencies lie in an oversampled set of nonangularly equispaced points. The pseudopolar FFT plays the role of a halfway point  a nearlypolar system from which conversion to Polar Coordinates uses processes relying purely on interpolation operations. We describe the conversion process, and compare accuracy results obtained by unequallysampled FFT methods to ours and show marked advantage to our approach.
3d image registration using fast fourier transform, with potential applications to geoinformatics and bioinformatics
 In Proceedings of the International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems IPMU’06
, 2006
"... ..."
Rafael de la Llave, Supervisor Oscar Gonzalez
"... certifies that this is the approved version of the following dissertation: Existence and persistence of invariant objects in dynamical systems and mathematical physics Committee: ..."
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certifies that this is the approved version of the following dissertation: Existence and persistence of invariant objects in dynamical systems and mathematical physics Committee:
Fast discrete curvlet transforms
, 2006
"... 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 unequallyspaced fast Fourier transforms (USFFT) while the second is based on the wrap ..."
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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 unequallyspaced 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 digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. And both implementations are fast in the sense that they run in O(n 2 log n) flops for n by n Cartesian arrays; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity. Our digital transformations improve upon earlier implementations—based upon the first generation of curvelets—in the sense that they are conceptually simpler, faster and far less redundant. The software CurveLab, which implements both transforms presented in this paper, is available at
NONUNIFORM FAST FOURIER MODE TRANSFORM (2DNUFFMT) FOR FULLWAVE INVESTIGATION OF MICROWAVE INTEGRATED CIRCUITS
"... Abstract—In this paper, a novel version of the transverse wave approach (TWA) based on twodimensional nonuniform fast Fourier mode transform (2DNUFFMT) is presented and developed for fullwave analysis of RF integrated circuits (RFICs). An adaptive mesh refinement is applied in this advanced TWA p ..."
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Abstract—In this paper, a novel version of the transverse wave approach (TWA) based on twodimensional nonuniform fast Fourier mode transform (2DNUFFMT) is presented and developed for fullwave analysis of RF integrated circuits (RFICs). An adaptive mesh refinement is applied in this advanced TWA process and CPU computation time is evaluated throughout 30 GHz patch antenna, application belonging to wireless systems. The TWA in its novel version is favorably compared with the conventional one in presence of AMT technique in the context of EM simulations. Another version of TWA is outlined to illustrate a computationally efficient way to handle an arbitrary mesh for RFICs analysis with high complexity problems.