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资源说明：Fast Fourier transform at nonequispaced nodes
NFFT3 - Nonequispaced FFT, generalisations, inversion, and applications
Overview
--------
NFFT3 is a software library written in C for computing nonequispaced fast Fourier
and related transformations. In detail, NFFT3 implements
1) The nonequispaced fast Fourier transform (NFFT)
- the forward transform (NFFT)
- the adjoint transform (adjoint NFFT)
2) Generalisations of the NFFT
- to arbitrary knots in time and frequency domain (NNFFT)
- to the sphere S^2 (NFSFT)
- to the hyperbolic cross (NSFFT)
- to real-valued data, i.e. (co)sine transforms, (NFCT, NFST)
- to the rotation group (NFSOFT)
3) Generalised inverses based on iterative methods, e.g. CGNR, CGNE
4) Applications in
- medical imaging
(i) magnetic resonance imaging
(ii) computerised tomography
- summation schemes
(i) fast Gauss transform (FGT)
(ii) singular kernels
(iii) zonal kernels
- polar FFT, discrete Radon transform, ridgelet transform
For an introduction, please read the "NFFT 3.0 - Tutorial" first. It is
available in the subdirectory doc/tutorial/tutorial.pdf. Detailed API
documentation can be found in HTML format in /doc/api/html/index.html
or in LaTeX format for self compilation in /doc/api/latex/refman.tex.
For installation instructions, you can also refer to the file INSTALL
in this directory.
The most current general paper, and the one that we recommend if you wish
to cite NFFT, is: The paper by Keiner, J., Kunis, S., and Potts, D.
''Using NFFT 3 - a software library for various nonequispaced fast Fourier transforms''
ACM Trans. Math. Software,36, Article 19, 1-30, 2009
Directory structure
-------------------
3rdparty (dir) Third-party source code
aclocal.m4 Macros for configure script
applications (dir) Application programs (see 4) above)
AUTHORS Information about the authors of NFFT3
bootstrap.sh Bootstrap shell script that call Autoconf and friends
ChangeLog A short version history
config.guess Used by configure script
config.sub Used by configure script
configure Configure script
configure.in Autoconf configure script template
COPYING Information about redistributing NFFT3
depcomp Used by configure script
doc (dir) User and developer documentation
examples (dir) Simple examples for using NFFT3 routines
include (dir) Header files
INSTALL Installation instructions
install-sh Used by configure script
kernel (dir) Source code for core library routines
ltmain.sh Used by configure script
Makefile.am Automake Makefile template
Makefile.in Makefile template generated from Makefile.am,
processed by configure script
missing Used by configure script
NEWS New and noteworthy
README This file
TODO Current work to be done
util (dir) Source code for auxilliary routines
Feedback
--------
Your comments are welcome! This is the third version of the library and may
not be as robust or well documented as it should be. Please keep track of bugs
or missing/confusing instructions and report them to
Prof. Dr. Daniel Potts
TU Chemnitz, Fakultaet fuer Mathematik
Reichenhainer Str. 39
09107 Chemnitz, GERMANY
or
Stefan Kunis
Jens Keiner
If you find NFFT3 useful, we would be delighted to hear about what application
you are using NFFT3 for!
Legal Information & Credits
---------------------------
Copyright (C) 2002-2009 Daniel Potts
This software was written by Jens Keiner, Stefan Kunis and Daniel Potts.
It was developed at the Mathematical Institute, University of
Luebeck, and at the Faculty of Mathematics, Chemnitz University of Technology.
NFFT3 is free software. You can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version. If not stated otherwise, this applies to all files contained in this
package and its sub-directories.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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