Fourier series approximation of separable models
Journal of Computational and Applied Mathematics
An accurate nonuniform fourier transform for SPRITE magnetic resonance imaging data
ACM Transactions on Mathematical Software (TOMS)
Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
ACM Transactions on Mathematical Software (TOMS)
Spectral analysis of nouniformly sampled data: a new approach versus the periodogram
IEEE Transactions on Signal Processing
Optimized least-square nonuniform fast Fourier transform
IEEE Transactions on Signal Processing
Efficient NUFFT algorithm for non-Cartesian MRI reconstruction
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
A Fast Algorithm for Fourier Continuation
SIAM Journal on Scientific Computing
Structured errors in reconstruction methods for Non-Cartesian MR data
Computers in Biology and Medicine
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For any triple of positive integers (m,N,q), the matrix F(m,N,q), called the (m,N,q)-regular Fourier matrix, is defined. The regular Fourier matrices F(m,N,q) are then applied to set up new algorithms for nonuniform fast Fourier transforms. Numerical results show that the accuracies obtained by our algorithms are much better than previously reported results with the same computation complexity. The algorithms require $O(N\cdot\log_2N)$ arithmetic operations, where N is the number of data points.