Applications
The NFFT and its generalisations are the basis of fast algorithms in a number of
applications. Most of them are included in the NFFT package in the folder
./applications.
- Fast summation
- Fast evaluation of sums \(f(y_j) = \sum_{k} \alpha_k K(y_j - x_k)\) for various kernels \(K\) based on the NFFT.
- Fast Gauss transform
- Fast Gauss transforms with complex parameters using the NFFT.
- Summation on the sphere
- Fast summation on the sphere based on the NFSFT.
- MRI
- Fast iterative image reconstruction in magnetic resonance imaging from non-Cartesian k-space data.
- Polar FFT
- Polar and pseudo-polar FFT, and reconstruction of a 2d signal from its Fourier samples on a (pseudo-)polar grid.
- Radon transform, CT
- NFFT-based discrete Radon transform and its inverse for computerized tomography.
- Ridgelet transform
- Discrete ridgelet transform based on the NFFT-based Radon transform and a dual-tree complex wavelet transform.
- Quadrature rules on manifolds
- Putatively optimal quadrature rules on the sphere \(\mathbb{S}^2\) and the rotation group \(SO(3)\).