Discrete-time signal processing
Discrete-time signal processing
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
Efficient numerical methods in non-uniform sampling theory
Numerische Mathematik
The nonuniform discrete Fourier transform and its applications in signal processing
The nonuniform discrete Fourier transform and its applications in signal processing
The Regular Fourier Matrices and Nonuniform Fast Fourier Transforms
SIAM Journal on Scientific Computing
Numerical analysis of the non-uniform sampling problem
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 vol. II: interpolation and extrapolation
Quantitative Fourier analysis of approximation techniques. I.Interpolators and projectors
IEEE Transactions on Signal Processing
Sampling of periodic signals: a quantitative error analysis
IEEE Transactions on Signal Processing
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
On the approximation power of convolution-based least squaresversus interpolation
IEEE Transactions on Signal Processing
Wavelet descriptor of planar curves: theory and applications
IEEE Transactions on Image Processing
Computationally attractive reconstruction of bandlimited images from irregular samples
IEEE Transactions on Image Processing
High-quality image resizing using oblique projection operators
IEEE Transactions on Image 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 & accurate non-iterative algorithm for regularized non-Cartesian MRI
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
| Hi-index | 35.68 |
The main focus of this paper is to derive a memory efficient approximation to the nonuniform Fourier transform of a support limited sequence. We show that the standard nonuniform fast Fourier transform (NUFFT) scheme is a shift invariant approximation of the exact Fourier transform. Based on the theory of shift-invariant representations, we derive an exact expression for the worst-case mean square approximation error. Using this metric, we evaluate the optimal scale-factors and the interpolator that provides the least approximation error. We also derive the upper-bound for the error component due to the lookup table based evaluation of the interpolator; we use this metric to ensure that this co~ponent is not the dominant one. Theoretical and experimental comparisons with standard NUFFT schemes clearly demonstrate the significant improvement in accuracy over conventional schemes, especially when the size of the uniform fast Fourier transform (FFT) is small. Since the memory requirement of the algorithm is dependent on the size of the uniform FFT, the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands.