Accurate NUFFT using optimized interpolator and scale factors
Download Matlab Code: NUFFT
Installation: Uncompress the above folder and run the demo functions Demo_NUFFT_1_knee.m and Demo_NUFFT_2_brain.m. These programs will replicate the results in the references below.
Motivation: The main motivation is to optimize the NUFFT interpolator and the scale factors jointly to improve the accuracy of the NUFFT approximation. Classical schemes are designed to provide reasonable approximations in the twofold oversampled (K=2N) regime. However, the resulting memory demand (4/8 fold for 2D/3D) implementations is often unacceptable for implentation on GPU devices with limited onboard memory. The proposed optimal approximations considerably reduces the approximation error, thus providing similar image quality for the K~N setting.
Illustration
Demonstration of the optimal NUFFT schemes (MOLSU and WOLS) in the context of recovering a knee image from its radial samples. The different rows correspond to the reconstructions, the errors, and zoomed reconstructions from regions in the top and middle portions of the image, respectively. The first two columns correspond to reconstruction with the classical K=2N (4 times more memory demand than the original image), the reconstruction using the classical Kaiser Bessel kernel with K=N+2 (~ the same memory demand as the original image). The last two columns correspond to K=N+2 reconstructions using the proposed worstcase ( WOLS) and mean square optimal (MOLSU) NUFFT schemes. Note that the MOLSU scheme provides reconstructions that are quite comparable to the classical K=2N scheme.
References:

 Z. Yang, M. Jacob, "Mean square optimal NUFFT approximation for nonCartesian MRI reconstruction", JMR, in press
 M. Jacob,"Optimized least square non uniform fast Fourier transform (OLSNUFFT)" , IEEE Transactions of Signal Processing, vol. 57, issue 6, pp. 21652177, Feb 2009
 Z. Yang, M. Jacob, "Efficient NUFFT algorithm for nonCartesian MRI reconstruction",, IEEE international symposium on biomedical imaging, 2009