Evaluation of optimal density weighting for regridding.

Density weighting is a necessary component of the regridding algorithm for interpolating nonuniformly sampled data points onto a regular grid. Differing concepts of optimality for the density weighting have been proposed previously. The present study reviews some of these concepts and evaluates the accuracy of different techniques by comparison with the image obtained by a computationally intensive least squares minimization. A variant on one of the techniques is proposed that yields the highest accuracy of those studied.

[1]  Jeffrey A. Fessler,et al.  Iterative tomographic image reconstruction using Fourier-based forward and back-projectors , 2004, IEEE Transactions on Medical Imaging.

[2]  Linda Kaufman,et al.  Maximum likelihood, least squares, and penalized least squares for PET , 1993, IEEE Trans. Medical Imaging.

[3]  Hossein Sedarat,et al.  On the optimality of the gridding reconstruction algorithm , 2000, IEEE Transactions on Medical Imaging.

[4]  P. Boesiger,et al.  Advances in sensitivity encoding with arbitrary k‐space trajectories , 2001, Magnetic resonance in medicine.

[5]  J. D. O'Sullivan,et al.  A Fast Sinc Function Gridding Algorithm for Fourier Inversion in Computer Tomography , 1985, IEEE Transactions on Medical Imaging.

[6]  A. Macovski,et al.  Selection of a convolution function for Fourier inversion using gridding [computerised tomography application]. , 1991, IEEE transactions on medical imaging.

[7]  William H. Press,et al.  Numerical Recipes in C, 2nd Edition , 1992 .

[8]  D Rosenfeld,et al.  An optimal and efficient new gridding algorithm using singular value decomposition , 1998, Magnetic resonance in medicine.

[9]  Mark Bydder,et al.  Magnetic Resonance: An Introduction to Ultrashort TE (UTE) Imaging , 2003, Journal of computer assisted tomography.

[10]  Volker Rasche,et al.  Resampling of data between arbitrary grids using convolution interpolation , 1999, IEEE Transactions on Medical Imaging.

[11]  Rik Van de Walle,et al.  Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation , 2000, IEEE Transactions on Medical Imaging.

[12]  J. Pipe,et al.  Sampling density compensation in MRI: Rationale and an iterative numerical solution , 1999, Magnetic resonance in medicine.

[13]  William H. Press,et al.  Numerical recipes in C , 2002 .

[14]  R. Edelman,et al.  Magnetic resonance imaging (2) , 1993, The New England journal of medicine.