Testing for nonlinearity in time series: the method of surrogate data
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
The Regular Fourier Matrices and Nonuniform Fast Fourier Transforms
SIAM Journal on Scientific Computing
Digital Image Processing: PIKS Inside
Digital Image Processing: PIKS Inside
Gaussian and Laplacian of Gaussian weighting functions for robust feature based tracking
Pattern Recognition Letters
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
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Background: Reconstruction methods for Non-Cartesian magnetic resonance imaging have often been analyzed using the root mean square error (RMSE). However, RMSE is not able to measure the level of structured error associated with the reconstruction process. Methods: An index for geometric information loss was presented using the 2D autocorrelation function. The performances of Least Squares Non Uniform Fast Fourier Transform (LS-NUFFT) and gridding reconstruction (GR) methods were compared. The Direct Summation method (DS) was used as reference. For both methods, RMSE and the loss in geometric information were calculated using a digital phantom and a hyperpolarized ^1^3C dataset. Results: The performance of the geometric information loss index was analyzed in the presence of noise. Comparing to GR, LS-NUFFT obtained a lower RMSE, but its error image appeared more structured. This was observed in both phantom and in vivo experiments. Discussion: The evaluation of geometric information loss together with the reconstruction error was important for an appropriate performance analysis of the reconstruction methods. The use of geometric information loss was helpful to determine that LS-NUFFT loses relevant information in the reconstruction process, despite the low RMSE.