Rapid, Embeddable Design Method for Spiral Magnetic Resonance Image Reconstruction Resampling Kernels

After formulating the design problem for Resampling Kernels used in Magnetic Resonance Spiral Image Reconstruction, we show that an iterative Gauss-Seidel-type interior-point optimization method is suitable (fast and light-weight) for embedded uses. In contrast to previous practice, we directly optimize a computationally efficient, piecewise-linear kernel rather than an analytic function (Kaiser-Bessel). We also optimize our kernels for worst-case (infinity-norm) signal aliasing, rather than the usual proxy energy function (2-norm) minimization. In numerical simulations of undesirable near-frequency systematic noise the new kernel significantly outperforms a conventional Kaiser-Bessel-based solution.

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

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

[3]  Yasser M. Kadah,et al.  Image reconstruction using shift-variant resampling kernel for magnetic resonance imaging , 2002, SPIE Medical Imaging.

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

[5]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

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

[7]  R. Vanderbei.  LOQO user's manual — version 3.10 , 1999 .

[8]  P. Lafrance,et al.  Digital filters , 1974, Proceedings of the IEEE.

[9]  F. Marvasti.  Nonuniform sampling : theory and practice , 2001 .

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

[11]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

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

[13]  Weili Lin,et al.  Principles of magnetic resonance imaging: a signal processing perspective [Book Review] , 2000 .

[14]  Jacek Gondzio,et al.  Implementation of Interior Point Methods for Large Scale Linear Programming , 1996 .

[15]  Yu-Chung N. Cheng,et al.  Magnetic Resonance Imaging: Physical Principles and Sequence Design , 1999 .

[16]  Akram Aldroubi,et al.  Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces , 2001, SIAM Rev..

[17]  Jeffrey A. Fessler,et al.  Nonuniform fast Fourier transforms using min-max interpolation , 2003, IEEE Trans. Signal Process..