A new method of magnetic resonance image reconstruction with short acquisition time and truncation artifact reduction

A method for the reconstruction of magnetic resonance images that allows for a substantial reduction of the quantity of measured data and, therefore, of the acquisition time is described. The truncation artifact is also reduced, improving the image quality. The method is based on techniques for getting superresolution in spectral analysis such as autoregressive modeling and Prony's method. Moreover, some new ideas about the autoregressive order selection are introduced. The method is compared to the standard one for reconstructing simulated, phantom, and medical magnetic resonance images. The numerical stability and the computational cost issues of the resulting algorithm are also addressed.

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

[2]  J. Gillis,et al.  Linear Differential Operators , 1963 .

[3]  Harry Dym,et al.  Fourier series and integrals , 1972 .

[4]  E M Haacke,et al.  Constrained reconstruction: a superresolution, optimal signal-to-noise alternative to the Fourier transform in magnetic resonance imaging. , 1989, Medical physics.

[5]  J. A. Grant,et al.  Two Algorithms for the Solution of Polynomial Equations to Limiting Machine Precision , 1975, Computer/law journal.

[6]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[7]  Cédric J. Demeure.  Fast QR factorization of Vandermonde matrices , 1989 .

[8]  S. T. Nichols,et al.  Application of Autoregressive Moving Average Parametric Modeling in Magnetic Resonance Image Reconstruction , 1986, IEEE Transactions on Medical Imaging.

[9]  Piero Barone,et al.  Mathematical principles of basic magnetic resonance imaging in medicine , 1991, Signal Process..

[10]  R. Gerchberg.  Super-resolution through Error Energy Reduction , 1974 .

[11]  R. Mark Henkelman,et al.  Truncation Artifacts in Magnetic Resonance Imaging , 1985, Magnetic resonance in medicine.

[12]  Joel F Martin,et al.  Modified linear prediction modeling in magnetic resonance imaging , 1989 .

[13]  W N Hanafee,et al.  Boundary artifact due to truncation errors in MR imaging. , 1986, AJR. American journal of roentgenology.

[14]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[15]  B. S. Garbow,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[16]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[17]  Zhi-Pei Liang,et al.  Image reconstruction using projection onto convex sets, model constraints, and linear prediction theory for the removal of phase, motion, and Gibbs artifacts in magnetic resonance and ultrasound imaging , 1990 .

[18]  Miha Fuderer.  Ringing Artefact Reduction By An Efficient Likelihood Improvement Method , 1989, Other Conferences.

[19]  D. Slepian,et al.  Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .