Reconstruction in NMR by the method of signal matrix pseudoinversion

M. V. Kononov; O. A. Nagulyak; A. V. Netreba; Oleksandr O. Sudakov

doi:10.3103/S0735272708100038

Authors

M. V. Kononov Taras Shevchenko National University of Kyiv, Ukraine
O. A. Nagulyak Taras Shevchenko National University of Kyiv, Ukraine
A. V. Netreba Taras Shevchenko National University of Kyiv, Ukraine
Oleksandr O. Sudakov Taras Shevchenko National University of Kyiv, Ukraine https://orcid.org/0000-0002-6588-1801

DOI:

https://doi.org/10.3103/S0735272708100038

Abstract

Tomogram reconstruction in NMR tomography is based on the calculation of the spatial distribution of spin density or relaxation characteristics of the signal. The Fourier reconstruction method is frequently used for solving inverse problems. The present paper proposes a new alternative method of reconstruction based on data pseudoinversion. The method operability and efficiency was tested by using a mathematical model.

References

D. Huo, D. Xu, Zh. Liang, and D. Wilson, “Application of Perceptual Difference Model on Regularization Techniques of Parallel MR Imaging,” Magnetic Resonance Imaging 24, 123 (2006).

E. Carmi, S. Liu, N. Alon, et al., “Resolution Enhancement in MRI,” Magnetic Resonance Imaging 24, 133 (2006).

H. Peng and K. Arfanakis, “Diffusion Tensor Encoding Schemes Optimized for White Matter Fibers with Selected Orientations,” Magnetic Resonance Imaging 25, 147 (2007).

Q. Ji, J. O. Glass, and W. E. Reddick, “A Novel, Fast Entropy–Minimization Algorithm for Bias Field Correction in MR Images”.