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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.14 No.1
- 발행연도
- 2010.3
- 수록면
- 35 - 42 (8page)
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초록· 키워드
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A goal of Magnetic Resonance Imaging is reproducing a spatial map of the effective spin density from the measured Fourier coefficients of a specimen. The imaging procedure can be done by inverse Fourier transformation or backward fast Fourier transformation if the data are sampled on a regular grid in frequency space; however, it is still a challenging question how to reconstruct an image from a finite set of Fourier data on irregular points in k-space. In this paper, we describe some mathematical and numerical properties of imaging techniques from non-uniform MR data using the pseudo-inverse or the diagonal-inverse weight matrix. This note is written as an easy guide to readers interested in the non-uniform MRI techniques and it basically follows the ideas given in the paper by Greengard-Lee-Inati [10, 11].
목차
ABSTRACT
1. INTRODUCTION
2. BASICS OF MAGNETIC RESONANCE IMAGING
3. CONTINUOUS-TO-DISCRETE FOURIER TRANSFORMATION
4. RECONSTRUCTION ERROR OF PSEUDO-INVERSE AND DIAGONAL-INVERSE
5. NUMERICAL IMPLEMENTATION ISSUES
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2010-410-002236861