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Reconstruction from NMR data acquired with imaging gradients having arbitrary time dependence
IEEE Transactions on Medical Imaging
|January 1, 1986
Summary
A new algebraic reconstruction method enables Nuclear Magnetic Resonance (NMR) imaging with flexible gradient timing. This approach simplifies calculations for efficient and accurate image reconstruction.
Area of Science:
- Nuclear Magnetic Resonance (NMR) Imaging
- Medical Imaging
- Biophysics
Background:
- Nuclear Magnetic Resonance (NMR) imaging is a powerful non-invasive technique.
- Current methods often require specific gradient waveforms.
- Reconstructing images from NMR data can be computationally intensive.
Purpose of the Study:
- To present a novel algebraic reconstruction method for NMR imaging.
- To accommodate imaging gradients with arbitrary time dependence.
- To develop a computationally efficient reconstruction scheme.
Main Methods:
- Developed an algebraic reconstruction approach for NMR data.
- Utilized discretization to form an overdetermined linear system.
- Employed factorized 1-inverses of coefficient matrices for simplification.
Main Results:
- The method allows for NMR imaging with arbitrary gradient time dependence.
- An overdetermined linear system is achieved through discretization.
- Computationally efficient reconstruction is demonstrated via factorized 1-inverses.
Conclusions:
- The presented algebraic method offers flexibility in NMR imaging gradient design.
- The technique provides a computationally efficient pathway for image reconstruction.
- Numerical simulations support the validity and efficiency of the proposed method.
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