Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot...

Area of Science:

• Medical Imaging
• Applied Mathematics
• Biophysics

Background:

• Accurate estimation of spin density R2* decay and off-resonance frequency maps is crucial for magnetic resonance imaging (MRI).
• Standard multi-echo MRI techniques provide high accuracy but suffer from long acquisition times due to extensive k-space sampling.
• Accelerated acquisition methods, such as trajectory-based sampling, are desirable but pose reconstruction challenges due to disrupted Fourier relationships.

Purpose of the Study:

• To develop and evaluate novel accelerated reconstruction methods for MRI.
• To improve the speed and stability of joint estimation of R2* decay and off-resonance frequency maps.
• To address the challenges posed by trajectory-based sampling in MRI reconstruction.

Main Methods:

• Introduction of two trust region methods utilizing different linearization strategies for the nonlinear MRI signal model.
• Definition of trust regions to ensure the reliability of local linear approximations during iterative reconstruction.
• Application of a continuation scheme to gradually reduce regularization, aiding convergence from suboptimal initializations.

Main Results:

• The proposed trust region methods demonstrated superior performance compared to nonlinear conjugate gradients and gradual refinement algorithms.
• Experimental results on synthetic and phantom data confirmed a significant advantage in both speed and stability for the trust region methods.
• The methods effectively handle the reconstruction challenges arising from fast, trajectory-based k-space sampling.

Conclusions:

• The developed trust region methods offer a promising solution for accelerated MRI acquisition.
• These methods provide a substantial improvement in reconstruction speed and stability for joint R2* and off-resonance mapping.
• The approach facilitates more efficient and robust MRI data acquisition and analysis.