Sparse MRI: The application of compressed sensing for rapid MR imaging

Area of Science:

• Medical Imaging
• Signal Processing
• Applied Mathematics

Background:

• Magnetic Resonance Imaging (MRI) data acquisition relies on sampling k-space.
• Image sparsity, either inherent or in transform domains (e.g., wavelets), is a key property of many MR images.
• Traditional MRI requires dense k-space sampling, leading to long acquisition times.

Purpose of the Study:

• To exploit image sparsity for significant undersampling of k-space in MRI.
• To develop and analyze practical incoherent undersampling schemes for MRI.
• To demonstrate improved spatial resolution and accelerated acquisition using compressed-sensing MRI.

Main Methods:

• Utilized the mathematical theory of compressed-sensing (CS) for image recovery from undersampled data.
• Developed incoherent undersampling strategies via pseudo-random variable-density undersampling of phase-encodes.
• Employed nonlinear recovery schemes, specifically minimizing the L1 norm of the transformed image under data fidelity constraints.

Main Results:

• Demonstrated that sparse MR images can be reconstructed from randomly undersampled k-space data.
• Showcased improved spatial resolution and accelerated acquisition in multislice fast spin-echo brain imaging.
• Achieved enhanced performance in 3D contrast-enhanced angiography reconstructions.

Conclusions:

• Image sparsity is a powerful tool for accelerating MRI acquisition.
• Compressed-sensing MRI with nonlinear reconstruction effectively recovers images from undersampled data.
• The developed incoherent undersampling schemes offer practical benefits for clinical MRI applications.