Creating a library of generalized Fourier sampling patterns for irregular 2D regions of support

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Signal Processing
• Image Reconstruction

Background:

• The Shannon sampling theorem is fundamental to MRI, but requires dense k-space sampling.
• Multiple-region MRI (mrMRI) offers sparse sampling for objects confined to specific regions.
• Existing analytical solutions for mrMRI patterns are limited to simple geometries (2-3 regions).

Purpose of the Study:

• To develop a robust numerical method for generating optimal mrMRI sampling patterns.
• To extend mrMRI applicability to more complex object geometries.
• To evaluate the noise performance of mrMRI with these new patterns.

Main Methods:

• Development of a numerical algorithm for constructing mrMRI sampling patterns.
• Application of the method to generate a library of patterns for complex geometries.
• Analysis of noise amplification characteristics for the generated patterns.

Main Results:

• A robust numerical method for creating mrMRI sampling patterns was successfully developed.
• The generated patterns demonstrated minimal noise amplification, averaging only 4%.
• A significant portion (30%) of the tested patterns exhibited no noise amplification.

Conclusions:

• The numerical method effectively generates optimal and near-optimal mrMRI sampling patterns for complex geometries.
• mrMRI, utilizing these advanced sampling strategies, can achieve noise levels comparable to conventional MRI.
• This work significantly broadens the potential applications of sparse MRI techniques.