Rapid compressed sensing reconstruction of 3D non-Cartesian MRI

Area of Science:

• Medical Imaging
• Computational Science

Background:

• Conventional non-Cartesian compressed sensing (CS) reconstruction is computationally intensive due to repeated nonuniform Fourier transforms.
• Slow reconstruction times hinder the clinical integration of undersampled 3D non-Cartesian magnetic resonance imaging (MRI) acquisitions.

Purpose of the Study:

• To investigate methods for minimizing reconstruction times in 3D non-Cartesian compressed sensing without compromising accuracy.
• To accelerate the adoption of undersampled 3D non-Cartesian MRI into clinical workflows.

Main Methods:

• Exploited the Toeplitz structure of matrices for reconstruction, comparing its speed against standard nonuniform Fourier transforms on GPU and CPU.
• Developed a method to minimize matrix sizes by estimating image support to prevent aliasing.
• Proposed a generalized preconditioning scheme for improved convergence, balancing accuracy and speed.

Main Results:

• The Toeplitz approach demonstrated superior speed across practical parameters on GPUs.
• Image support estimation effectively prevented aliasing with minimal impact on reconstruction time.
• The novel preconditioning scheme enhanced convergence rates significantly with negligible noise increase.

Conclusions:

• Achieved clinically relevant 3D non-Cartesian compressed sensing reconstruction times (<2 minutes) using practical computational resources.
• The developed methods facilitate the integration of accelerated 3D non-Cartesian MRI into routine clinical practice.