Rapid analysis of non-uniformly sampled pulsed field gradient data for velocity estimation

Area of Science:

• Medical Imaging
• Signal Processing
• Fluid Dynamics

Background:

• Non-uniform sampling in pulsed field gradient MRI (PFG-MRI) poses challenges for accurate velocity estimation.
• Traditional Fourier Transform (FFT) methods can be computationally intensive with sparse data.
• Bretthorst's generalized Lomb-Scargle periodogram offers a novel approach for frequency estimation from such data.

Purpose of the Study:

• To develop and implement an efficient algorithm for rapid analysis of PFG-MRI data with non-uniform q-sampling.
• To enhance the precision of velocity measurements in PFG-MRI within a fixed acquisition time.
• To demonstrate the applicability and computational efficiency of the generalized periodogram for PFG-MRI.

Main Methods:

• Applied Bretthorst's generalized Lomb-Scargle periodogram to non-uniformly sampled PFG-MRI data.
• Implemented a direct periodogram calculation for computational efficiency with sparse q-samples.
• Utilized repeated apodization, grid searching, and quadratic interpolation for robust peak finding and refinement.

Main Results:

• Achieved significant improvements in velocity measurement precision for non-uniformly sampled PFG-MRI data.
• Demonstrated the computational efficiency of the direct periodogram method over FFT for sparse data.
• Validated the method using Poiseuille flow of a Newtonian fluid, showing high accuracy.

Conclusions:

• The generalized Lomb-Scargle periodogram provides a computationally efficient and robust method for PFG-MRI velocity analysis.
• The technique offers enhanced precision in velocity measurements, particularly beneficial for time-constrained acquisitions.
• The algorithm is readily extendible to multidimensional MRI data and image analysis.