Optimization in the space domain for density compensation with the nonuniform FFT

Nicholas Dwork; Daniel O'Connor; Ethan M I Johnson; Corey A Baron; Jeremy W Gordon; John M Pauly; Peder E Z Larson

doi:10.1016/j.mri.2023.03.003

Optimization in the space domain for density compensation with the nonuniform FFT

Magn Reson Imaging. 2023 Jul:100:102-111. doi: 10.1016/j.mri.2023.03.003. Epub 2023 Mar 17.

Authors

Nicholas Dwork¹, Daniel O'Connor², Ethan M I Johnson³, Corey A Baron⁴, Jeremy W Gordon⁵, John M Pauly⁶, Peder E Z Larson⁵

Affiliations

¹ Biomedical Informatics and Radiology, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, USA. Electronic address: nicholas.dwork@cuanschutz.edu.
² Mathematics and Statistics, University of San Francisco, San Francisco, CA, USA.
³ Biomedical Engineering, Northwestern University, Evanston, IL, USA.
⁴ Center for Functional and Metabolic Mapping, Western University, Ontario, Canada.
⁵ Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, CA 94158, USA.
⁶ Electrical Engineering Department, Stanford University, Palo Alto, CA, USA.

PMID: 36934830
PMCID: PMC10288563 (available on 2024-07-01)
DOI: 10.1016/j.mri.2023.03.003

Abstract

The non-uniform Discrete Fourier Transform algorithm has shown great utility for reconstructing images from non-uniformly spaced Fourier samples in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Common methods for generating density compensation values are either sub-optimal or only consider a finite set of points in the optimization. This manuscript presents an algorithm for generating density compensation values from a set of Fourier samples that takes into account the point spread function over an entire rectangular region in the image domain. We show that the reconstructed images using the density compensation values of this method are of superior quality when compared to other standard methods. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.

Keywords: Density compensation; Gridding; NUFFT.

Publication types

Research Support, N.I.H., Extramural

MeSH terms

Abdomen
Algorithms*
Fourier Analysis
Image Processing, Computer-Assisted* / methods
Magnetic Resonance Imaging / methods
Phantoms, Imaging

Abstract

Publication types

MeSH terms

Grants and funding