title: Mean square optimal NUFFT approximation for efficient non-Cartesian MRI reconstruction.
abstract: The fast evaluation of the discrete Fourier transform of an image at non-uniform sampling locations is key to efficient iterative non-Cartesian MRI reconstruction algorithms. Current non-uniform fast Fourier transform (NUFFT) approximations rely on the interpolation of oversampled uniform Fourier samples. The main challenge is high memory demand due to oversampling, especially when multidimensional datasets are involved. The main focus of this work is to design an NUFFT algorithm with minimal memory demands. Specifically, we introduce an analytical expression for the expected mean square error in the NUFFT approximation based on our earlier work. We then introduce an iterative algorithm to design the interpolator and scale factors. Experimental comparisons show that the proposed optimized NUFFT scheme provides considerably lower approximation errors than the previous designs [1] that rely on worst case error metrics. The improved approximations are also seen to considerably reduce the errors and artifacts in non-Cartesian MRI reconstruction.
authors.affiliation: University of Rochester, 659 W Randolph Street, Apt 717, Chicago, IL 60661, United States. Electronic address: yangwendy85@gmail.com.
authors.forename: Zhili
authors.initials: Z
authors.lastname: Yang
authors.affiliation: University of Iowa, 3314 Seamans Center for the Engineering Arts and Sciences, Iowa City, IA 52240, United States. Electronic address: mathews-jacob@uiowa.edu.
authors.forename: Mathews
authors.initials: M
authors.lastname: Jacob
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: Histogram; Interpolators; Non-Cartesian MRI; Non-uniform fast Fourier transform