Least Squares Optimal Density Compensation for the Gridding Non-uniform Discrete Fourier Transform

TL;DR

This paper introduces a novel least squares-based density compensation method for the Gridding algorithm, improving image reconstruction quality from non-uniform Fourier samples across various imaging modalities.

Contribution

It presents the first density compensation algorithm that considers the entire point spread function over a continuous set, enhancing reconstruction accuracy.

Findings

Superior image quality with the proposed method

Validated on numerical phantom and MRI images

Outperforms existing density compensation techniques

Abstract

The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Existing methods for generating density compensation values are either sub-optimal or only consider a finite set of points (a set of measure 0) in the optimization. This manuscript presents the first density compensation algorithm for a general trajectory that takes into account the point spread function over a set of non-zero measure. We show that the images reconstructed with Gridding using the density compensation values of this method are of superior quality when compared to density compensation weights determined in other ways. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee.