A New k-Space Model for Non-Cartesian Fourier Imaging

TL;DR

This paper introduces a Fourier-domain basis model for non-Cartesian MRI reconstruction, addressing limitations of voxel-based models by improving image quality and computational efficiency.

Contribution

The paper proposes a novel Fourier-domain basis expansion model that overcomes longstanding limitations of voxel-based approaches in Fourier imaging.

Findings

Enhanced image quality with fewer artifacts

Reduced computational complexity and faster convergence

Demonstrated improvements in non-Cartesian MRI reconstruction

Abstract

For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common modeling approach is to represent the continuous image as a linear combination of shifted "voxel" basis functions. Although well-studied and widely-deployed, this voxel-based model is associated with longstanding limitations, including high computational costs, slow convergence, and a propensity for artifacts. In this work, we reexamine this model from a fresh perspective, identifying new issues that may have been previously overlooked (including undesirable approximation, periodicity, and nullspace characteristics). Our insights motivate us to propose a new model that is more resilient to the limitations (old and new) of the previous approach. Specifically, the new model is based on a Fourier-domain basis expansion rather than the standard image-domain voxel-based approach. Illustrative results, which are presented in the context of non-Cartesian MRI reconstruction, demonstrate that the new model enables improved image quality (reduced artifacts) and/or reduced computational complexity (faster computations and improved convergence).