# Accelerating Non-Cartesian MRI Reconstruction Convergence using k-space Preconditioning

## TL;DR

This paper introduces a k-space preconditioning method for MRI reconstruction that accelerates convergence without sacrificing accuracy or increasing per-iteration computation, demonstrated to converge in about ten iterations.

## Contribution

The paper presents a novel dual formulation-based k-space preconditioning approach that improves MRI reconstruction speed without added computational complexity.

## Key findings

- Converges in about ten iterations in practice.
- Outperforms existing methods in convergence speed.
- Does not require inner loops or extra computation per iteration.

## Abstract

We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density compensations which sacrifice reconstruction accuracy, or circulant preconditioners which increase per-iteration computation. Our approach overcomes both shortcomings. Concretely, we show that viewing the reconstruction problem in the dual formulation allows us to precondition in k-space using density-compensation-like operations. Using the primal-dual hybrid gradient method, the proposed preconditioning method does not have inner loops and are competitive in accelerating convergence compared to existing algorithms. We derive l2-optimized preconditioners, and demonstrate through experiments that the proposed method converges in about ten iterations in practice.