A general framework for compressed sensing and parallel MRI using annihilating filter based low-rank Hankel matrix

TL;DR

This paper introduces a unified low-rank Hankel matrix framework called ALOHA that improves k-space interpolation in parallel and compressed sensing MRI, achieving optimal sampling rates and outperforming existing methods.

Contribution

It presents a novel, unified approach that combines pMRI and CS-MRI via low-rank Hankel matrices, leveraging transform domain sparsity and matrix completion.

Findings

Achieves near-optimal sampling rates for MRI reconstruction.

Outperforms state-of-the-art pMRI and CS-MRI methods in experiments.

Validates effectiveness with in vivo multi-coil and dynamic imaging data.

Abstract

Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter based low-rank Hankel matrix approach (ALOHA) is proposed as a general framework for sparsity-driven k-space interpolation method which unifies pMRI and CS-MRI. Specifically, our framework is based on the fundamental duality between the transform domain sparsity in the primary space and the low-rankness of weighted Hankel matrix in the reciprocal space, which converts pMRI and CS-MRI to a k-space interpolation problem using structured matrix completion. Using theoretical results from the latest compressed sensing literatures, we showed that the required sampling rates for ALOHA may achieve the optimal rate. Experimental results with in vivo data for single/multi-coil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI.