Accelerating Hankel low-rank MR reconstruction with a patch-based Hankel scheme

Magnetic resonance imaging (MRI) and spectroscopy (MRS) play critical roles in medical diagnosis, clinical research, and various scientific fields. However, they are often limited by the slow nature of data acquisition. Undersampling has become an effective strategy to address this issue, necessitating advanced data reconstruction methods to ensure high-quality results. Hankel low-rank methods have shown the ability to produce high-quality reconstructions with reduced reconstruction error and are robust to sampling patterns. However, their high computational complexity poses a significant challenge, particularly in higher-dimensional scenarios, limiting their applicability in situations requiring fast processing. In this paper, we develop a new approach for accelerating Hankel low-rank reconstruction without sacrificing reconstruction quality. We focus on addressing the fundamental but significant cause of the slow reconstruction process: the large-scale dimensionality of the low-rank Hankel matrix. We propose a patch-based Hankel matrix formation scheme that significantly decreases the Hankel matrix dimensions while preserving its low-rank properties. We demonstrate the effectiveness of the proposed scheme through two biomedical applications: MRS and MRI reconstructions. For state-of-the-art Hankel low-rank methods, experimental results indicate that the proposed approach achieves over 8-fold acceleration in reconstruction time for MRS and 4-fold for MRI, while reducing memory requirements by over 70%. It maintains the high-quality reconstruction performance in terms of quantitative metrics, e.g., RLNE, PSNR, and SSIM. Moreover, examples are included to demonstrate the feasibility of applying the proposed approach to accelerate other existing Hankel low-rank methods. The implementation of our proposed method is available on GitHub at https://github.com/Xinlin1219/PHLR.