Low-to-High Frequency Progressive K-Space Learning for MRI Reconstruction

Xiaohan Xing, Liang Qiu, Lequan Yu, Lingting Zhu, Lei Xing, Lianli Liu

Abstract: Magnetic Resonance Imaging (MRI) is a crucial non-invasive diagnostic tool. The image quality, however, is often limited by k-space under-sampling and noise, which is exacerbated for low-field systems. K-space learning has the potential to support high quality MRI reconstruction by exploiting correlation in the raw data domain and recovering the noise-corrupted or under-sampled measurements. However, the magnitude of the low-frequency (LF) component is usually thousands of times higher than the high-frequency (HF) component in the k-space, thus the network training might be dominated by LF learning while ignoring the recovery of the HF component. To support the effective recovery of all frequency components on the k-space data, we propose a Low-to-High Frequency Progressive (LHFP) learning framework, consisting of a cascade of k-space learning networks. In the first round, the model focuses on the learning of the LF component. Starting from the second round, we propose a High-Frequency Enhancement (HFE) module to emphasize the HF learning based on a predicted patient-specific low-high frequency boundary. To avoid degradation in LF learning during the subsequent rounds that focus on the HF component, we propose a Low-Frequency Compensation (LFC) module that compensates the current prediction of LF component by the last-round prediction with an estimated weight. For the reconstruction of fully-sampled and 4X under-sampled low-field brain MRI on the BraTs dataset, our method demonstrates superior performance than existing k-space learning methods, and surpasses dual-domain learning methods when combined with a simple image domain denoiser. The source codes will be released upon acceptance.