Framelet Regularized SENSE Calibration in \({k}\)-Space with Conditional Sensitivity-Map Updates for Parallel MRI Reconstruction

Abstract. Parallel Magnetic Resonance Imaging (pMRI) shortens scan time by reducing the amount of k-space data acquired from multiple receiver coils. Conventional model-based reconstruction algorithms typically exploit either coil sensitivity information in the image domain or intercoil correlations in the frequency domain. However, both approaches rely on assumptions that may fail in certain scenarios, and each has its own strengths and limitations. In this work, we propose a Calibration Observation Model (COM) that integrates the advantages of both image-domain and frequency-domain methods to achieve efficient reconstruction. Furthermore, we introduce a three-dimensional multi-coil regularization term based on the Two-Level Nonstationary Tight Framelet (TNTF) system, resulting in the TNTF-COM model, which effectively suppresses artifacts and noise. Moreover, we develop a sensitivity update (US) method to further enhance reconstruction quality, leading to the TNTF-COMEUS model. To ensure stable and reproducible calibration, our method performs conditional sensitivity-map updates: the sensitivity-map is refreshed when the reconstructed slice image becomes stable (i.e., the mean absolute error between consecutive reconstructions falls below [Formula: see text]), with at most [Formula: see text] updates per run. Experimental results demonstrate that the proposed model-based reconstruction approach achieves, and in some cases surpasses, the performance of state-of-the-art deep learning-based methods, delivering high reconstruction accuracy and robustness. The implementation code and datasets used in this work are publicly available at https://github.com/Chenvp/COMEUS/ .