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Abstract PurposeTo introduce a novel deep model‐based architecture (DMBA), SPICER, that uses pairs of noisy and undersampled k‐space measurements of the same object to jointly train a model for MRI reconstruction and automatic coil sensitivity estimation. MethodsSPICER consists of two modules to simultaneously reconstructs accurate MR images and estimates high‐quality coil sensitivity maps (CSMs). The first module, CSM estimation module, uses a convolutional neural network (CNN) to estimate CSMs from the raw measurements. The second module, DMBA‐based MRI reconstruction module, forms reconstructed images from the input measurements and the estimated CSMs using both the physical measurement model and learned CNN prior. With the benefit of our self‐supervised learning strategy, SPICER can be efficiently trained without any fully sampled reference data. ResultsWe validate SPICER on both open‐access datasets and experimentally collected data, showing that it can achieve state‐of‐the‐art performance in highly accelerated data acquisition settings (up to ). Our results also highlight the importance of different modules of SPICER—including the DMBA, the CSM estimation, and the SPICER training loss—on the final performance of the method. Moreover, SPICER can estimate better CSMs than pre‐estimation methods especially when the ACS data is limited. ConclusionDespite being trained on noisy undersampled data, SPICER can reconstruct high‐quality images and CSMs in highly undersampled settings, which outperforms other self‐supervised learning methods and matches the performance of the well‐known E2E‐VarNet trained on fully sampled ground‐truth data. 

Parallel magnetic resonance imaging (MRI) is a widely-used technique that accelerates data collection by making use of the spatial encoding provided by multiple receiver coils. A key issue in parallel MRI is the estimation of coil sensitivity maps (CSMs) that are used for reconstructing a single high-quality image. This paper addresses this issue by developing SS-JIRCS, a new self-supervised model-based deep-learning (DL) method for image reconstruction that is equipped with automated CSM calibration. Our deep network consists of three types of modules: data-consistency, regularization, and CSM calibration. Unlike traditional supervised DL methods, these modules are directly trained on undersampled and noisy k-space data rather than on fully sampled high-quality ground truth. We present empirical results on simulated data that show the potential of the proposed method for achieving better performance than several baseline methods.