Accelerated multi-coil magnetic resonance imaging reconstruction has seen a\nsubstantial recent improvement combining compressed sensing with deep learning.\nHowever, most of these methods rely on estimates of the coil sensitivity\nprofiles, or on calibration data for estimating model parameters. Prior work\nhas shown that these methods degrade in performance when the quality of these\nestimators are poor or when the scan parameters differ from the training\nconditions. Here we introduce Deep J-Sense as a deep learning approach that\nbuilds on unrolled alternating minimization and increases robustness: our\nalgorithm refines both the magnetization (image) kernel and the coil\nsensitivity maps. Experimental results on a subset of the knee fastMRI dataset\nshow that this increases reconstruction performance and provides a significant\ndegree of robustness to varying acceleration factors and calibration region\nsizes.\n