The application of current quantitative MRI techniques is limited by the long scan time. In this study, we propose a deep learning strategy to derive quantitative T1 map and B1 map from two incoherently undersampled variable contrast images. Furthermore, radiofrequency field (B1) inhomogeneity is automatically corrected in the derived T1 map. The tasks are accomplished in two steps: joint reconstruction and parameter quantification, both employing self-attention convolutional neural networks. Significant reduction in data acquisition time has been successfully achieved, including an acceleration in variable contrast image acquisition caused by undersampling and a waiver of B1 map measurement.