We provide a novel solution to the inverse problem in medical imaging that takes as input the undersampled k-space data from Magnetic Resonance Imaging (MRI) scans and outputs both the reconstructed images and the segmented myocardium. Previously, the undersampled k-space data is first transformed into a reconstructed MRI image. From this image, the myocardium is contours are subsequently extracted using a segmentation method. However, this sequential approach is not optimal and requires manual intervention. In order to automate and improve the results of these approaches, we propose a new method to solve the reconstruction and segmentation problems simultaneously. Our method is based on a novel deep learning approach we term “Joint-FR-Net”, which consists of a reconstruction module derived from the fast iterative shrinkage-thresholding algorithm (FISTA) and a segmentation module. We test our approach on an undersampled short-axis (SAX) cardiac dataset and show the effectiveness of the Joint FR-Net in both image reconstruction and myocardium joint segmentation.