Magnetic Resonance Imaging (MRI) acquisition is performed sequentially in the spatial-frequency domain (kspace) and involves several views of the object/subject. To accelerate the acquisition, k-space lines are often undersampled on a cartesian grid. Parallel imaging reconstruction algorithms are then applied to recover unseen lines. We consider this super-resolution problem in k-space to further reduce the acquisition time with deep learning and to reduce the costs associated with this expensive medical imaging technology. Because the sensors are specific to anatomical regions and experimental setups, it pushes toward learning a reconstruction model on a per-image basis, i.e. for every scan and image. Here, we propose an extension of state-of-the-art MRI reconstruction methods where the super-resolution task in k-space is solved with a convolutional neural network, and where an adversarial strategy using a patch discriminator in image space is used to reach higher undersampling rates. Both parts are trained in a one-shot learning setting. It is demonstrated both using simulated and in vivo brain experiments that this combined approach provides enhanced image quality for undersampling rates larger than the ones used in a clinical routine on multi-slice 2D T2-weighted imaging sequences, making the approach readily applicable as an alternative reconstruction strategy in MRI systems for 2D parallel imaging, and which could be further extended to accelerate 3D imaging sequences.