A parallel-imaging algorithm is proposed based on deep convolutional neural networks. This approach eliminates the need to collect calibration data and the need to estimate sensitivity maps or k-space interpolation kernels. The proposed network is applied entirely in the k-space domain to exploit known properties. Coil compression is introduced to generalize the method to different hardware configurations. Separate networks are trained for different k-space regions to account for the highly non-uniform energy. The network was trained and tested on both knee and abdomen volumetric Cartesian datasets. Results were comparable to L2-ESPIRiT and L1-ESPIRiT which required calibration data from the ground truth.