One advantage of photon-counting CT compared to dual-energy CT is the possibility to perform K-edge imaging, where contrast agents such as iodine can be distinguished from other substances based on spectral characteristics. However, for iodine K-edge imaging in clinical CT, the three-basis decomposition problem is ill-conditioned due to the low K-edge energy of iodine, meaning that the decomposition is highly sensitive to both noise and miscalibrations. This makes robust three-basis decomposition difficult using standard techniques. In this simulation study we evaluate a novel method of performing K-edge imaging, which circumvents the challenging three-basis decomposition step by replacing it with multiple two-basis decompositions followed by a deep convolutional neural network to generate three basis images. Based on the XCAT phantom, we generated 1224 spectral phantom image slices of the neck, with iodine-filled blood vessels and calcifications, and simulated CT imaging in CatSim with a silicon-based detector model without quantum noise, i.e. in the high-dose limit. For each simulated slice, we used maximum likelihood to perform three two-basis decompositions, into PE-PVC, PE-iodine, and PVC-iodine, yielding six basis images in total. We then trained a U-Net to map these six input images to the ground-truth basis images, PE, PVC and iodine. Our results show that the proposed method can reproduce PE, PVC and iodine basis images with high accuracy, in the high-dose limit. This suggests that the proposed three-basis decomposition method may be a feasible way of performing K-edge CT imaging with iodine, with important potential implications for imaging of the carotid arteries.