Photon-counting detectors (PCD) are the most recent advancement in computed tomography (CT). PCDs allow, among other things, for material decomposition, which decomposes the imaged object into a set of basis materials. Another field that is gaining attention, is the use of deep learning to improve the image reconstruction process in CT. In this work, we study the use of deep learning, specifically convolutional neural networks trained on the KiTS19 Challenge kidney data set, to improve the image quality of basis images resulting from three-material decomposition, a problem that is difficult due to its high sensitivity to noise. Our objective is to compare different network architectures and investigate whether these are best implemented in the projection domain or in the image domain. We study three different network architectures: U-Net, Dilated U-Net and ResNet, each applied in either the image domain or in the projection domain. The resulting image quality is evaluated in terms of contrast-to-noise ratio, task transfer function and noise power spectrum. Results show that for the type of phantoms the networks were trained on, the most effective option is to implement the network in the image domain and to use either the U-Net or Dilated U-Net architectures. However, when applying the networks to other phantoms, it seems that the networks in the sinogram generalize better, and produce better results. We also discuss why this might be the case, compare it with previous research, and consider what further improvements can be made.