Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups have recently shown that convolutional neural networks (CNNs) can be trained to perform high-fidelity MMF image reconstruction. We find that a considerably simpler neural network architecture, the single hidden layer dense neural network, performs at least as well as previously-used CNNs in terms of image reconstruction fidelity, and is superior in terms of training time and computing resources required. The trained networks can accurately reconstruct MMF images collected over a week after the cessation of the training set, with the dense network performing as well as the CNN over the entire period.