Interferometric Synthetic Aperture Radar (InSAR) imagery for estimating ground movement, based on microwaves reflected off ground targets is gaining increasing importance in remote sensing. However, noise corrupts microwave reflections received at satellite and contaminates the signal's wrapped phase. We introduce Convolutional Neural Networks (CNNs) to this problem domain and show the effectiveness of autoencoder CNN architectures to learn InSAR image denoising filters in the absence of clean ground truth images, and for artefact reduction in estimated coherence through intelligent preprocessing of training data. We compare our results with four established methods to illustrate superiority of proposed method.