Interferometric Synthetic Aperture Radar (InSAR) imagery based on microwaves reflected off ground targets is becoming increasingly important in remote sensing for ground movement estimation. However, the reflections are contaminated by noise, which distorts the signal's wrapped phase. Demarcation of image regions based on degree of contamination ("coherence") is an important component of the InSAR processing pipeline. We introduce Convolutional Neural Networks (CNNs) to this problem domain and show their effectiveness in improving coherence-based demarcation and reducing misclassifications in completely incoherent regions through intelligent preprocessing of training data. Quantitative and qualitative comparisons prove superiority of proposed method over three established methods.