A critical issue for the safe operation of nuclear power plants is to quickly and accurately detect possible anomalies and perturbations in the reactor. Defects in operation are principally identified through changes in the neutron flux, as captured by detectors placed at various points inside and outside of the core. This work presents a novel technique for anomaly detection on nuclear reactor signals through the combined use of wavelet-based analysis and convolutional neural networks. In essence, the wavelet transform is applied to the signals and the corresponding scaleograms are produced, which are subsequently used to train a convolutional neural network that detects possible perturbations in the reactor core. The overall methodology is experimentally validated on a set of simulated nuclear reactor signals generated by a well established relevant tool. The obtained results indicate that the trained network achieves high levels of accuracy in failure detection, while at the same time being robust to noise.