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In synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR), an imaging radar emits electromagnetic waves of varying frequencies towards a target and the backscattered waves are collected. By either moving the radar antenna or rotating the target and combining the collected waves, a much longer synthetic aperture can be created. These radar measurements can be used to determine the radar cross-section (RCS) of the target and to reconstruct an estimate of the target. However, the reconstructed images will suffer from spectral leakage effects and are limited in resolution. Many methods of enhancing the images exist and some are based on deep learning. Most commonly the deep learning methods rely on high-resolution ground truth data of the scene to train a neural network to enhance the radar images. In this thesis, a method that does not rely on any high-resolution ground truth data is applied to train a convolutional neural network to enhance radar images. The network takes a conventional ISAR image subject to spectral leakage effects as input and outputs an enhanced ISAR image which contains much more defined features. New RCS measurements are created from the enhanced ISAR image and the network is trained to minimise the difference between the original RCS measurements and the new RCS measurements. A sparsity constraint is added to ensure that the proposed enhanced ISAR image is sparse. The synthetic training data consists of scenes containing point scatterers that are either individual or grouped together to form shapes. The scenes are used to create synthetic radar measurements which are then used to reconstruct ISAR images of the scenes. The network is tested using both synthetic data and measurement data from a cylinder and two aeroplane models. The network manages to minimise spectral leakage and increase the resolution of the ISAR images created from both synthetic and measured RCSs, especially on measured data from target models which have similar features to the synthetic training data.  The contributions of this thesis work are firstly a convolutional neural network that enhances ISAR images affected by spectral leakage. The neural network handles complex-valued signals as a single channel and does not perform any rescaling of the input. Secondly, it is shown that it is sufficient to calculate the new RCS for much fewer frequency samples and angular positions and compare those measurements to the corresponding frequency samples and angular positions in the original RCS to train the neural network.