This work investigates the application of artificial neural networks (ANNs) to deblur galaxy postcards of the GREAT10 challenge. High resolution models are created and convolved with a given Point Spread Function (PSF) to generate the corresponding blurred images. These are then downsampled in Fourier space to obtain the resolution used in the challenge. Training examples for the ANN are created from original and the blurred postcards. An n X n, for some odd n, window in a blurred image is compared to the same window in the original images and the ANN learns to output the correct intensity of the middle pixel. This means that the intensities of neighbouring pixels are used in the input vector. Different weightings schemes for translating the output vector from the ANN into pixel values are investigated. The advantages gained by using different window sizes, pixel encoding methods, and the number of hidden neurons in the ANN are also researched. The chi-squared error between the deblurred image and the original model is used to measure the performance.