This document reports on a study using a multi-layer perceptron (MLP) neural network to reduce blocking artifacts in JPEG compressed images. The MLP takes gradients of pixel values near block borders as input and outputs differences between original and compressed pixel values to post-process images. Experiments showed the MLP can improve quality of grayscale images compressed to low bit rates when trained on high quality data, but did not significantly improve color images. Further research is needed on MLP structures for reducing artifacts in color images.