The compression of gray scale images is an interesting problem because of the large number of variations between data elements while maintaining a high degree of correlation. The goal of image data compression is to obtain the best possible image for a fixed information rate. In recent years, there has been a lot of research into the efficient coding of gray scale images. Vector quantization (Va) methods have been successfully applied to the efficient coding of images. These methods, however, are computationally intensive. Full search Multiple Bases Representation (MBR) is similar to Va in many respects. The Recursive Residual Projection (RRP) algorithm, a sub-optimal implementation of full search MBR, has been found to perform well. In this thesis, we apply MBR (using the RRP algorithm) to the compression of image data. We develop an image coding system that allows for a comparison of MBR with some well studied transform coding methods: the Discrete Cosine Transform (DeI) and the Fast Haar Transform (FHT) coding methods. We find that the DCf based coder performs at 1.5 bits/pixel with good image quality and that the FlIT based coder performs at 0.81 bits/pixel with some disconcerting characteristics. The RRP based coder outperforms the ncr based coder at 1.1 bits/pixel with very good image quality. We also tested a modified version of the RRP algorithm that used 3 orthogonal sets of basis vectors. We found that the modified RRP algorithm generally reduced the number of representation coefficients and improved image quality. We also found that the modified RRP algorithm performed worse than the RRP algorithm due to an increase in symbol entropy. / Master of Science