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The issues of image compression and pattern classification have been a primary focus of researchers among a variety of fields including signal and image processing, pattern recognition, data classification, etc. These issues depend on finding an efficient representation of the source data. In this paper we collate our earlier results where we introduced the application of the Hilbert scan to a principal component algorithm (PCA) with adaptive principal component extraction (APEX) neural network model. We apply these techniques to medical imaging, particularly image representation and compression. We apply the Hilbert scan to the APEX algorithm to improve results.