This thesis contains the application of the DWT [Discrete Wavelet Transform] for classification and compression of biomedical images (mammograms, small bowel and retinal). The shift-invariant DWT and several textural descriptors were used to provide scale, translation and semi-rotational (RST) invariant features. The features were classified using LDA with the leave one out method to combat small database sizes. The small bowel images achieved a classification rate of 75% and is the first reported work in the area, the retinal images achieved 81% classification rate and the mammograms achieved a rate of 59%. The success of the system is a [sic] due to the RST-invariant features which accounted for various sized masses, different camera angles and textural differences between pathologies. Any failures are a result of overlapping tissues which masked the pathologies. JPEG 2000 was the wavelet-based compressor used and it was compared to JPEG-LS, LJPEG, adaptive Huffman, arithmetic and LZW codes. For 12bpp mammgrams, JPEG 2000 offered the best compression (CR of 9.319 and R of 1.288bpp), but suffered from slow compression speeds (501.3 Ksymbols/s). Compression was investigated solely for mammograms since they were the only images stored in raw formats.