Subband/transform functions for image processing

Functions for image data processing written for use with the MATLAB(TM) software package are presented. These functions provide the capability to transform image data with block transformations (such as the Walsh Hadamard) and to produce spatial frequency subbands of the transformed data. Block transforms are equivalent to simple subband systems. The transform coefficients are reordered using a simple permutation to give subbands. The low frequency subband is a low resolution version of the original image, while the higher frequency subbands contain edge information. The transform functions can be cascaded to provide further decomposition into more subbands. If the cascade is applied to all four of the first stage subbands (in the case of a four band decomposition), then a uniform structure of sixteen bands is obtained. If the cascade is applied only to the low frequency subband, an octave structure of seven bands results. Functions for the inverse transforms are also given. These functions can be used for image data compression systems. The transforms do not in themselves produce data compression, but prepare the data for quantization and compression. Sample quantization functions for subbands are also given. A typical compression approach is to subband the image data, quantize it, then use statistical coding (e.g., run-length coding followed by Huffman coding) for compression. Contour plots of image data and subbanded data are shown.