In the context of codification of remote sensing images ---which are those obtained by air- or space-born sensors---, there is a particular kind of images that require special attention: hyperspectral images, or otherwise, those that instead of representing images in grayscale or using the three primary colors, have hundreds of representations of a spatial location, where each representation corresponds to a small fraction of the light spectrum. Hyperspectral images contain more information than traditional images and allow for, as an example, the remote detection of the ground composition or for the measure of vegetation lushness. Hyperspectral images contain high amounts of redundancy because of the multiple versions of the same location. Taking into account such redundancy yields significant increases in compression factors. Common techniques to remove redundancy from hyperspectral images are the use of a spectral transform like the Karhunen-Loêve transform or wavelets. Best results are obtained with the former transform or derived versions; nonetheless, it presents, among other problems, a very high computational cost that prevents its use in environments where computational resources are scant, e.g., a satellite sensor. In order to address this issue, derivations of the Karhunen-Loêve transform based on a divide-and-conquer strategy have been introduced. The idea behind these derivations is to decompose the transform in a collection of small parts, and only apply those parts which yield an effective improvement in terms of compression performance. Following such strategy, various decompositions are presented and exhaustively analyzed in the scope of this dissertation.
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