The most common signal expansions are produced by linear transforms and filter banks. The existence of fast algorithms and hardware for their implementation makes them extremely viable for practical systems. Some applications, such as real-time video coding, necessitate low complexity at both the encoder and decoder. These applications allow for little adaptivity in the signal expansion. As a consequence, fixed transforms such as the DCT have become most common for image and video compression.
However, there are many new applications that support an asymmetric model for coding whereby the objectives at the encoder and the decoder differ greatly. For example, in digital image and video libraries the data is typically encoded once - off-line, and is stored. Real-time compression is not required and the encoder does not need to be of low complexity. The compressed data may be retrieved later for purposes of analysis, decompression and viewing. This requires that the encoded images and videos are still quickly and cheaply decompressed and possibly analyzed directly in the compressed domain. In general, digital and image libraries require new and efficient compression systems that jointly (1) decrease the code size, (2) lower the visible distortion, and (3) improve access to visual content and image features [Pic94]. Given these new applications, it is worthwhile to investigate new procedures for the adaptive decomposition of images in the design of image compression systems.
Recently new algorithms have been proposed for adaptive transformation of images. The purpose is to derive a transform or filter bank that is customized to each image. However, it must be done in such a way that the overhead from the representation of the basis does not off-set the bit reduction attained by encoding the data in the new basis.