Multiple-rate structured vector quantization of image pyramids

Abstract A recently introduced tree growth algorithm, the marginal returns algorithm, is used to grow multiple-rate tree-structured vector quantizers for the pyramid coding of rectangularly as well as hexagonally sampled images. The use of a structured multirate codebook solves two problems that normally arise in vector quantization of subbands. The multiple-rate codebook can operate over a wide range of rates, thus dispensing with the need to transmit the codebook as overhead, while the tree structure reduces the search complexity. Search complexity is a crucial issue even in low-rate pyramid coding since subbands with more information content are coded at high rates. In addition, the design technique makes it possible to tune the coder to the spectral properties of the image by optimally allocating rate to the different subbands. It has been shown in an earlier paper that the marginal returns algorithm yields codebooks that are optimal for sources that meet the law of diminishing marginal returns. However, even for sources that do not satisfy these conditions, the algorithm gives coders that perform close to the optional. Image coding results at rates below 1 bit per pixel are presented.