This paper constructs a set partition coding system (SPACS) to combine the advantages of different types of set partition coding algorithms. General tree (GT) is an important conception introduced in this paper, which can represent tree set and square set simultaneously. With the help of GT, SPIHT is generalized to construct degree-   $k$    SPIHT based on the analysis of two kinds of set partition operations. Using the same coding mechanism, SPACS   $(k,p)$    is constructed, aided with virtual subbands that are generated by recursive division on the    $LL$    band. SPACS belongs to tree-set partition coding algorithms if    $k$    and    $p$    take smaller values. In particular, SPACS(2,1) is the classical SPIHT. SPACS tends toward a block-set partition coding algorithm as    $k,p$    increases. Location bit, amplitude bit, and unnecessary bit are presented, which can be used to analyze the coding efficiency of SPACS. We compress 256 images with    $512\times 512$    using SPACS. The numerical results show SPACS achieves some improvements in coding efficiency over SPIHT, especially at very low bitrate. On average, to code every image, SPACS(3,1) (at an average of 3.93 bpp) needs 7792 more location bits but saves 10 218 unnecessary bits, compared with SPIHT (3.94 bpp).
['Qiufu Li', 'Derong Chen', 'Wei Jiang', 'Bingtai Liu', 'Jiulu Gong']
Generalization of SPIHT: Set Partition Coding System