Low memory implementation of generic hierarchical transforms for parent–children tree (PCT) production and its application in image compression

This paper presents a unified approach for low-memory and on-the-fly implementation of generic hierarchical transforms (GHTs) suited for parent–children tree (PCT) production, called the stripe-based hierarchical transform (SBHT). Here, the term “generic” means that totally different FBs may appear in different decomposition levels. This approach generates the exactly same subband coefficients as the traditional global implementation of GHTs with a low memory budget that is unrelated to the input signal length and only dependent on the GHT. The SBHT lends itself to the PCT-based image coding algorithm in the sense that the basic data unit generated by the SBHT is row-based collections of PCT structures, the most widely used data entity in subband coding. To demonstrate the SBHT's application in image coding, a PCT coder based on the LLEC is proposed to encode the PCTs generated by the SBHT. No intermediate buffering is needed between the SBHT and the codec. The experiments show that when the GHT is configured appropriately, the proposed coder provides competitive coding efficiency relative to the SPIHT and JPEG2000 with a very low memory budget and low computation complexity.