Filter Banks and Wavelet Compression

The purpose of this chapter is to describe an alternative approach to the block-transform approach to spatial decorrelation, based on hierarchical subband decompositions. This chapter firstly examines the basic two-channel filter bank structure and then investigates the filter properties that enable perfect reconstruction in the absence of quantization. It then goes on to consider the more general case of multirate filtering, showing how, through the appropriate combination of filters and up- and downsampling operations, critical sampling can be achieved. It next examines specific cases of useful subband and wavelet filters and extends the basic architecture to the case of a multistage (multiscale) decomposition and to two dimensions, as required for image compression applications. Finally, bit allocation strategies and scalability are discussed in the context of the JPEG2000 still image coding standard. Examples are provided throughout.