In this paper, the design and analysis of adaptive subband coders is discussed. Both the analysis/synthesis filters and quantizers of the subband coding system are adapted to exploit non-stationarities of the image data. These adaptive systems are designed so that theoretical coding gain (TCG) is maximized, thereby minimizing mean-squared-error. The relative merits of adapting various components of a subband codec are investigated.

A size-limited filter bank (SLFB) is a maximally decimated filter bank operating on a finite length (duration) input signal resulting in subband components whose total number of independent samples is equal to the number of input samples. A theoretical framework for the design, analysis, and implementation of such filter banks resulting from applying FIR separable filter banks to finite length signals is presented. The concept of maximizing theoretical coding gain (TCG) using optimal bit allocation is generalized for this special case. Using TCG, the relative merits of various different SLFBs are addressed.

A multirate (MR) filter bank is called size-limited if the total number of output samples equals the number of input samples. A method called symmetric extension improved performance in subband image compression systems compared to the earlier method of circular convolution. However, the symmetric extension method was developed only for two-band uniform filter banks, and required even-length linear phase analysis filters. The authors generalize the symmetric extension method to the M-band, possibly nonuniform filter banks, where M=/>2. The length restriction on the analysis filters is relaxed.