This paper presents a filter design algorithm in order to realize high efficient image codec system based on subband decomposition, and also describes unified frameworks to interpret various image coding techniques. First, various image coding techniques based on the linear transform are dealt with in an unified manner, where both the matrix representation in time domain and the multirate filter bank concept are introduced. Reconsideration about the DPCM is stressed here because the subband coding and the transform coding have been already formulated in some common frameworks. Neither the filter's frequency response nor its orthogonality are taken into consideration because they don't necessarily play an important role in our formulation, particularly in case of the DPCM and the SSKF. Secondly, statistical optimization of short tap and linear phase PR (perfect reconstruction) filter banks is considered. The UCG (unified coding gain) that we proposed at the VSIP '91 as a performance measure of energy compaction properties of the multirate filter bank is expanded to multiple layer cases, and several new examples are presented. The short tap structure leads to low computational complexity, and the linear phase property contributes not only to remove phase distortion but also to solve the so-called border problem. Simulation results are also shown, and the validity of our approach is confirmed.