Lossless transforms and lossy transforms using IIR filters and their application to image coding

It is known that an IIR filter can provide an excellent amplitude characteristic that is of lower order than an FIR filter. Further, the IIR filter using all-pass circuits can realize an identical characteristic with fewer multipliers than in the conventional IIR filter. In this paper, a configuration and design method are given for a two-channel filter bank consisting of IIR filters with all-pass circuits. Lossless transforms and lossy transforms using these filter banks are proposed. One lossless transform is the S transform based on the Haar transform, but there is a problem that correlation remains in the output signals. In this paper, in place of the Haar transform in the S transform, a lossless transform based on two-channel integer IIR filter banks consisting of delay lines and all-pass circuits is proposed. On the other hand, the Haar transform is the only lossy transform based on the two-channel FIR filter bank that offers linear phase and orthogonality. Also, there are no design methods and no proof of effectiveness in applications of the two-channel IIR filter bank with both characteristics for image coding. In this paper, a two-channel orthogonal linear-phase IIR filter bank with a parallel structure of the all-pass circuits is proposed in order to maximize the coding gain, with the order of regularities as the constraint. Finally, the proposed methods are applied to stationary image coding and the effectiveness of the present method is shown.