Signal extension for orthogonal filter banks and its application to image coding

In this paper, a signal extension method is proposed for realization of nonextension convolution in a two-channel orthogonal FIR filter bank. Methods of performing nonextension convolution include the symmetric extension method for a linear phase filter bank and the periodic extension method applicable to an arbitrary filter bank. However, the periodic extension method is not appropriate for image compression because it becomes discontinuous at the signal edge. In this paper, for application to an orthogonal filter bank, the input signal of the decomposed filter bank is extended in such a way that the input signal in the synthesized filter bank has symmetry similar to that in the symmetric extension method. In this way, nonextension convolution is realized. In this case, it is shown that there are degrees of freedom in the extension signals determined by the input signal and the coefficients of the decomposed filter bank. The extended signal is calculated by singularity decomposition in such a way that the extended signal becomes smooth. Finally, the proposed method is applied to the coding of static images and the effectiveness of the method is demonstrated.