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Signal extension and noncausal filtering for subband coding of images

This paper addresses two issues of concern when implementing filter banks for subband coding of images: filter causality and filtering of the finite-length rows and columns of the image. A new framework for analyzing the effect of noncausal analysis filtering on the aliasing cancellation properties of the two-band filter bank system is presented. A general solution is given to the problem of how to extend finite-length signals before filtering so that expansion of the subband signal size can be avoided but perfect reconstruction remains. It will be shown how the methods of circular convolution and symmetric extension provide this solution. When using the symmetric extension method, how the signal is extended and the amount of delay the analysis filters may impart are highly constrained. Both even-length and odd-length FIR filters may be used, but extension is different in the two cases.