Biorthogonal filterbanks and energy preservation property in image compression

The energy preservation property is among the most widely used properties o f orthogonal transforms in image compression because the reconstruction err or can be computed as the sum of the subband distortions, Thus, this is a k ey point in the use of efficient bit allocation techniques such as rate-dis tortion algorithms, Therefore, we study the nonorthogonality of biorthogona l filterbanks with reference to energy preservation from both theoretical a nd applicative points of view. We calculate the Riesz bounds as energy pres ervation bounds for filterbanks and discrete wavelet transforms, and then c onnect these results with the Riesz hounds of the related continuous wavele t transform. The simultaneous use of biorthogonal filterbanks and rate-dist ortion algorithms is then discussed as the issue of estimating the reconstr uction error as an additive function of the subband distortion. We propose a weighted sum of the subband distortions as an estimate. whose accuracy is calculated by a wide range of experiments. This accuracy is shown to be co rrelated to the Riesz bounds of the filterbanks. We conclude that from this point of view, most of the usual biorthogonal filterbanks may be considere d as nearly orthogonal.