Moreau de Saint-Martin F, Siohan P, Cohen A
TDF-Direction des Oper., Les Lilas.
IEEE Trans Image Process. 1999;8(2):168-78. doi: 10.1109/83.743852.
The energy preservation property is among the most widely used properties of orthogonal transforms in image compression because the reconstruction error can be computed as the sum of the subband distortions. Thus, this is a key point in the use of efficient bit allocation techniques such as rate-distortion algorithms. Therefore, we study the nonorthogonality of biorthogonal filterbanks with reference to energy preservation from both theoretical and applicative points of view. We calculate the Riesz bounds as energy preservation bounds for filterbanks and discrete wavelet transforms, and then connect these results with the Riesz bounds of the related continuous wavelet transform. The simultaneous use of biorthogonal filterbanks and rate-distortion algorithms is then discussed as the issue of estimating the reconstruction 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 correlated to the Riesz bounds of the filterbanks. We conclude that from this point of view, most of the usual biorthogonal filterbanks may be considered as nearly orthogonal.
能量保持特性是图像压缩中正交变换应用最为广泛的特性之一，因为重构误差可以计算为子带失真之和。因此，这是使用诸如率失真算法等高效比特分配技术的关键点。所以，我们从理论和应用两个角度研究双正交滤波器组关于能量保持的非正交性。我们计算里兹界作为滤波器组和离散小波变换的能量保持界，然后将这些结果与相关连续小波变换的里兹界联系起来。接着讨论了双正交滤波器组和率失真算法的同时使用，即把估计重构误差作为子带失真的加性函数的问题。我们提出将子带失真的加权和作为一种估计，并通过大量实验计算其精度。结果表明这种精度与滤波器组的里兹界相关。我们得出结论，从这个角度来看，大多数常用的双正交滤波器组可被视为近似正交的。
