AT&T Bell Lab., Holmdel, NJ.
IEEE Trans Image Process. 1992;1(2):133-47. doi: 10.1109/83.136591.
The authors consider the encoding of image subbands with a tree code that is asymptotically optimal for Gaussian sources and the mean squared error (MSE) distortion measure. They first prove that optimal encoding of ideally filtered subbands of a Gaussian image source achieves the rate distortion bound for the MSE distortion measure. The optimal rate and distortion allocation among the subbands is a by-product of this proof. A bound is derived which shows that subband coding is closer than full-band coding to the rate distortion bound for a finite length sequence. The tree codes are then applied to encode the image subbands, both nonadaptively and adaptively. Since the tree codes are stochastic and the search of the code tree is selective, a relatively few reproduction symbols may have an associated squared error a hundred times larger than the target for the subband. Correcting these symbols through a postcoding procedure improves the signal-to-noise ratio and visual quality significantly, with a marginal increase in total rate.
作者考虑使用一种树码对图像子带进行编码，该树码对于高斯源和均方误差 (MSE) 失真度量是渐近最优的。他们首先证明了对高斯图像源的理想滤波子带进行最佳编码可以实现 MSE 失真度量的率失真边界。最佳的子带之间的速率和失真分配是该证明的副产品。得出了一个界，表明子带编码比全带编码更接近有限长度序列的率失真边界。然后将树码应用于对图像子带进行非自适应和自适应编码。由于树码是随机的，并且代码树的搜索是选择性的，因此相对较少的再现符号可能具有与子带的目标相关的一百倍大的平方误差。通过后编码过程纠正这些符号可以显著提高信噪比和视觉质量，同时总速率略有增加。
