A new nonunitary transform called the prediction-based lower triangular transform (PLT) is introduced for signal compression. The new transform has the same decorrelation property as the Kahurnen-Loeve transform (KLT), but its implementational cost is less than one half of KLT. Compared with the KLT, the design cost of an M/spl times/M PLT is much lower and is only of the order of O(M/sup 2/). Moreover, the PLT can be factorized into simple building blocks. Using two different factorizations, we introduce two minimum noise structures that have roughly the same complexity as the direct implementation of PLT. These minimum noise structures have the following properties: (1) its noise gain is unity even though the transform is nonunitary; (2) perfect reconstruction is structurally guaranteed; (3) it can be used for both lossy/lossless compression. We show that the coding gain of PLT implemented using the minimum noise structure is the same as that of KLT. Furthermore, universal transform coders using PLT are derived. For AR(1) process, the M/spl times/M PLT has a closed form and needs only (M-1) multiplications and additions.
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机译:引入了一种新的非单位变换,称为基于预测的下三角变换(PLT),用于信号压缩。新的变换具有与Kahurnen-Loeve变换(KLT)相同的解相关属性,但是其实现成本不到KLT的一半。与KLT相比,M / spl倍/ M PLT的设计成本要低得多,仅约为O(M / sup 2 /)。此外,可以将PLT分解为简单的构建块。使用两种不同的分解,我们介绍了两种最小噪声结构,它们的复杂度与直接实施PLT大致相同。这些最小的噪声结构具有以下特性:(1)即使变换是非单一的,其噪声增益也是单一的; (2)在结构上保证了完美的重建; (3)它可用于有损/无损压缩。我们表明,使用最小噪声结构实现的PLT的编码增益与KLT相同。此外,推导了使用PLT的通用变换编码器。对于AR(1)过程,M / spl次数/ M PLT具有封闭形式,并且仅需要(M-1)个乘法和加法。
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