Prediction-based lower triangular transform

Abstract—In this paper, a new nonunitary transform called the prediction-based lower triangular transform (PLT) is introduced for signal compression. The new transform has the same decorre-lation 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 PLT is much lower and is only of the order of ( 2). Moreover, the PLT can be factor-ized 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 min-imum 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 will 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 PLT has a closed form and needs only ( 1) multiplications and additions. Index Terms—Compression, Karhunen–Loeve transform (KLT), subband coding, transform coding, wavelet coding