Prediction-based lower triangular transform

In this paper, a new nonunitary transform called the prediction-based lower triangular transform (PLT) is introduced for signal compression. The new t ransform has the same decorrelation property as the Kahurnen-Loeve transfor m (KLT), but its implementational cost is less than one half of KLT, Compar ed with the KLT, the design cost of an M x M PLT is much lower and is only of the order of O(M-2). Moreover, the PLT can be factorized into simple bui lding blocks, Using two different factorizations, we introduce two minimum noise structures that have roughly the same complexity as the direct implem entation of PLT. These minimum noise structures have the following properti es: 1) Its noise gain is unity even though the transform is nonunitary; 2) perfect reconstruction is structurally guaranteed; 3) it can be used for bo th. lossy/lossless compression. We will show that the coding gain of PLT im plemented using the minimum noise structure is the same as that of KLT. Fur thermore, universal transform coders using PLT are derived. For AR(1) proce ss, the M x M PLT has a closed form and needs only (M - 1) multiplications and additions.