Optimumization of lifting structure of reversible KLT based on permutation of signal's order and sign

This paper proposes a “reversible” three-point Karhunen Loeve transform (KLT) for de-correlation of RGB color components of an image signal. It is composed of “reversible” two point rotation transforms which have singular points (SP) and their rotation angles change depending on correlation of an input signal. When the angle is close to SP, rounding errors inside the transform are magnified to huge amount. To avoid this problem, we introduce permutation “order” and “sign” of signals. We also make it clear that the proposed method can shift SP by 0, 90, 180 or 270 degrees so that distance between SP and the rotation angle is maximized. It was observed that the proposed method reduces variance of the error by 10 [%].