Sequential structures for vector quantization and functional approximation

In this research, we developed the technique of optimal sequential scalar quantization of vectors. This is an efficient vector quantization technique with a sequential structure which is amenable to fast implementation. We then extended this sequential structure to the problem of approximating nonlinear multidimensional functions, which has a variety of applications in image and signal processing. The technique we developed is called the optimal sequential linear interpolation of functions. This technique uses muitidimensional linear splines with a partially separable sequential structure to approximate a nonlinear function. Asymptotic vector quantization theory is applied to analyse the error performance of these sequential structures; and the procedures for designing the optimal structures to minimize the quantization or interpolation error are obtained from the asymptotic analysis. We applied the sequential linear interpolation technique to the practical problem of color device calibration where highly nonlinear multidimensional transformations must be efficiently implemented