A subjective distortion measure for vector quantization

The authors present some preliminary results of their ongoing study on subjective VQ distortion measure in the time/spatial domain. They first propose a context based distortion measure between two vectors. The new measure is intuitively appealing, and they include some empirical evidence for its subjective significance. Although the measure is formulated as a matrix norm, it is computationally no more difficult than the mean-squares error. This measure quantifies the quantization distortion in the context (shape) of the signal waveform, but it is amplitude-invariant. So they combine the context distortion measure with a weighted mean distortion measure to obtain a unified subjective distortion measure D. They show that D is a distance measure and can be easily computed. Moreover, the process of computing the centroid of a set of training vectors and designing the VQ codebook under the new subjective distortion measure D is as simple as the conventional VQ. Specifically, the LBG algorithm can be applied to design the subjective VQ codebook after a simple linear transformation of the vector space in which signal samples are originally taken. They also analytically relate their subjective distortion measure to the ubiquitous mean-squares measure, and demonstrate that the latter is only a special case of the former. They also observe that the mean-removed VQ in a sense clusters training vectors under the proposed context distortion measure