Gain/shape vector quantizer for multidimensional spherically symmetric random source

The probability density of normalized ac orthogonal transform coefficients of image data can be modeled as a spherically symmetric distribution. On the other hand, the gain/shape vector quantizer [8] proposed by Buzo et al. is expected to provide a good quantization performance and a flexible design method for spherically symmetric random source. Therefore, it may be possible to realize a flexible vector quantizer by designing a gain/shape vector quantizer in the orthogonal transform domain. With this expectation the asymptotic performance and optimal allocation of the number of quantization levels of the gain/shape vector quantizer for an n-dimensional spherically symmetric random source was derived and it was shown that for n ≤ 10 the gain/shape vector quantizer yields the asymptotic performance between its upper bounds derived by Zador [10] and those by Conway and Sloane [11], and that for n > 11 its asymptotic performance is similar to the Zador's upper bounds. Also, comparison with the asymptotic performance of scalar quantizers [12] was made and it was shown that possible improvement of coding performance can be obtained by applying the gain/shape vector quantizer to orthogonal transform image coding, for which conventionally scalar quantizers have been used. Furthermore, a simple and flexible design method for the suboptimal gain/shape vector quantizer for a given spherically symmetric distribution was presented.