Approximating vector quantisation by transformation and scalar quantisation

Vector quantization provides better ratedistortion performance over scalar quantization even for a random vector with independent dimensions. However, the design and implementation complexity of vector quantizers is much higher than that of scalar quantizers. To reduce the complexity while achieving performance close to optimal vector quantization and better than scalar quantization, we propose a new quantization scheme, which consists of a transformation and scalar quantization. The transformation is to convert a two-axis representation to a triaxis representation; then scalar quantization is applied to each of the three axes. The proposed quantizer is asymptotically optimal/suboptimal for low/high rate quantization, especially for the quantization with certain prime number of quantization levels. The proposed quantizer has O(N) design complexity, while VQ has O(N !) design complexity, where N is the number of quantization levels per dimension. The experimental results show that it achieves average bit-rate saving of 0.4%-24.5% over restricted/unrestricted polar quantizers and rectangular quantizers for signals of circular and elliptical Gaussian distributions and Laplace distributions. It holds potential of improving the performance of existing image and video coding schemes.