Approximating vector quantisation by transformation and scalar quantisation

Vector quantisation provides better rate-distortion performance over scalar quantisation even for a random vector with independent dimensions. However, the design and implementation complexity of vector quantisers is much higher than that of scalar quantisers. To reduce the complexity while achieving performance close to optimal vector quantisation or better than scalar quantisation, the authors propose a new quantisation scheme, which consists of transformation and scalar quantisation. The transformation is to decorrelate and raise the dimensionality of the input data, for example, to convert a two-axis representation in two-dimensional into a tri-axis representation; then scalar quantisation is applied to each of the raised dimensions, for example, along three axes. The proposed quantiser is asymptotically optimal/suboptimal for low/high rate quantisation, especially for the quantisation with certain prime number of quantisation levels. The proposed quantiser has O(N²) design complexity, whereas the design complexity of VQ is O(N!), where N is the number of quantisation levels per dimension. The experimental results show that the average bit-rate achieves 0.4-24.5% lower than restricted/unrestricted polar quantisers and rectangular quantisers for signals of circular and elliptical Gaussian and Laplace distributions. It holds the potential of improving the performance of the existing image and video coding schemes.