Sequential scalar quantization of vectors: an analysis

R. Balasubramanian, C.A. Bouman, J.P. Allebach
1995 IEEE Transactions on Image Processing  
We propose an efficient vector quantization (VQ) technique which we call sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit inter-data correlation. At the same time, since quantization is performed on scalar rather than
more » ... r variables, SSQ offers a significant computational advantage over conventional VQ techniques, and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, we appeal to asymptotic quantization theory where the codebook size is assumed to be large. Closed form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. We also demonstrate the use of asymptotic theory in designing SSQ for a practical application, color image quantization, where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE, while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.
doi:10.1109/83.413172 pmid:18292024 fatcat:7f54abmzbncotb5g5oo2b6rrwu