Zhu C, Po L M
Dept. of Comput. Sci., Southwest China Normal Univ., Chongqing.
IEEE Trans Image Process. 1998;7(10):1400-9. doi: 10.1109/83.718481.
The design of the optimal codebook for a given codebook size and input source is a challenging puzzle that remains to be solved. The key problem in optimal codebook design is how to construct a set of codevectors efficiently to minimize the average distortion. A minimax criterion of minimizing the maximum partial distortion is introduced in this paper. Based on the partial distortion theorem, it is shown that minimizing the maximum partial distortion and minimizing the average distortion will asymptotically have the same optimal solution corresponding to equal and minimal partial distortion. Motivated by the result, we incorporate the alternative minimax criterion into the on-line learning mechanism, and develop a new algorithm called minimax partial distortion competitive learning (MMPDCL) for optimal codebook design. A computation acceleration scheme for the MMPDCL algorithm is implemented using the partial distance search technique, thus significantly increasing its computational efficiency. Extensive experiments have demonstrated that compared with some well-known codebook design algorithms, the MMPDCL algorithm consistently produces the best codebooks with the smallest average distortions. As the codebook size increases, the performance gain becomes more significant using the MMPDCL algorithm. The robustness and computational efficiency of this new algorithm further highlight its advantages.
针对给定的码本大小和输入源设计最优码本是一个仍有待解决的具有挑战性的难题。最优码本设计中的关键问题是如何有效地构建一组码矢量，以最小化平均失真。本文引入了一种最小化最大部分失真的极小极大准则。基于部分失真定理，研究表明，最小化最大部分失真和最小化平均失真在渐近意义上对于相等且最小的部分失真将具有相同的最优解。受此结果的启发，我们将交替极小极大准则纳入在线学习机制，并开发了一种用于最优码本设计的新算法，称为极小极大部分失真竞争学习（MMPDCL）算法。利用部分距离搜索技术实现了MMPDCL算法的计算加速方案，从而显著提高了其计算效率。大量实验表明，与一些著名的码本设计算法相比，MMPDCL算法始终能产生平均失真最小的最优码本。随着码本大小的增加，使用MMPDCL算法的性能提升变得更加显著。这种新算法的鲁棒性和计算效率进一步凸显了其优势。
