Recursive computation method for fast encoding of vector quantization based on 2-pixel-merging sum pyramid data structure

Abstract

Vector quantization (VQ) is a popular signal compression method. In the framework of VQ, fast search method is one of the key issues because it is the time bottleneck for VQ applications. In order to speed up VQ encoding process, how to construct some lower dimensional feature vectors for a k-dimensional original vector so as to measure the distortion between any vectors lightly becomes important. To reduce the dimension for approximately representing a k-dimensional vector, the multi-resolution concept is a natural consideration. By introducing a pyramid data structure, the multi-resolution concept used in fast VQ encoding includes two aspects, which are (1) a multi-resolution distortion check method and (2) a multi-resolution distortion computation method. Some fast search methods that are based on a 4-pixel-merging (4-PM) mean pyramid data structure [Lin, S.J., Chung, K.L., Chang, L.C. 2001. An improved search algorithm for vector quantization using mean pyramid structure. Pattern Recognition Lett. 22 (3/4) 373] and a 2-pixel-merging (2-PM) sum pyramid data structure [Pan, Z., Kotani, K., Ohmi, T. 2004. An improved fast encoding algorithm for vector quantization using 2-pixel-merging sum pyramid data structure. Pattern Recognition Lett. 25 (3) 459] have already been proposed. Both of them realized the multi-resolution concept by using a multi-resolution distortion check method. However, both of them ignored the multi-resolution distortion computation method, which can also be guaranteed by the multi-resolution concept if a recursive computation way is introduced. In principle, a multi-resolution distortion computation method can completely reuse the obtained computation result that is already executed at a lower resolution level so that no waste to it will occur at all. This paper aims at improving the search efficiency of the previous work [Pan, Z., Kotani, K., Ohmi, T. 2004. An improved fast encoding algorithm for vector quantization using 2-pixel-merging sum pyramid data structure. Pattern Recognition Lett. 25 (3) 459] further by introducing a multi-resolution distortion computation method into multi-resolution distortion check method so that about half of its computational cost can be reduced mathematically. Experimental results confirmed the proposed method outperforms the previous works obviously.