A Novel Optimizer Based on Particle Swarm Optimizer and LBG for Vector Quantization in Image Coding Huilian Liao Faculty of Information Engineering, Shenzhen University, Shenzhen 518060, China liaohuilian@163.com Yiwei Wang Faculty of Information Engineering, Shenzhen University, Shenzhen 518060, China Jiarui Zhou Faculty of Information Engineering, Shenzhen University, Shenzhen 518060, China 030bug@gmail.com Zhen Ji Faculty of Information Engineering, Shenzhen University, Shenzhen 518060, China jizhen@szu.edu.cn Abstract This paper presents an optimizer based on particle swarm optimization and LBG (PSO-LBG) for vector quantization in image coding. Three swarms, including two initial swarms and one elitist swarm whose particles are selected from two initial swarms respectively, are applied to find the global optimum. At each iteration of a swarm’s updating process, particles perform the basic operations of PSO, but with smaller parameter values and population size compared with conventional PSO, followed by the well-known vector quantizer, i.e. LBG algorithm. Experimental results have demonstrated that the quality of codebook design using this optimizer is much better than that of Fuzzy K-means (FKM), Fuzzy Reinforcement Learning Vector Quantization (FRLVQ) and FRLVQ as the pre-process of Fuzzy Vector Quantization (FRLVQ-FVQ) consistently with shorter computation time and faster convergence rate. The final codevectors are scattered reasonably and the dependence of the final optimum codebook on the selection of the initial codebook is reduced effectively. 1. Introduction Vector Quantization (VQ) is a lossy data compression technique in block coding. The generation of codebook is known as the most important process of VQ. LBG was proposed by Linde, Buzo and Gray[1] in 1980 as a well-known method of VQ. Fuzzy k-means (FKM)[2], as the most famous one among various emerging algorithms based on LBG, is prominent for it reduces the probability of becoming trapped in a local minimum. Karayiannis[3] This work was partially supported by the National Natural Science Foundation of China under grant no. 60572100, Royal Society (U.K.) International Joint Projects 2006/R3 - Cost Share with NSFC, Foundation of State Key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications, CHINA) and Science Foundation of Shenzhen City under grant no. 200408. proposed a fuzzy vector quantization algorithm (FVQ), however, the algorithm is unable to ensure improvement in terms of the quality of codebook design, compared with FKM. In 2003, Xu et al.[4] proposed Fuzzy Reinforcement Learning Vector Quantization (FRLVQ), by which the quality of codebook design is improved in comparison with that of FKM. However, it suffers from a longer computation time. In order to reduce the computation load, Xu et al.[5] introduced a strategy which applies FRLVQ as the pre-process of FVQ (FRLVQ-FVQ). Particle swarm optimization (PSO) was proposed by Eberhart and Kennedy[6][7] in 1995, to emulate the swarm behaviors by which the swarm search for food in a collaborative manner. In this paper, a new optimizer based on conventional particle swarm optimization and LBG (PSO-LBG) for vector quantization is proposed. Experimental results have demonstrated that the PSO-LBG performed better than well-known FKM, FRLVQ and FRLVQ-FVQ algorithms consistently. 2. Vector quantization Let X be M L-dimensional training vectors, 1 2 X { }, , , , , , i M x x x x = … … , L i x ∈ℜ 1, 2, , i M ∀= " , where L ℜ is L-dimensional Euclidean space. A codebook Y comprises N L-dimensional codevectors, i.e. 1 2 Y { }, , , , , , j N y y y y = … … , L j y ∈ℜ 1, 2, , j N ∀= " . VQ assigns each training vector to a related codevector, and the codevector will replaces the associated training vectors finally to obtain the aim of compression. The quality of codebook design is evaluated by Mean Square Error, represented by D  : [ ] 2 min 1 1 ( ) M i i D M d x = = ∑  (1) where min Y min ( ) ( , ) j i i j y d x dx y ∈ = with Euclidean distance: