Markov system for image vector quantization coding

Vector quantization (VQ) has been accepted as one of the most effective image compression methods with provable rate-distortion optimality. The outputs of VQ are a collection of indices, which correspond to the addresses of the codevectors in the codebook. The indices are, however, not mutually independent. They are in fact very highly correlated and are thus appropriately described by a Markov system. In this paper, a Markov system for VQ indices is introduced. Statistics are gathered for various scans, such as the zig-zag, Peano, row-major and column-major scans. The proposed method, like address VQ, achieves the same image quality as conventional VQ. Simulation results show that the proposed method achieves a better bit-rate reduction than Address-VQ. Besides, both the computational complexity and memory needed for the proposed method are lower. Nevertheless, the only extra operation needed by the proposed method is a simple table retrieval operation on both the encoder side and the decoder side. We believe that it is a method worth further exploration.