A Comparative Study of LBG and SOA Codebooks Concerning the Computational Complexity of the Minimum Distortion Encoding for VQ

Signal compression is essential for applications which require the minimization of the storage and/or transmission requirements, such as multimedia communications, integrated services digital networks (ISDN), web browsing, voice response systems, cellular telephony, storage of medical images, archiving of fingerprints, and transmission of remote sensing images obtained from satellites. Vector quantization (VQ), which may be seen as an extension of scalar quantization to a multidimensional space, is a well-known compression technique which has been widely used in many speech and image coding systems. It consists on a mapping Q from an input vector ~x in k-dimensional Euclidean space, R, into a finite subset W of R. Thus, Q : R ! W , where the codebook W = f~ wi; i = 1; 2; : : : ; Ng is the set of reproduction vectors (codevectors, reconstruction vectors, prototype vectors), k is the dimension of the vector quantizer and N is the codebook size. The corresponding code rate, which measures the number of bits per vector component, is R = 1 k log 2 N . Codebook design plays a fundamental role in the performance of signal compression systems based on VQ [2]. Techniques for codebook design attempt to produce a codebook that is optimum for a given source in the sense that the average distortion in representing the source vectors by the corresponding VQ codevectors may be kept to a minimum. To date, the most widely used technique for VQ codebook design is the LBG (Linde-Buzo-Gray) algorithm [3], also known as GLA (generalized Lloyd algorithm). In a recent paper [4], it was shown that an unsupervised neural network algorithm, referred to as SOA (selforganizing algorithm), provides good VQ codebooks, leading to reconstructed signals with better quality (for a variety of compression rates) when compared to the ones obtained by using LBG codebooks. A serious problem of VQ is the computational complexity of the encoding process. In fact, the minimum distortion encoding (MDE) of a given source vector, using the squared-error distortion measure for performing the nearest neighbor search, requires N = 2 multiplications by sample. In this paper, an investigation is carried out to evaluate the “inherent” quality of SOA and LBG codebooks regarding the computational complexity of MDE. By using two well-known algorithms (introduced in [1] and [5]) for improving the efficiency of MDE, the present work shows that the SOA codebooks overperforms the LBG codebooks in the sense that they yield a smaller average number of multiplications per sample for image VQ.