<title>Comparison of different quantization strategies for subband coding of medical images</title>

Abstract

In this paper different methods for the quantization of wavelet transform coefficients are compared in view of medical imaging applications. The goal is to provide users with a comprehensive and application-oriented review of these techniques. The performance of four quantization methods (namely standard scalar quantization, embedded zerotree, variable dimension vector quantization and pyramid vector quantization) are compared with regard to their application in the field of medical imaging. In addition to the standard rate-distortion criterion, we took into account the possibility of bitrate control, the feasibility of real-time implementation, the genericity (for use in non-dedicated multimedia environments) of each approach. In addition, the diagnostical reliability of the decompressed images has been assessed during a viewing session and with the help of a specialist. Classical scalar quantization methods are briefly reviewed. As a result, it is shown that despite the relatively simple design of the optimum quantizers, their performance in terms of rate-distortion tradeoff are quite poor. For high quality subband coding, it is of major importance to exploit the existing zero-correlation across subbands as proposed with the embedded zerotree wavelet (EZW) algorithm. In this paper an improved EZW-algorithm is used which is termed embedded zerotree lossless (EZL) algorithm -- due to the importance of lossless compression in medical imaging applications -- having the additional possibility of producing an embedded lossless bitstream. VQ based methods take advantage of statistical properties of a block or a vector of data values, yielding good quality results of reconstructed images at the same bitrates. In this paper, we take in account two classes of VQ methods, random quantizers (VQ) and geometric quantizers (PVQ). Algorithms belonging to the first group (the most widely known being that developed by Linde-Buzo-Gray) suffer from the common drawback of requiring a computationally demanding training procedure in order to produce a codebook. The second group represents an interesting alternative, based on the multidimensional properties of the distribution of the source to code. In particular a pyramid vector quantization has been taken into account. Despite being based on the implicit geometry of independent and identically distributed (i.i.d.) Laplacian sources, this method proved to achieve good results with other distributions. Tests show that zerotree yields the most promising results in the rate- distortion sense. Moreover, this approach allows an exact rate control and has the possibility of a progressive bitstream which can be used either for data browsing or up to a lossless representation of the input image.