Multispectral Image Compression for Improvement of Colorimetric and Spectral Reproducibility by Nonlinear Spectral Transform Shanshan YU 1  , Yuri MURAKAMI 1;2 , Takashi OBI 3 , Masahiro YAMAGUCHI 1;2 and Nagaaki OHYAMA 1;2 1 Imaging Science and Engineering Lab., Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan 2 Akasaka Natural Vision Research Center, Telecommunication Advancement Organization of Japan, 1-8-6 Akasaka, Minato-ku, Tokyo 107-0052, Japan 3 Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan (Received January 6, 2006; Accepted May 30, 2006) The article proposes a multispectral image compression scheme using nonlinear spectral transform for better colorimetric and spectral reproducibility. In the method, we show the reduction of colorimetric error under a defined viewing illuminant and also that spectral accuracy can be improved simultaneously using a nonlinear spectral transform called Labplus, which takes into account the nonlinearity of human color vision. Moreover, we show that the addition of diagonal matrices to Labplus can further preserve the spectral accuracy and has a generalized effect of improving the colorimetric accuracy under other viewing illuminants than the defined one. Finally, we discuss the usage of the first- order Markov model to form the analysis vectors for the higher order channels in Labplus to reduce the computational complexity. We implement a multispectral image compression system that integrates Labplus with JPEG2000 for high colorimetric and spectral reproducibility. Experimental results for a 16-band multispectral image show the effectiveness of the proposed scheme. # 2006 The Optical Society of Japan Key words: multispectral image compression, nonlinear spectral transform, color reproduction, spectral accuracy, L  a  b  color space 1. Introduction Multispectral images have been used mostly in remote sensing, but have recently been extended to fields requiring high fidelity color reproductions such as tele-medicine, electronic commerce, etc. 1,2) These multispectral imaging systems are valued because they offer improved color reproduction quality not only for a standard observer under a particular illuminant, but for any other individual exhibiting normal color vision capability under any other illuminant. 3) In response to the huge volume of multispectral images, many compression algorithms have been developed for efficient transmission; yet most of these are in the field of remote sensing, and aim to preserve spectral accuracy and minimize the difference between the original and the reconstructed multispectral images, e.g., algorithms that use Karhunen–Loe ´ve transform (KLT) as the spectral transform, followed by two-dimensional (2D)-discrete wave- let transform as the spatial compression scheme. 4) However, in the applications that require high colorimetric accuracy, it is of vital importance to keep the difference between the original and reconstructed color images small. In response to this problem, some linear transforms have been proposed as spectral transforms for multispectral image compression, e.g., one mode analysis (OMA) 5) and weighted KLT (WKLT). 6) In these methods, the colorimetric errors have been decreased compared with conventional KLT based methods by incorporating a weighting matrix that accounts for the color matching functions of the human observer as well as the viewing illuminant. To consider the nonlinearity characteristics of the human visual system (HVS), Murakami proposed a nonlinear quantization method called adaptive quantization (AQ), which takes into account the fact that the error in the low- luminance colors is perceived larger than in the high- luminance colors. 7) By incorporating AQ, the perceived chromatic error could be equalized by allowing some error in high-luminance colors and reducing the error in low- luminance colors. Mase used a similar quantization method termed adaptive preprocessing (AP) together with WKLT and reported that the combination of linear spectral trans- form (WKLT) and the nonlinear quantization can reduce the colorimetric error in reconstructed images. 8) However, in order to implement AQ or AP, the transform coefficients of WKLT are classified into several classes according to the luminance of the corresponding pixel; and different classes of coefficients will multiply different weightings. Ideally, optimal result could be gained when the number of classes is equal to the number of pixels, while in practice, it is impractical to make too many classes, because the improvement in the performance is on the cost of additional class information and will in turn affect the compression ratio, thus improvement through the combina- tion of linear transform and nonlinear quantization is limited. In this paper, we propose a multispectral image com-  E-mail address: yss@isl.titech.ac.jp OPTICAL REVIEW Vol. 13, No. 5 (2006) 346–356 346