REVERSIBLE AND PROGRESSIVE CODING OF’ MULTISPECTRAL SPOT IMAGES A. Benaxxa-Benyahia (l), 2. Belhadj (‘i2), J-. C. Pesquet (3), M. Humdi (‘1 (1) Dept. MASC, Ecole Suphrieure des Communications de Tunis, TUNISIA, Route de Raoued 3.5 Km, Cith El Ghazala, 2083 Ariana, TUNISIA, Tel: (+216-1) 857 000, Fax: (+216-1) 856-829 (2) LTSIRS, Ecole Nationale d’Inghnieurs de Tunis,TUNISIA, (3) LSS (CNRS/UPS), FRANCE E-mail: ben.yahia@planet.tn, ziad.belhadj@supcom.rnu.tn, pesquet@univ-mlv.fr Abstract In this paper, a nonlinear subband decomposition scheme with perfect reconstruction is proposed for lossless and progressive coding of multispectral images. Such new scheme has the merit of exploiting efficiently the spatial and the spectral redundancies contained in the multispec- tral images, related to a same scene. Besides, it is suitable for telebrowsing applications. Simulation tests performed on SPOT allow t o assess its performances. 1 INTRODUCTION Since image data is often voluminous compared to the storage/transmission capabilities, image compression has become a great challenge to the source coding commu- nity. We give attention to exact coding schemes because we are interested in image archiving applications. Indeed, archival storage of images requires exact reproductibility of the data because the original image must be always avalaible in the database. Considerable research has al- ready been performed on lossless compression of satel- lite/aerial images. For instance, the Consultative Com- mittee for Space Data Systems has adopted a standard for lossless data compression, based on extended version of Rice algorithm (previously referred as USES) [l]. Furthermore, progressive reconstruction is a desirable fea- ture for telebrowsing through images databases. By pro- gressive, we mean that the image is encoded in levels, the first level corresponds to a very highly compressed version of the source image and each successive level pro- vides more detail until ultimately the encoding is com- pletely lossless. Such gradual reconstruction requires a compact and non-redundant pyramidal representation of the input image. Multiresolution decompositions of still images based on lifting schemes have been developped re- cently [2, 3, 41. They are considered as the stateof-art in the context of lossless and progressive coding because they provide hierarchical and compact representations for the gradual coding of the images. This paper is concerned with the reversible and hierarchical coding of multispec- tral satellite images. Considered images are supplied by the SPOT satellite which observes the earth in three chan- nels: XS1 channel covering the wavelengths 0.5 t o 0.59 pm, the XS2 channel covering 0.61 to 0.78 pm and the XS3 covering 0.79 to 0.89 pm. To the best of our knowl- edge, the problem of extending such kind of representation for color images has not been yet addressed. We develop a new algorithm which exploits the mutual dependencies between spectral bands thanks to generalized nonlinear subband decompositions. This paper is organized as follows. Section 2 describes the proposed nonlinear subband decomposition which ex- ploits the spectral redundancies and we develop a method to select appropriate operators for achieving a compact hierarchical representation of the considered spectral im- ages. In section 3, we describe the related works in the field of lossless coding of multispectral images in order to better understand our contribution. Finally, in section 4, we provide some experimental results and we compare the performances of the proposed scheme to those of the state-of-& methods. 2 PROPOSED DECOMPOSI- TION SCHEME A 1D nonlinear subband decomposition structure is de- fined by the following equations: (1) dj+l (n) = ~j(2n) - LpTaj(2n + 1)1 aj+l(n) = ~j(2n + 1) + Li(dj+l(n - 1) + dj+l(n))l where 1.1 denotes the rounding operation. The decompo- sition process is initialized by setting ~(n) to the signal to be coded. We can interpret dj+l (n) as the error of pre- diction of the even samples by the odd ones with a pre- dictor p. The update step in evaluating uj+l (n) provides a smoother low-pass signal as compared to direct down- sampling uj+l (n) = uj (271). The approximation signal is 0-7803-6359-0100/$10.00 0 2000 IEEE 582