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This paper proposes a new vector quantization based (VQ-based) technique for very low bit rate encoding of multispectral images. We rely on the assumption that the shape of a generic spatial block does not change significantly from band to band, as is the case for high spectral-resolution imagery. In such a hypothesis, it is possible to accurately quantize a three-dimensional (3-D) block-composed of homologous two-dimensional (2-D) blocks drawn from several bands-as the Kronecker-product of a spatial-shape codevector and a spectral-gain codevector, with significant computation saving with respect to straight VQ. An even higher complexity reduction is obtained by representing each 3-D block in its minimum-square-error Kronecker-product form and by quantizing the component shape and gain vectors. For the block sizes considered, this encoding strategy is over 100 times more computationally efficient than unconstrained VQ, and over ten times more computationally efficient than direct gain-shape VQ. The proposed technique is obviously suboptimal with respect to VQ, but the huge complexity reduction allows one to use much larger blocks than usual and to better exploit both the statistical and psychovisual redundancy of the image. Numerical experiments show fully satisfactory results whenever the shape-invariance hypothesis turns out to be accurate enough, as in the case of hyperspectral images. In particular, for a given level of complexity and image quality, the compression ratio is up to five times larger than that provided by ordinary VQ, and also larger than that provided by other techniques specifically designed for multispectral image coding