In previous works, we defined the Optimal Transform Code (OTC) assuming high rate coding and using the asymptotical Bennett approximation of the rate. We showed that the OTC gives the optimal linear transform of a multicomponent image compression scheme which consists in applying a linear transform that adapts to the encoded image for reducing the spectral redundancy and a fixed 2-D Discrete Wavelet Transform (DWT) per component for reducing the spatial redundancy. The performances in terms of rate vs PSNR (Peak of Signal to Noise Ratio) are very attractive when evaluated with the Verification Model version 9 of the JPEG2000 committee which is a JPEG2000 codec (coding-decoding). The transform in OTC performs better than the Karhunen Loeve Transform (KLT). The drawback of the OTC is its high computing complexity, since the optimal linear transform must be computed for each encoded image. In order to implement the OTC in an on- board satellite real-time codec system, we propose to pass round the problem of computing complexity by learning only one fixed transform with the OTC algorithms from a set of images instead of computing a new transform for each image. We call the fixed transform computed in this way an exogenous quasi-optimal linear transform. In this paper, we focus the study on hyperspectral images. Our set of images is constituted of ten Hyperion3 hyperspectral images. We have separated the VNIR and the SWIR bands (since they are obtained with two different sensors on- board) and we just focus on the VNIR spectral bands.