Our research focuses on reducing complexity of hyperspectral image codecs based on transform and/or subband coding, so they can be on-board a satellite. It is well-known that the Karhunen-Loève Transform (KLT) can be sub-optimal in transform coding for non Gaussian data. However, it is generally recommended as the best calculable linear coding transform in practice. Now, the concept and the computation of optimal coding transforms (OCT), under low restrictive hypotheses at high bit-rates, were carried out and adapted to a compression scheme compatible with both the JPEG2000 Part2 standard and the CCSDS recommendations for on-board satellite image compression, leading to the concept and computation of Optimal Spectral Transforms (OST). These linear transforms are optimal for reducing spectral redundancies of multi- or hyper-spectral images, when the spatial redundancies are reduced with a fixed 2-D Discrete Wavelet Transform (DWT). The problem of OST is their heavy computational cost. In this paper we present the performances in coding of a quasi optimal spectral transform, called exogenous OrthOST, obtained by learning an orthogonal OST on a sample of superspectral images from the spectrometer MERIS. The performances are presented in terms of bit-rate versus distortion for four various distortions and compared to the ones of the KLT. We observe good performances of the exogenous OrthOST, as it was the case on Hyperion hyper-spectral images in previous works.