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 Loeve transform (KLT) can be sub-optimal for non Gaussian data. However, it is generally recommended as the best calculable coding transform in practice. Now, for a compression scheme compatible with both the JPEG2000 Part2 standard and the CCSDS recommendations for onboard satellite image compression, the concept and computation of optimal spectral transforms (OST), at high bit-rates, were carried out, under low restrictive hypotheses. 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. 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 hyperspectral images from the spectrometer MERIS. Moreover, we compute an integer variant of OrthOST for lossless compression. The performances are compared to the ones of the KLT in both lossy and lossless compressions. We observe good performances of the exogenous OrthOST.