The high spectral redundancy of hyper/ultraspectral Earth-observation satellite imaging raises three challenges: (a) to design accurate noise estimation methods, (b) to denoise images with very high signal-to-noise ratio (SNR), and (c) to secure unbiased denoising. We solve (a) by a new noise estimation, (b) by a novel Bayesian algorithm exploiting spectral redundancy and spectral clustering, and (c) by accurate measurements of the interchannel correlation after denoising. We demonstrate the effectiveness of our method on two ultraspectral Earth imagers, IASI and IASI-NG, one flying and the other in project, and sketch the major resolution gain of future instruments entailed by such unbiased denoising.