This paper introduces two very fast and competitive hyperspectral image (HSI) restoration algorithms: Fast Hyperspectral Denoising (FastHyDe), a denoising algorithm able to cope with Gaussian and Poissonian noise, and Fast Hyperspectral Inpainting (FastHyIn), an inpainting algorithm to restore HSIs where some observations from known pixels in some known bands are missing. FastHyDe and FastHyIn fully exploit extremely compact and sparse HSI representations linked with their low-rank and self-similarity characteristics. In a series of experiments with simulated and real data, the newly introduced FastHyDe and FastHyIn compete with state-of-the-art methods, with much lower computational complexity. A MATLAB demo of this work is available at www.lx.it.pt/ ∼ bioucas/code/Demo FastHyDe FastHyIn.rar for the sake of reproducibility.

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