**Abstract:**
In this paper, a sparse representation of noise reduction method for hyper spectral imagery is developed, which is dependent on the assumption that the non-noise component in an observed signal can be sparsely decomposed over a redundant dictionary while the noise component does not have this property. Non locality means the self-similarity of image, by which a whole image can be partitioned into some groups containing similar patches. The similar patches in each group are sparsely represented with a shared subset of atoms in a dictionary making true signal and noise more easily separated.Sparse representation with spectral-spatial structure can exploit spectral and spatial joint correlations of hyper spectral imagery by using 3-D blocks instead of 2-D patches for sparse coding, which also makes true signal and noise more distinguished. Moreover, hyper spectral imagery has both signal independent and signal-dependent noises, so a mixed Poisson and Gaussian noise model is used. In order to make sparse representation be insensitive to the various noise distributions in different blocks, a variance-stabilizing transformation (VST) is used to make their variance comparable.

**Keywords:**
Variance-fitting transformation (VFT), noise reduction, nonlocal similarity, sparse representation, variance-stabilizing transformation.