Hyperspectral Imagery Restoration Using Nonlocal Spectral-Spatial Structured Sparse Representation With Noise Estimation

Noise reduction is an active research area in image processing due to its importance in improving the quality of image for object detection and classification. In this paper, we develop a sparse representation based noise reduction method for hyperspectral imagery, 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. The main contribution of the paper is in the introduction of nonlocal similarity and spectral-spatial structure of hyperspectral imagery into sparse representation. 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 hyperspectral imagery by using 3-D blocks instead of 2-D patches for sparse coding, which also makes true signal and noise more distinguished. Moreover, hyperspectral 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 distribution in different blocks, a variance-stabilizing transformation (VST) is used to make their variance comparable. The advantages of the proposed methods are validated on both synthetic and real hyperspectral remote sensing data sets.