Fast Superpixel Based Subspace Low Rank Learning Method for Hyperspectral Denoising

Abstract-Sequential data, such as video frames and event data, have been widely applied in the realworld. As a special kind of sequential data, hyperspectral images (HSIs) can be regarded as a sequence of 2-D images in the spectral dimension, which can be effectively utilized for distinguishing different landcovers according to the spectral sequences. This paper presents a novel noise reduction method based on superpixel-based subspace low rank representation for hyperspectral imagery. First, under the framework of a linear mixture model, the original hyperspectral cube is assumed to be low rank in the spectral domain, which could be represented by decomposing HSI data into two sub-matrices of lower ranks. Meanwhile, due to the high correlation of neighboring pixels, the spectra within each neighborhood would also promote low rankness, and the local spatial low rankness could be exploited by enforcing the nuclear norm within superpixel-based regions in the decomposed subspace. The superpixels are easily and effectively generated by utilizing state-of-the-art superpixel segmentation algorithms in the first principal component of the original HSI. Moreover, benefiting from the subspace decomposition, the proposed method has an overwhelming superiority in computational cost than the state-of-the-art LR-based methods. The final model could be efficiently solved by the augmented Lagrangian method. Experimental results on simulated and real hyperspectral data sets validate that the proposed method produces superior performance than other stateof-the-art denoising methods in terms of quantitative assessment and visual quality.