Joint spatial and spectral low-rank regularization for hyperspectral image denoising

Hyperspectral image (HSI) noise reduction is an active research topic in HSI processing due to its significance in improving the performance for object detection and classification. In this paper, we propose a joint spectral and spatial low-rank (LR) regularized method for HSI denoising, based on the assumption that the free-noise component in an observed signal can exist in latent low-dimensional structure while the noise component does not have this property. The proposed HSI denoising method not only considers the traditional LR property across the spectral domain but also leverages nonlocal LR property over the spatial domain. The main contribution of this paper is the incorporation of the low-rankness-based nonlocal similarity into sparse representation to characterize the spatial structure. Specially, the similar patches in each cluster usually contain similar sharp structure such as edges and textures; LR performed on cluster entitles to achieve a lower rank than that on the global spectral correlation. To make the proposed method more tractable and robust, we develop a variable splitting-based technique to solve the optimization problem. Experiment results on both simulated and real hyperspectral data sets demonstrate that the proposed method outperforms state-of-the-art methods with significant improvements both visually and quantitatively.