Hyperspectral Image Denoising via Nonlocal Spectral Sparse Subspace Representation

Hyperspectral image (HSI) denoising based on nonlocal subspace representation has attracted a lot of attention recently. However, most of the existing works mainly focus on refining the representation coefficient images (RCIs) using certain nonlocal denoiser but ignore the understanding why these pseudoimages have a similar spatial structure as the original HSI. In this work, we revisit such vein from the respective of principal component analysis (PCA). Inspired by an alternative sparse PCA, we propose a spectral sparse subspace representation strategy to simultaneously learn low-dimensional spectral subspace and novel RCIs with sparse loadings. It turns out that the resulting RCIs possess a more significant spatial structure due to the adaptive sparse combination of spectral bands. A simple nonlocal low-rank approximation is then employed to further remove the residual noise of the RCIs. Finally, the entire denoised HSI is obtained by inverse spectral sparse PCA. Extensive experiments on the simulated and real HSI datasets show that the proposed nonlocal spectral sparse subspace representation method, dubbed as NS3R , has excellent performance both in denoising effect and running time compared with many other state-of-the-art methods.