Denoising and Destriping Hyperspectral Images Using Double Graph Laplacian Regularizers

Abstract

This article proposes a novel hyperspectral image (HSI) denoising and destriping method based on graph signal processing that fully exploits the HSI properties. Double graph Laplacian regularizers (DGLR) are established to illustrate the spectral and spatial connections of an HSI. An HSI is of low-rank property, and its spectral differences exhibit a lower rank than the HSI itself. To characterize this property, we construct our first graph by using the difference between every two adjacent bands as the graph nodes. In addition, to preserve the spatial connection of the HSIs and avoid oversmoothing, the second graph takes the full-band HSI blocks as graph nodes. We use the Euclidean distance between nodes and the $\ell _{2}$ norm between graph signals to compute the edge weights of these two graphs. Besides, we also consider removing the sparse/impulse noise and stripe noise by using an $\ell _{1}$ norm and a nuclear norm as constraints. An augmented Lagrange multiplier method is developed to solve the proposed optimization problem. To testify the competitive performance of our method, we conduct numerous experiments on both simulated noisy HSIs and real noisy HSIs. The quantitative evaluation indices and visual performance show that DGLR surpasses many mainstream denoising methods within less or comparable time.

Keywords

• Denoising
• destriping
• graph Laplacian regularizer (GLR)
• graph signal processing (GSP)
• hyperspectral image (HSI)