Hyperspectral Image Denoising Using Spectral-Spatial Transform-Based Sparse and Low-Rank Representations

This article proposes a denoising method based on sparse spectral–spatial and low-rank representations (SSSLRR) using the 3-D orthogonal transform (3-DOT). SSSLRR can be effectively used to remove the Gaussian and mixed noise. SSSLRR uses 3-DOT to decompose noisy HSI to sparse transform coefficients. The 3-D discrete orthogonal wavelet transform (3-D DWT) is a representative 3-DOT suitable for denoising since it concentrates on the signal in few transform coefficients, and the 3-D discrete orthogonal cosine transform (3-D DCT) is another example. An SSSLRR using 3-D DWT will be called SSSLRR-DWT. SSSLRR-DWT is an iterative algorithm based on the alternating direction method of multipliers (ADMM) that uses sparse and nuclear norm penalties. We use an ablation study to show the effectiveness of the penalties we employ in the method. Both simulated and real hyperspectral datasets demonstrate that SSSLRR outperforms other comparative methods in quantitative and visual assessments to remove the Gaussian and mixed noise.