We propose a new regularization technique, named Hybrid Spatio-Spectral Total Variation (HSSTV), for hyperspectral (HS) image denoising and compressed sensing. Regularization techniques based on total variation (TV) focus on local differences of an HS image to model its underlying smoothness and have been recognized as a popular approach to HS image restoration. However, existing TVs do not fully exploit underlying spectral correlation in their designs and or require a high computational cost in optimization. Our HSSTV is designed to simultaneously evaluates two types of local differences: direct local spatial differences and local spatio-spectral differences in a unified manner with a balancing weight. This design resolves the said drawbacks of existing TVs. Then, we formulate HS image restoration as a constrained convex optimization problem involving HSSTV and develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) for solving it. In the experiments, we illustrate the advantages of HSSTV over several state-of-the-art methods.
He proposed ASSTV @cite_58 for HS image denoising. ASSTV simultaneously evaluates direct spatial and spectral differences, which is defined by where @math , @math , and @math are vertical, horizontal, and spectral differences for the @math th pixel of an HS image, respectively, and @math , @math and @math are balancing parameters for each difference (Fig. , blue lines). Although the parameters play a very important role, their suitable values are changed for each HS image and noise intensity. Therefore, their settings are very difficult.
@cite_58
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Hyperspectral images (HSIs) are usually contaminated by various kinds of noise, such as stripes, deadlines, impulse noise, Gaussian noise, and so on, which significantly limits their subsequent application. In this paper, we model the stripes, deadlines, and impulse noise as sparse noise, and propose a unified mixed Gaussian noise and sparse noise removal framework named spatial–spectral total variation regularized local low-rank matrix recovery (LLRSSTV). The HSI is first divided into local overlapping patches, and rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise. Differing from the previous low-rank-based HSI denoising approaches, which process all the patches individually, a global spatial–spectral total variation regularized image reconstruction strategy is utilized to ensure the global spatial–spectral smoothness of the reconstructed image from the low-rank patches. In return, the globally reconstructed HSI further promotes the separation of the local low-rank components from the sparse noise. An augmented Lagrange multiplier method is adopted to solve the proposed LLRSSTV model, which simultaneously explores both the local low-rank property and the global spatial–spectral smoothness of the HSI. Both simulated and real HSI experiments were conducted to illustrate the advantage of the proposed method in HSI denoising, from visual quantitative evaluations and time cost.