Local Low-Rank Matrix Recovery for Hyperspectral Image Denoising with ℓ0 Gradient Constraint

Abstract Hyperspectral images (HSIs) acquisition often suffers from the mixed noise, which greatly limits its subsequent applications. This paper proposes a novel HSI denoising method by using local low-rank matrix recovery and l0 gradient, which can simultaneously identify the low-rank structures of the clean HSI and the sparse components of the mixed noise. Specifically, the HSI is modeled locally and a scheme of rank-fixed low-rank matrix recovery is employed to separate the latent clean HSI patches from the noisy counterpart. Meanwhile, the l0 gradient constraint mechanism is utilized to characterize the piecewise smooth structure along both the spectral and spatial dimensions of the reconstructed image from the patches. Moreover, the l1 norm regularization is adopted to suppress the sparse noise, such as stripes, deadlines, impulse noise, and so on. Also, an efficient iterative schema is developed based on an augmented Lagrange algorithm. The corresponding closed-form solutions of the subproblems are derived for calculating an approximate result of the nonconvex optimization problem. Extensive experiments on both simulated and real HSIs prove that the l0 gradient constraint can preserve the edge details well and the proposed method can yield better performance than the state-of-the-art methods for HSI denoising.