Hyperspectral image restoration via RPCA model based on spectral-spatial correlated total variation regularizer

Junheng Gao, Hailin Wang, Jiangjun Peng

Abstract: Highlights•We introduce a novel regularizer called Spectral–Spatial Correlated Total Variation (SSCTV) that can embed the low-rank property and joint sparsity of hyper-spectral images (HSI). Compared to nuclear norm, SSCTV can embed the joint local smoothness (i.e., the joint sparsity of gradient map ) property of HSI. Compared to spectral–spatial total variation (SSTV) regularizer, SSCTV not only embeds the global local-smoothness property but also offers a more holistic representation of low-rank property. Therefore, the newly introduced SSCTV regularizer can better embed the low-rank and local-smoothness property at one regularizer.•Robust Principal Component Analysis (RPCA) is a classical problem of separating the low-rank part and sparse part (i.e., the sparse noise or foreground) from observed noisy data. To fully utilize the low-rank and local-smoothness property of HSI, we propose the variant of RPCA model named SSCTV-RPCA model based on SSCTV regularizer, and the effectiveness of this model on HSI denoising and outlier detection is verified.•By modifying the construct process of dual certificate variables and the Karush–Kuhn–Tucker condition, we have established an exact recoverable theory for SSCTV-RPCA model. This theory ingeniously addresses the lack of recoverability guarantees when fusing SSTV with nuclear norms. What is more,the recoverability theory of the SSCTV-RPCA model extends to encompass spectral–spatial joint gradient maps, thereby compensating for the inability of the CTV-RPCA (i.e., the RPCA variant model based on CTV regularizer) model.•By using ADMM algorithm, we give a fast algorithm based on fast Fourier transform to solve the proposed SSCTV-RPCA model, and give the proof of its convergence theorem. The stability of the method is better than that of gradient descent.

External IDs:doi:10.1016/j.neucom.2024.128885