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

In the realm of hyperspectral image (HSI) restoration, numerous challenges revolve around the separation of low-rank and sparse components. Typical tasks include HSI denoising and anomaly detection. Effectively capturing the inherent priors of an HSI is pivotal for achieving pleasing outcomes, where the low-rankness among spectral dimension and the local smoothness/continuity among the spectral/spatial dimension are the most two significant ones. However, prevailing methods often struggle to accurately capture the above two priors and often lack theoretical guarantees. To tackle these challenges, we propose a novel regularizer called spectral-spatial correlated total variation (SSCTV), which can embed both low-rankness and joint local smoothness into one single regularizer. This integration enables the new regularizer to offer improved prior characterization. Furthermore, by integrating SSCTV regularizer with the Robust Principal Component Analysis (RPCA) framework, we create the new variant RPCA model named SSCTV-RPCA model. Leveraging the incoherence condition and golf scheme techniques, we establish the exact recoverable guarantee of SSCTV-RPCA model. Besides, relying on the Fast Fourier Transform (FFT), we design a computationally efficient solution method that guarantees convergence. Thorough experiments substantiate the efficacy of both the model and its theoretical foundation. The code is available at https://github.com/self-controler/SSCTV-RPCA.git.