A Continuous Low-Rank Tensor Approach for Removing Clouds from Optical Remote Sensing Images

Optical remote sensing images are often partially obscured by clouds due to the inability of visible light to penetrate cloud cover, which significantly limits their subsequent applications. Most existing cloud removal methods formulate the problem using low-rank and sparse priors within a discrete representation framework. However, these approaches typically rely on manually designed regularization terms, which fail to accurately capture the complex geostructural patterns in remote sensing imagery. In response to this issue, we develop a continuous blind cloud removal model. Specifically, the cloud-free component is represented using a continuous tensor function that integrates implicit neural representations with low-rank tensor decomposition. This representation enables the model to capture both global correlations and local smoothness. Furthermore, a band-wise sparsity constraint is employed to represent the cloud component. To preserve the information in regions not covered by clouds during reconstruction, a box constraint is incorporated. In this constraint, cloud detection is performed using an adaptive thresholding strategy, and a morphological erosion function is employed to ensure accurate detection of cloud boundaries. To efficiently handle the developed model, we formulate an alternating minimization algorithm that decouples the optimization into three interpretable subproblems: cloud-free reconstruction, cloud component estimation, and cloud detection. Our extensive evaluations on both synthetic and real-world data reveal that the proposed method performs competitively against state-of-the-art cloud removal methods.