Multitemporal Thick Cloud Removal via Temporal Smoothness in Image and Gradient Domains

Most existing cloud removal methods primarily focus on reconstructing obscured regions by exploiting pixel correlations within the image domain. However, multitemporal remote sensing (RS) images exhibit temporal smoothness in the gradient domain, that is, spatial gradient similarities across adjacent time nodes. Methods that overlook this valuable information in the gradient domain often result in blurred restorations and loss of essential details. To address this limitation, we introduce an innovative blind cloud removal model that incorporates temporal smoothness in both image and gradient domains (TSIGDs), where spatial gradient similarities along the temporal dimension are captured by $\ell _{1}$ -norm. Moreover, we leverage low-rank tensor regularization to characterize the global correlation of cloud-free image components and structural sparse regularization to model the complex structures of the cloud component. The proposed model simultaneously captures relationships in both domains and results in a clearer restoration with improved detail preservation. To optimize the model, we propose an efficient algorithm based on proximal alternating minimization (PAM). Comprehensive experiments conducted on both simulated and real-world datasets show that the proposed TSIGD method achieves competitive performance, particularly in restoring texture details.