Remote Sensing Image of The Landsat 8–9 Compressive Sensing via Non-Local Low-Rank Regularization with the Laplace Function

Utilizing low-rank prior data in compressed sensing (CS) schemes for Landsat 8–9 remote sensing images (RSIs) has recently received widespread attention. Nevertheless, most CS algorithms focus on the sparsity of an RSI and ignore its low-rank (LR) nature. Therefore, this paper proposes a new CS reconstruction algorithm for Landsat 8–9 remote sensing images based on a non-local optimization framework (NLOF) that is combined with non-convex Laplace functions (NCLF) used for the low-rank approximation (LAA). Since the developed algorithm is based on an approximate low-rank model of the Laplace function, it can adaptively assign different weights to different singular values. Moreover, exploiting the structural sparsity (SS) and low-rank (LR) between the image patches enables the restored image to obtain better CS reconstruction results of Landsat 8–9 RSI than the existing models. For the proposed scheme, first, a CS reconstruction model is proposed using the non-local low-rank regularization (NLLRR) and variational framework. Then, the image patch grouping and Laplace function are used as regularization/penalty terms to constrain the CS reconstruction model. Finally, to effectively solve the rank minimization problem, the alternating direction multiplier method (ADMM) is used to solve the model. Extensive numerical experimental results demonstrate that the non-local variational framework (NLVF) combined with the low-rank approximate regularization (LRAR) method of non-convex Laplace function (NCLF) can obtain better reconstruction results than the more advanced image CS reconstruction algorithms. At the same time, the model preserves the details of Landsat 8–9 RSIs and the boundaries of the transition areas.