Tensor Low-Rank Approximation via Plug-and-Play Priors for Anomaly Detection in Remote Sensing Images

Optical remote sensing images (RSIs) have received widespread attention in fields such as agricultural monitoring, mineral exploration, and military defense. However, the detection performance will be seriously degraded when interfered with by noise. To overcome this issue, we first present a novel method called tensor low-rank approximation (TLRA), which leverages the weighted tensor nuclear norm (WTNN) to exploit the spectral overall structure, introduces a new tensor sparse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{F,0}$ </tex-math></inline-formula> term to characterize the local anomalies, and embeds an auxiliary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{F}$ </tex-math></inline-formula> term to reduce the impact of Gaussian noise. Compared to existing tensor low-rank methods, the proposed TLRA has shown improvements in feature recognition performance and robustness. Moreover, by integrating pretrained neural networks instead of the WTNN, we further construct a plug-and-play (PnP) deep prior variant, dubbed PnP-TLRA, which can automatically learn nonlocal self-similarity. In addition, we have devised a consolidated optimization strategy utilizing the alternating direction method of multipliers (ADMM). The numerical experiments verify the advantages of the proposed methods over benchmark detectors and also show that PnP-TLRA has a better performance compared to TLRA with respect to effectiveness, efficiency, separability, and convergence. The code of the proposed methods will be published at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/EMXlight</uri>.