Remote sensing image restoration aims to reconstruct missing or corrupted areas within images. To date, low-rank based models have garnered significant interest in this field. This paper proposes a novel low-rank regularization term, named the Haar nuclear norm (HNN), for efficient and effective remote sensing image restoration. It leverages the low-rank properties of wavelet coefficients derived from the 2-D frontal slice-wise Haar discrete wavelet transform, effectively modeling the low-rank prior for separated coarse-grained structure and fine-grained textures in the image. Experimental evaluations conducted on hyperspectral image inpainting, multi-temporal image cloud removal, and hyperspectral image denoising have revealed the HNN's potential. Typically, HNN achieves a performance improvement of 1-4 dB and a speedup of 10-28x compared to some state-of-the-art methods (e.g., tensor correlated total variation, and fully-connected tensor network) for inpainting tasks.

翻译：遥感影像修复旨在重建图像中缺失或损坏的区域。迄今为止，基于低秩的模型在该领域引起了广泛关注。本文提出了一种新颖的低秩正则化项，称为Haar核范数（HNN），用于高效且有效的遥感影像修复。该方法利用二维正面切片Haar离散小波变换所得小波系数的低秩特性，有效建模了图像中分离的粗粒度结构和细粒度纹理的低秩先验。在高光谱图像修复、多时相图像云去除和高光谱图像去噪上进行的实验评估揭示了HNN的潜力。通常，在修复任务中，与一些最先进的方法（例如，张量相关全变分和全连接张量网络）相比，HNN实现了1-4 dB的性能提升和10-28倍的加速。