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：遥感图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图像修复。该方法利用从二维正面切片Haar离散小波变换导出的小波系数的低秩特性，有效地对图像中分离的粗粒度结构和细粒度纹理的低秩先验进行建模。在高光谱图像修复、多时相图像去云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，对于修复任务，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。