  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.
