Haar Nuclear Norms with Applications to Remote Sensing Imagery Restoration
This work addresses efficient and effective restoration of remote sensing imagery, which is incremental as it builds on low-rank models with a new regularization approach.
The paper tackled remote sensing image restoration by proposing a novel low-rank regularization term called Haar nuclear norm (HNN), which leverages wavelet coefficients to model image structure and textures, resulting in performance improvements of 1-4 dB and speedups of 10-28x compared to state-of-the-art methods in tasks like inpainting.
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.