Haar Nuclear Norms with Applications to Remote Sensing Imagery Restoration

TL;DR

This paper introduces the Haar nuclear norm (HNN), a new low-rank regularization method leveraging wavelet coefficients for improved remote sensing image restoration, demonstrating significant performance gains and speed improvements over existing methods.

Contribution

It proposes the Haar nuclear norm (HNN), a novel low-rank regularization technique based on Haar wavelet transform for remote sensing image restoration.

Findings

HNN improves restoration performance by 1-4 dB.

HNN achieves 10-28x faster processing.

HNN outperforms state-of-the-art methods in experiments.

Abstract

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.