Transductive gradient injection for improved hyperspectral image denoising

In real-world hyperspectral imaging, noise disproportionately affects specific spectral bands. However, existing denoising techniques struggle to discern the varied contributions of different signal-to-noise ratios across spectral bands, leading to suboptimal performance. To fill this gap, we propose a transductive gradient learning framework that utilizes high signal-to-noise ratio bands to guide the inference of gradient patterns in low signalto-noise ratio bands, substantially enhancing denoising effectiveness. Unlike existing approaches that only recover global low-rank structures, our framework introduces a transductive gradient injection regularization term to capture both global low-rank and local sparse gradient patterns. This term combines a low-rank matrix for global patterns and a sparse matrix for local patterns, leveraging pre-learned feature matrices from high signal-to-noise ratio band gradients to accurately inject spatial gradient textures, avoid excessive singular value constraints, and achieve efficient noise separation. Additionally, we have developed an efficient alternating direction method of multipliers algorithm for optimization. Extensive synthetic and real experiments on hyperspectral image datasets, along with applications in remote sensing, highlight significant performance gains. Across all datasets and noise conditions, our method achieves an average improvement of nearly 33% in overall peak signal-to-noise ratio and a 23% increase in spectral angle mapper compared to state-of-the-art hyperspectral image denoising methods.