A survey on hyperspectral image restoration: from the view of low-rank tensor approximation

The ability to capture fine spectral discriminative information enables hyperspectral images (HSIs) to observe, detect and identify objects with subtle spectral discrepancy. However, the captured HSIs may not represent the true distribution of ground objects and the received reflectance at imaging instruments may be degraded, owing to environmental disturbances, atmospheric effects, and sensors' hardware limitations. These degradations include but are not limited to complex noise, heavy stripes, deadlines, cloud/shadow occlusion, blurring and spatial-resolution degradation, etc. These degradations dramatically reduce the quality and usefulness of HSIs. Low-rank tensor approximation (LRTA) is such an emerging technique, having gained much attention in the HSI restoration community, with an ever-growing theoretical foundation and pivotal technological innovation. Compared to low-rank matrix approximation (LRMA), LRTA characterizes more complex intrinsic structures of high-order data and owns more efficient learning abilities, being established to address convex and non-convex inverse optimization problems induced by HSI restoration. This survey mainly attempts to present a sophisticated, cutting-edge, and comprehensive technical survey of LRTA toward HSI restoration, specifically focusing on the following six topics: denoising, fusion, destriping, inpainting, deblurring, and super-resolution. For each topic, state-of-the-art restoration methods are introduced, with quantitative and visual performance assessments. Open issues and challenges are also presented, including model formulation, algorithm design, prior exploration, and application concerning the interpretation requirements.