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Combining rich spectral and spatial information, a hyperspectral image (HSI) can provide a more comprehensive characterization of the Earth’s surface. To better exploit HSIs, a large number of algorithms have been developed during the past few decades. Due to their very high correlation between spectral channels and spatial pixels, HSIs have intrinsically sparse and low-rank structures. The sparse representation (SR) and low-rank representation (LRR)-based methods have proven to be powerful tools for HSI processing and are widely used in different HS fields. In this article, we present a survey of low-rank and sparse-based HSI processing methods in the fields of denoising, superresolution, dimension reduction, unmixing, classification, and anomaly detection. The purpose is to provide guidelines and inspiration to practitioners for promoting the development of HSI processing. For a listing of the key terms …