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Sparse unmixing (SU) is a semisupervised learning problem, which performs abundance estimation when a spectral library is given. In this way, the essence of SU is to select the most suitable subset from the spectral library for representing all mixed pixels. Many SU methods adopt joint-sparse and low-rank constraints to guide the abundance estimation. However, the spatial correlation learning in these algorithms is not accurate enough, which seriously affects the unmixing performance. Besides, most pruning-based unmixing methods suffer from complicated pruning strategies and ignore the relationship between the spectral library and mixed pixels. This article proposes a reweighted low-rank and joint-sparse unmixing approach, which combines an effective pruning strategy (RLSU-LP). The RLSU-LP approach consists of rough unmixing stage, library pruning, and fine-tuning unmixing stage. First, the proposed method utilizes image segmentation to obtain different homogeneous regions, i.e., superpixels. A confidence index is introduced to describe the superpixel homogeneity, which is conducive to learning the meticulous spatial correlation. The RLSU-LP method reasonably relaxes or tightens the sparse and low-rank constraints of the abundance matrix by using the confidence index. Furthermore, a supervised library pruning strategy is proposed, which aims to eliminate the inactive endmembers by considering the contribution of representing mixed pixels. Experiments on the synthesized dataset and authentic hyperspectral images verify the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]