Coal mining is the most important methane emission source, yet a key reason for the low accuracy of its emission inventories is the lack of capability to accurately identify and locate this type of emission source. In recent years, cutting-edge research has shown that it is possible to use satellite hyperspectral data to invert high-resolution methane anomalies and thus help to identify emission sources. However, this algorithm will fail completely inareas with complex surface types. To address this problem, the paper proposes the L1 reweighted iterative shrinkage thresholding algorithm (ISTA) matched filter algorithm for the first time. Experiments in Shanxi region using GF-5 advanced hyperspectral imager (AHSI) data show that the performance of the modified method is significantly better than that of the other existing methods. In the experiments, this method identifies 23 strong methane point sources, all of which are located in the methane high value area of TROPOMI, and the high-resolution remote sensing images also show the presence of typical coal mining facilities at these point sources. This method has laid a technical foundation for the worldwide implementation of methane point source identification using GF-5 AHSI data.