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Laser ultrasonic technology can provide a non-contact, reliable and efficient inspection of train rails. However, the laser-generated signals measured at the railhead are usually contaminated with a high level of noise and unwanted wave components that complicate the identification of defect echoes in the signal. This study explores the possibility of combining laser ultrasonic technology (LUT) and an enhanced matching pursuit (MP) to achieve a fully non-contact inspection of the rail track. A completely non-contact laser-based inspection system was used to generate and sense Rayleigh waves to detect artificial surface horizontal, surface edge, subsurface horizontal and subsurface vertical defects created at railheads of different dimensions. MP was enhanced by developing two novel dictionaries, which include a finite element method (FEM) simulation dictionary and an experimental dictionary. The enhanced MP was used to analyze the experimentally obtained laser-generated Rayleigh wave signals. The results show that the enhanced MP is highly effective in detecting defects by suppressing noise, and, further, it could also overcome the deficiency in the low repeatability of the laser-generated signals. The comparative analysis of MP with both the FEM simulation and experimental dictionaries shows that the enhanced MP with the FEM simulation dictionary is highly efficient in both noise removal and defect detection from the experimental signals captured by a laser-generated ultrasonic inspection system. The major novelty contributed by this research work is the enhanced MP method with the developments of, first, an FEM simulation dictionary and, second, an experimental dictionary that is especially suited for Rayleigh wave signals. Third, the enhanced MP dictionaries are created to process the Rayleigh wave signals generated by laser excitation and received using a 3D laser scanner. Fourth, we introduce a pioneer application of such laser-generated Rayleigh waves for inspecting surface and subsurface detects occurring in train rails.