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Under uneven lighting conditions, power inspection (PI) images captured by drones exhibit low contrast, lost details and severe noise, which affects the efficiency of monitoring. In response to these issues, this paper proposes a new method for enhancing PI images based on discrete fractional wavelet transform (DFRWT). Firstly, according to the image entropy feature, an appropriate fractional order of DFRWT is selected to decompose the PI image. Secondly, we introduce a low-frequency fusion enhancement method based on complex number domain. It employs different mapping functions to enhance the brightness and contrast of PI image, then the results are combined to reconstruct a new low-frequency component. Here, an improved quantum-behaved particle swarm optimization (QPSO) algorithm is proposed to determine the optimal parameters of the functions, preventing over-enhancement. Finally, an adaptive threshold function is applied to handle noise and edge coefficients in high-frequency components. Using 5 quality metrics to evaluate 8 existing algorithms on 9 datasets, the results indicate that the proposed algorithm can effectively enhance the clarity of PI images, performing excellently in noise suppression and edge detail enhancement. [ABSTRACT FROM AUTHOR]