Abstract: The existing low light image enhancement methods are mostly caculated based on integer order differentiation, which can lead to the loss of textural details. Moreover, most low light images have potential noise, which is amplified during the enhancement process of low light images. To solve the problem of noise amplification during low light image enhancement, the reflection layer of the image is researched, and a low rank regularization term is proposed to suppress heavy noise in low light images. In addition, adding fractional order gradient to the Retinex decomposition process enables the preservation of texture details in the image while enhancing low light images. The experimental results show that the feature similarity index measure (FSIM) of the proposed model has been improved by 2%, the autoregressive based image sharpness metric (ARISMC1) that only evaluates brightness and the autoregressive based image sharpness metric (ARISMC2) that simultaneously evaluates brightness and color have both been improved by 20%. Compared with several classic low light image enhancement methods, the proposed method shows better performance in both qualitative evaluation and quantitative metrics.