###### Abstract  
Tunnel lining defects are one of the most common problems that tunnels experience during operation, and they can pose severe safety risks. The most popular nondestructive testing method for detecting tunnel lining defects is ground penetrating radar (GPR), one of the basic geophysical applications. However, detection responses might differ significantly from the real shape of tunnel lining defects, making it challenging to identify and interpret. When data quality is poor, interpretation and identification become more challenging, resulting in a high cost of tunnel repairs. The improved back projection (BP) imaging and robust principal component analysis (RPCA) are used in this work to offer a GPR data processing method. Even in the event of poor data quality, our method could recover GPR responses, allowing the shapes and locations of tunnel lining flaws to be clearly depicted. With BP imaging, this approach recovers the tunnel defects' responses to better forms and positions, and with RPCA, it further isolates the target imaging from clutters. Several synthetic data demonstrate that the approach presented in this work may successfully repair and extract the positions and forms of lining defects, making them easier to identify and comprehend. Furthermore, our technique was used to GPR data gathered from the Qiyue Mountain Tunnel in China, yielding more accurate findings than the traditional method, which was validated by the actual scenario to illustrate the efficiency of our method on real data. t 11 2021 4 October 2021 1 10.224 4 October 2021 1 10.224 4 October 2021 1 10.  
imaging of the detected targets [11; 12; 13; 14]. [PERSON] et al. proposed a novel BP algorithm for GPR, which is both fast and with good effect of suppressing artifacts [11]. [PERSON] et al. made a satisfactory GPR imaging of water leaks from buried pipes based on BP method [12]. [PERSON] and [PERSON] proposed a fast BP algorithm for stepped frequency continuous wave GPR imaging [13]. [PERSON] et al. used an improved back-projection algorithm to simulate and image common tunnel lining defects using GPR and made a good effect [14]. The GPR responses of tunnel lining defects can be restored by BP method. However, BP could induce artifacts in the imaging process [15]. Therefore, there is a need to develop a method that could extract the parts related to defects in the imaging results. Robust principal component analysis (RPCA) is an optimization method that divides complex matrices into low-rank and sparse matrices, with wide applications in various fields such as computer visual and image processing [15]. Low-rank matrices generally contain little information, and they are indicative of regular structures. A sparse matrix, on the other hand, only contains a few non-zero elements, and they are indicative of prominent points or structures. Some scholars think that in GPR detection, ground reflection, antenna coupling, system ringing and other structural noises take on characteristics of low rank, while the reflected wave of the detected target presents sparse characteristics. Therefore, RPCA can be utilized to extract target responses from the detected data [16; 17; 18]. However, the GPR detection responses often have many hyperbolic reflections, which are insufficiently sparse and will reduce the effectiveness of RPCA to a certain extent. [PERSON] et al. proposed to first carry out a migration processing of the GPR detection data to improve the sparsity of the target responses, and then apply RPCA to extract the detection targets, achieving satisfactory results [19]. To extract the effective information from GPR detection results of tunnel lining defects and make it easier to be identified and explained, this paper refers to [PERSON] et al. and combines the BP algorithm and the RPCA algorithm to process GPR detection results. The BP method could first restore the responses of tunnel lining defects and the RPCA method could extract the imaging of lining defects from the complex imaging result.