## 1 Introduction  
Pipeline systems are omnipresent in industry, shipbuilding, construction, petroleum, and other fields for transporting oil, gas, and petrochemical products. Over time, due to the material aging, stress concentration, humid environment, and other adverse factors, defects like cracks, corrosion, and notches are likely to appear in pipelines, which may compromise their safety and economy [1; 2; 3]. Hence, it is fundamental to apply nondestructive testing (NDT) on pipes to ensure reliable operation and avoid catastrophic failure. However, conventional NDT methods may fail to detect defects in inaccessible regions, where potential risks arise as a result of the long detection time [4]. Ultrasonic guided wave (UGW) testing shows high-efficiency, non-contact, long-distance, and large-scale detection capabilities, which can be applied to check the structural integrity of buried, coated, and liquid filled pipelines [5; 6]. At the aim of reducing the interpretation complexity of UGW signals, it is popular to utilize axisymmetric UGWs (longitudinal L(0,\(m\)) and torsional T(0,\(m\))) in their non-dispersive frequency bands instead of non-axisymmetric UGWs (flexural F (\(n\),\(m\)), where \(n\) and \(m\) denote the circumferential order and mode [7]). Two inherent characteristics of dispersion and multi-mode in UGW are inevitably manifested as the UGW velocity varies with the frequency, and as multiple modes of UGWs exist at a given frequency [8; 9]. In this context, it is almost impossible to excite the pure UGW at the desired mode, whilst UGWs at undesired modes may be excited for imperfect experimental conditions and multi-mode characteristics. In addition, for the mode conversion caused by the interaction between non-axisymmetric defects and UGWs, dispersive flexural UGWs may arise, which may increase the interpretation complexity and further weaken the ability of defects detection [10; 11]. In order to enhance the defect identification and classification of UGW testing, several signal processing methods based on time-frequency analysis have been introduced, including Winger-Ville distribution [12], Hilbert-Huang transform [13], wavelet transform [14], and Chirplet transform [15]. However, the improvement of UGW signal resolution processed by the above methods is limited, and more effective signal processing methods need to be found. At present, signal processing methods aimed at improving the signal-to-noise ratio (SNR) of UGW signals are mainly through separation and elimination of dispersive UGWs; the former is typically represented by matching pursuit (MP) [9; 16], and the latter includes dispersion compensation (DC) [17; 18], pulse compression (PuC) [19; 20], and split spectrum processing (SSP) [10; 21]. MP is a sparse approximation algorithm, which is based on the construction of an appropriate over-complete and redundant dictionary and finding the best matching of UGW signals in the dictionary. Although MP can separate overlapping UGWs at different modes, the processing results are highly dependent on the quality of the constructed dictionary, which is accompanied by high computational complexity [22]. DC is another signal processing method commonly applied in UGW testing, where the dispersive UGWs can be eliminated by reversing the effect of dispersion and multi-mode on the desired UGW in the time/space domain, and it can be utilized in combination with PuC [17; 18]. [PERSON] et al. [20] applied DC and PuC to improve the SNR of UGW signals of aluminum rods. [PERSON] et al. [23] proposed a method combining PuC and velocity DC in the wave-number domain to compensate for the wave distortion caused by dispersion, and the results showed that the time resolution and SNR of UGW signals were improved. However, DC and PuC need the prior knowledge of dispersion and pipeline structure, which is usually not available in the UGW testing of long-distance pipelines and unknown pipeline structures [24].