## 1 Introduction  
Pipeline transportation is one of the most economical and effective means to transport oil and gas to different regions [1]. However, the ferromagnetic pipeline is extremely vulnerable to damage due to internal and external defects, third-party damage, and manufacturing defects when it is buried underground, resulting in oil and gas leakage. To prevent the danger of oil and gas leakage caused by pipeline damage, we need to check the pipeline regularly to ensure the safety and health of the pipeline. The routine method of long-distance pipelines inspection is the In-Line Inspection (ILI) [2], such as Ultrasonic Testing [3] and Magnetic Flux Leakage testing [4; 5]. However, most of the small diameter pipes and urban underground pipelines have characteristics that restrict the piping, therefore non-contact detection of pipeline defects is an urgent problem to be solved. The use of non-contact approaches for inspection and damage detection is of great relevance. Not only this is indispensable for buried pipelines and other structural elements otherwise impossible to approach physically, but it also allows performing Structural Health Monitoring (SHM) without altering the structural element under investigation. This is, for instance, the case with video-based SHM and computer vision [6; 7]. While not directly applicable to buried pipelines, this is doable for external pipelined such as e.g., in industrial complexes and on offshore platforms. Some external detection techniques currently available include Eddy Current [8; 9], Guided Wave Testing [10], the Transient Electromagnetic Method [11], and Radiography Testing [12]. The mentioned detection methods are external electromagnetic excitation detection methods, which increase the difficulty of on-site detection. The Metal Magnetic Memory method [13], which is also known as the Magneto-Mechanical Memory method [14], has been only employed to close-range ferromagnetic pipeline defect detection by measuring the residual magnetic field [15] above a pipeline without external excitation sources. The essence of the residual magnetic field is an external manifestation of stress concentration which leads to an amplification of magnetic field change; however, the magnetization effect induced by stress induction cannot establish a corresponding exact formula between the stress and the residual magnetic field [16]. Magnetic anomaly detection (MAD) can detect and locate ferromagnetic targets, and is a non-contact passive magnetic detection technique [17]. Thus, defects of buried pipelines can be detected using the MAD method [18], where the ILI and electromagnetic excitation detection is difficult to implement. Because MAD is simple, efficient and does not need incentive source, it has become a research hotspot in pipeline inspection industry. For the detection of buried pipeline using MAD, the magnetic anomaly signal caused by pipeline defects, however, is affected by various factors such as interference of surrounding magnetic object, signal towers, high-voltage lines, and high lift-off distance form pipeline [19]. High lift-off distance is a challenge for buried pipeline defect characterization recognition. Several techniques were proposed to study the qualitative and quantitative of pipeline defects [20]. In qualitative research, the qualitative image of defect is obtained by using reflectivity information. In general, the technique uses an offset-based algorithm to reconstruct defect images in time domain or frequency domain, such as the microwave imaging method [21] and microwave synthetic aperture radar imaging method [19]. Quantitative analysis usually uses nonlinear inversion method to obtain the size, shape, and position of the detected object. Continuous iteration is used to linearize the nonlinear inverse problem with different approximation methods, such as sparse regularization [22], the Gauss-Newton method [23], and distorted Born iteration [24].