Bonding structure is widely used in aviation, aerospace, national defense and other fields. But during service, the bond interface may appear disbonding defects or damage, seriously reducing the bearing capacity of the structure and affecting the structure safety. Terahertz nondestructive testing technology is widely used in the nondestructive test of composite materials. Terahertz time-domain spectroscopy technology can effectively realize the nondestructive test and identification of internal defects of multilayer adhesives. However, the terahertz detection signal carries a large number of invalid redundant features, noise and other invalid information. With the gradual increase of detection data, the redundant and invalid information in the data, and the workload of data processing are also increasing. A large amount of invalid information not only consumes a lot of data processing and analysis time, but also brings great interference to the subsequent signal analysis work such as defect identification. To solve this problem, a gradient threshold adaptive sparse compression algorithm is proposed based on time-domain characteristics of terahertz signals with multi-layer adhesive structures.The gradient threshold adaptive sparse model is established. Effective time-domain features of terahertz signals were extracted using the second-order gradient (Fig.3), and the time-domain features of signals were used as constraints to determine the threshold sparse time-domain signals based on the time-domain features of signals, and the terahertz signals were recovered by the multi-Gaussian fitting function (Fig.4). The compression performance of the algorithm was evaluated according to the compression ratio, relative root mean variance and correlation coefficient, and the data processing time and memory occupied space were used to characterize the compression efficiency of the algorithm.Terahertz detection signals were divided into normal signals and defective signals (Fig.5), and signal characteristic peaks were extracted (Tab.1) to determine effective feature intervals. The maximum allowable error was set as 0.05, and the threshold was determined adaptively. The sparse recovery results of terahertz signals were shown (Fig.7). The reconstruction error of the recovered signal is less than 0.006 (Fig.8). The compression rate of this algorithm reaches 81%, which is 59% higher than that of discrete cosine transform, 75% higher than that of principal component analysis, and 26% higher than that of K-singular value decomposition. The relative root-mean-square error of the algorithm is less than 2%, and the correlation coefficient is greater than 0.97 (Fig.9). Compared with the traditional signal compression algorithm, the data processing time is reduced by 20%. Space utilization is reduced by 95% (Fig.12). This algorithm achieves effective compression of terahertz signal. Combined with terahertz imaging technology and binarized threshold segmentation method, the debonding defects of the sample were identified, and the identification deviation was less than 0.05 (Tab.3). The results show that the algorithm improves the efficiency of data analysis and guarantees the accuracy of defect identification.A gradient threshold adaptive sparse algorithm is proposed to solve the problem of terahertz signal feature redundancy and low processing efficiency. The algorithm has the advantages of strong adaptive ability, high compression rate, fast running speed and low complexity. The second order gradient is used to extract the signal feature peak and determine the effective feature region. Then, according to the time-domain characteristics of terahertz signals, sparse thresholds and sparse signals of effective and invalid feature regions are determined. Finally, signals are restored by using multiple Gaussian functions. The compression ratio of the algorithm is greater than 81%, the relative root mean square error is less than 2%, the correlation coefficient is greater than 0.97, and the defect identification error is less than 5%. Compared with the traditional signal compression algorithm, the data computation time is reduced by 20% and the space is reduced by 95%. The algorithm reduces a large number of invalid features and retains effective features, ensuring the accuracy of terahertz image defect recognition. It is suitable for compression of normal terahertz signals and defective terahertz signals with complex redundant characteristic information.