Compressed sensing algorithm can be utilized for solving the problems of dynamic spectrum detection at the airport terminal area, and determining on the precision and the efficiency of signal recovery. Based on sparsity adaptive matching pursuit (SAMP) signal reconstruction algorithm, this paper introduces generalized Jaccard coefficient, t-average correlation coefficient and variable step size idea, and proposes a JTVS-SAMP algorithm. The generalized Jaccard coefficient in the atomic screening part of the algorithm can reduce the accuracy degradation caused by atomic confusion, the t-average correlation coefficient can avoid calculating the rip coefficient of the measurement matrix, and reducing the complexity of the algorithm. And the large step iteration in the variable step idea and the small step approach step enable the efficiency and accuracy of the algorithm to be greatly improved. Taking the 1-D Gaussian random sparse signal as the measurement signal for simulation, the measured signal after energy detection in the airport terminal area can be effectively simulated . Through the simulation, the performance of JTVS-SAMP is better than that of the traditional compressed sensing algorithm in the algorithm reconstruction success rate under different measurement numbers and sparsity. Compared with the SAMP algorithm, JTVS-SAMP performs significantly in the reconstruction error and algorithm time.