Due to the property of infrared aerial imagery, the local prior is sufficient especially for low-subrate block compressive sensing (BCS) reconstruction of infrared aerial images, while its complexity is much lower than nonlocal prior. The typical low-subrates can effectively improve the BCS transmission efficiency and reduce the burden of transmitter hardware. Therefore, this paper proposes a low-subrate sparse reconstruction algorithm with threshold-adaptive denoising and basis learning (TDBL), which adopts both split Bregman iteration (SBI) and adaptive threshold to implement the model-based BCS reconstruction for infrared aerial imagery. The experimental results show that as compared with the state-of-the-art algorithms, the proposed algorithm can obtain better recovery quality and less runtime on both HIT-UAV and M200-XT2DroneVehicle datasets.