This study presents an approach that integrates compressed sensing technology with two-dimensional hyperchaotic coupled Fourier oscillator systems (2D-HCFOS) to address the challenge of slow encryption speeds in agricultural unmanned aerial vehicles (UAVs). The primary challenge in enhancing encryption speed lies in the limited capacity inherent in traditional chaotic-based systems and the computational complexity of their processes. The 2D-HCFOS utilizes a complex two-dimensional hybrid chaotic system, which significantly enhances the security of agricultural UAV image data. Notably, the image encryption process is performed on a personal computer connected to the drone, ensuring efficient processing. By integrating advanced Fourier series and nonlinear coupled oscillators, the model surpasses existing chaotic-based methods, improving both the pseudo-randomness and robustness of encryption. Additionally, incorporating Bonouille functions into the discrete cosine transform (DCT) domain results in a sparser measurement matrix, which is essential for efficient encryption on personal computers. The effectiveness of 2D-HCFOS in securely encrypting agricultural drone images has been rigorously validated through simulations and analytical evaluations using sophisticated row, rotation, and matrix encryption techniques. The improved security performance is further verified by comparative analysis. Compared with other models, the Lyapunov index of 2D-HCFOS is 15.1039, and the sample entropy is 2.4987, indicating that it possesses superior chaotic performance and encryption reliability.