This study introduces the Two-Dimensional Hybrid Chaotic Fourier Series and Nonlinear Coupled Oscillator Model (2- DHOCFSANCOM), which is integrated with compressed sensing technology, aiming to address the challenge of slow encryption speeds in agricultural Unmanned Aerial Vehicles (UAVs). The principal challenge in enhancing encryption speed is the inher- ently limited capacity of traditional chaos-based systems coupled with the complexity of their computational processes. By employing a sophisticated two-dimensional hybrid chaotic system, the 2-DHOCFSANCOM significantly enhances the security of image transmission in agricultural drones. This model surpasses existing chaos-based methods by integrating advanced Fourier series and nonlinear coupled oscillators, achieving improved pseudo-randomness and robustness in encryption. Moreover, incorporating the Bonouille function into the Discrete Cosine Transform (DCT) domain results in a sparser measurement matrix, which is pivotal for enabling efficient real-time encryption. The effectiveness of 2-DHOCFSANCOM in securely encrypting images from agricultural drones has been rigorously validated through simulations and analytical evaluations, employing sophisticated row, rotation, and matrix encryption techniques. Comparative analyses have further confirmed its enhanced safety performance. Compared to other models, the 2-DHOCFSANCOM demonstrates a notably higher Lyapunov exponent of 15.1039 and a sample entropy of 2.5, evidencing its superior chaotic performance and reliability in encryption.