In response to the large size of remote sensing images and the limitations of existing image compression and encryption algorithms, this paper proposes a novel compression and encryption algorithm. The proposed algorithm utilizes a new type of memristive chaotic mapping in combination with PSO-BP neural networks and multi-threaded parallelism. Specifically, the proposed novel two-dimensional memristive chaotic mapping involves a combination of new memristors based on HP memristors and Cubic chaotic mapping. Compared to existing chaotic systems, this method exhibits stronger randomness and hyperchaotic characteristics. Additionally, to improve the reconstruction accuracy of compressed images, a traditional BP neural network with an added hidden layer is combined with the PSO algorithm for image compression and reconstruction. Furthermore, to enhance the encryption efficiency of remote sensing images, a multi-threaded parallel encryption method is employed, enabling simultaneous permutation within and among threads. Experimental results demonstrate that the proposed algorithm achieves good compression reconstruction accuracy, excellent encryption performance, and resistance to attacks.