In order to improve the security of image transmission and reduce bandwidth and storage requirements, an simultaneous image compression and encryption scheme based on hyperchaotic system and sparse matrix is proposed. Using raster scanning and dictionary learning algorithms, the image is converted into a sparse matrix and the sparse vectors of the image are estimated, which greatly reduces the amount of encrypted data. After that, the non-zero coefficients of the sparse vectors and the corresponding address information are encrypted with a 4D Logistic hyperchaotic system, and different key sequences are used in different steps of the encryption process, which further improves the security level of the cipher image. Experimental results show that the proposed method provides higher compression ratio and security while guaranteeing the ideal reconstructed image quality, and its performance is better than other advanced methods.