With the advent of intelligent technologies, miscellaneous data containing sensitive information are explosively generated and shared. Compressive sensing methods are naturally suitable for such scenarios due to their joint compression and encryption capabilities. However, data users of most existing compressive sensing methods need to reconstruct original images before use, which brings two disadvantages. First, indiscriminately requiring every data user to reconstruct images without considering their exact requirements is neither advisable nor efficient. Second, allowing all data users to reconstruct original images may cause private or confidential information exposure. To address these issues, in this paper, a novel image sharing method is proposed, which realizes efficient multilevel privacy preservation. Specifically, data owners compress the original images with designed measurement matrices through the proposed Tℓ₁-B2DLDA algorithm, which outputs dimension-reduced data with the ability to simultaneously support the subsequent classification tasks for level I data users and reconstruction tasks for level II data users. Therefore, low level data users could achieve their goals without obtaining any private or confidential information in the original images. Experiments are conducted to verify the feasibility, performance and robustness of the proposed method. Furthermore, the security of the proposed method is analyzed both theoretically and practically. The source code of the proposed method is publicly available at https://github.com/xchuxiao23/TL1-B2DLDA.