In such bandwidth-constrained applications as wireless sensor networks, satellite communications, and Internet of Things, secure image communication poses significant challenges due to inherent conflicts between transmission demand and channel capacity. Although existing encryption schemes can ensure security, they often introduce high communication overhead, which is prohibitive for some scenarios with limited bandwidth resources. To solve this problem, this paper proposes a novel double-image encryption framework that integrates double random phase encoding (DRPE) with optimized compressive sensing (CS) to achieve simultaneous compression, encryption, and authentication. This framework introduces adaptive thresholding sparsification (ATS) to ensure consistent sparsity across diverse images and improve image recovery quality. Additionally, this framework also utilizes Lorenz chaos-based correlation-reduced measurement via variable-step gradient descent and QR decomposition (LCM-VSGQR) to construct optimized measurement matrices, which reduces the correlation between measurements and sparse matrices while enhancing column independence. Experimental results demonstrate that the proposed framework not only achieves high security and robustness against various attacks, but also significantly reduces the data requirements for transmission and authentication, which is particularly suitable for bandwidth-constrained application scenarios.