With the rapid advancement of cloud computing and increased emphasis on privacy protection, reversible data hiding in encrypted images (RDHEI) is garnering increasing attention. This is because it allows for the protection of the original image content, extraction of embedded data, and lossless reconstruction of the original image simultaneously. To notably enhance prediction accuracy and leverage the correlation among adjacent pixels, a novel high-capacity RDHEI approach is introduced, integrating a progressive CNN-based predictor with a bit-plane compression algorithm. Additionally, the median edge detector (MED) predictor is employed as a two-stage prediction mechanism to provide embedding capacity. Experimental results demonstrate that the proposed method achieves superior embedding capacity compared to state-of-the-art techniques.