Semantic communications, aiming at ensuring the successful delivery of the meaning of information, are expected to be one of the potential techniques for the next generation communications. However, the knowledge forming and synchronizing mechanism that enables semantic communication systems to extract and interpret the semantics of information according to the communication intents is still immature. In this paper, we propose a semantic image transmission framework with explicit semantic base (Seb), where Sebs are generated and employed as the knowledge shared between the transmitter and the receiver with flexible granularity. To represent images with Sebs, a novel Seb-based reference image generator is proposed to generate Sebs and then decompose the transmitted images. To further encode/decode the residual information for precise image reconstruction, a Seb-based image encoder/decoder is proposed. The key components of the proposed framework are optimized jointly by end-to-end (E2E) training, where the loss function is dedicated designed to tackle the problem of nondifferentiable operation in Seb-based reference image generator by introducing a gradient approximation mechanism. Extensive experiments show that the proposed framework outperforms state-of-art works by 0.5 - 1.5 dB in peak signal-to-noise ratio (PSNR) w.r.t. different signal-to-noise ratio (SNR).