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X-ray computed tomography (CT) is a mainstream medical imaging modality. The widespread use of CT has made image denoising of low-dose CT (LDCT) images a key issue in medical imaging. Deep learning (DL) methods have been successful in this area over the past few years, but most DL-based dual-domain methods directly filter the sinogram domain data, which is prone to induce new artifacts in the reconstructed image. This paper proposes a new method called DD-WGAN, which has an image domain generator network (IDG-Net) and two discriminator networks, namely the image domain discriminator network (ID-Net) and the sinogram domain discriminator network (SD-Net). We use dual-domain discriminators to balance the data weights of the sinogram and the image. Using the image domain generator can avoid artifacts from filtering sinogram data. Experimental results show that the proposed method achieves significantly improved LDCT denoising performance.