Metal artifact reduction (MAR) is important for clinical diagnosis with CT images. The existing state-of-the-art deep learning methods usually suppress metal artifacts in sinogram or image domains or both. However, their performance is limited by the inherent characteristics of the two domains, i.e., the errors introduced by local manipulations in the sinogram domain would propagate throughout the whole image during backprojection and lead to serious secondary artifacts, while it is difficult to distinguish artifacts from actual image features in the image domain. To alleviate these limitations, this study analyzes the desirable properties of wavelet transform in-depth and proposes to perform MAR in the wavelet domain. First, wavelet transform yields components that possess spatial correspondence with the image, thereby preventing the spread of local errors to avoid secondary artifacts. Second, using wavelet transform could facilitate identification of artifacts from image since metal artifacts are mainly high-frequency signals. Taking these advantages of the wavelet transform, this paper decomposes an image into multiple wavelet components and introduces multi-perspective regularizations into the proposed MAR model. To improve the transparency and validity of the model, all the modules in the proposed MAR model are designed to reflect their mathematical meanings. In addition, an adaptive wavelet module is also utilized to enhance the flexibility of the model. To optimize the model, an iterative algorithm is developed. The evaluation on both synthetic and real clinical datasets consistently confirms the superior performance of the proposed method over the competing methods.