There is increasing demand in the field of dental and medical radiography for effective metal artifact reduction (MAR) in computed tomography (CT) because artifact caused by metallic objects causes serious image degradation that obscures information regarding the teeth and/or other biological structures. This paper presents a new MAR method that uses the Laplacian operator to reveal background projection data hidden in regions containing data from metal. In the proposed method, we attempted to decompose the projection data into two parts: data from metal only (metal data), and background data in the absence of metal. Removing metal data from the projections enables us to perform sparsity-driven reconstruction of the metal component and subsequent removal of the metal artifact. The results of clinical experiments demonstrated that the proposed MAR algorithm improves image quality and increases the standard of 3D reconstruction images of the teeth and mandible.