In this paper, we proposed a new projection completion metal artifact reduction (MAR) algorithm in x-ray computed tomography (CT) using a sparsity based sinogram inpainting (interpolation) technique. We developed the MAR algorithm on a Bayesian framework in which a wavelet-based generalized Gaussian (ℓp) prior was applied and then the inpainting problem was formulated as a constrained optimization problem. For the optimization, we derived a projected gradient descent algorithm using a majorization-minimization technique. The gradient step was performed by a soft thresholding operator for an ℓ1 prior, and a hard thresholding with a decaying threshold for an ℓ0 prior. We utilized a tight frame of translation-invariant wavelets implemented by undecimated discrete wavelet transform. As in the clinical setting there is no ground truth CT image to objectively evaluate the performance of a proposed MAR algorithm, we also introduced a novel approach to simulate metal artifacts in a real CT dataset. The results showed that the proposed MAR algorithm using hard thresholding efficiently recovers and inpaints the sinogram projections corrupted by metallic implants.