The iterative denoising models and their solving algorithms in the sparse computed tomoyraphy reconstruction were researched. The theoretical derivations and simulation experiments demonstrate that the Algebraic Reconstruction Technique (ART) have the denoising ability. Two models for the sparse computed tomoyraphy denoise were proposed. One is based on the Euclidean norm inequality constraint, and the other is based on the infinity norm inequality constraint. Inspaired by the iterative method in ART, we use projection onto convex sets method to solve these two denoising models. The algorithm derivation is provided. The results indicate that the Euclidean norm based denoise model is better than the infinity norm based denoise model, and the ART method has the ability of denoising.