In this paper, we study alternating direction methods for solving constrained total-variation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting and image cartoon+texture decomposition. As the constrained model is employed, we only need to input the noise level and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the eectiveness of the proposed method. We show that the alternating direction method is very ecient for solving image restoration and reconstruction problems.