This paper is devoted to the total variation (TV) based approach to image denoising and restoration. The restored image minimizes total variation in the class of images which satisfy the contraints given by the image acquisition model. We compute some explicit solutions of the denoising model which explain some of the features observed in numerical experiments. We also comment on some alternatives recently proposed by Y. Meyer which lead to u + v image decompositions. Finally we propose a total variation approach to image restoration, i.e., deconvolution and denoising, in which the image acquisition model is incorporated as a set of local constraints.