Two families of algorithms for MSE and MMSE estimation respectively will be presented and applied to a monoenergetic X-ray Computed Tomography acquisition model. For the MAP problem, a randomized second order solver for model-based reconstruction is analysed; to reduce the computational complexity, a partial randomized Hessian sketch is used only for the convex likelihood function and the regularization is designed using the regularization by denoising which retains the complex prior structure. Finally, a fist order iterative method, called approximate message passing, will be presented for performing MMSE estimation efficiently.