Bolometry is an essential diagnostic for calculating the power balances and for the understanding of different physical aspects of tokamak experiments. The reconstruction method based on the Maximum Likelihood (ML) principle, developed initially for JET, has been implemented for ASDEX Upgrade. Due to the availability of a limited number of views, the reconstruction problem is mathematically ill-posed. A regularizing procedure, based on the assumption of smoothness along the magnetic surfaces, given by plasma equilibrium, must also be implemented. A new anisotropic smoothing technique, which acts along locally oriented kernels, has been implemented. The performances of the method have been evaluated, in terms of shapes, resolution and of the derived radiated power, and compared with the bolometry method used routinely on ASDEX Upgrade. The specific advantage of the ML reconstruction algorithm consists of the possibility to assess the uncertainties of the reconstruction and to derive confidence intervals in the emitted radiation levels. The importance of this capability is illustrated.