Methods are presented in this paper for estimating solutions of illposed problems in the form of Fredholm integral equations of the first kind, given noisy data. These regularization methods and regularization is effected by maximum likelihood technique and regular filtering by WCV Method. In these methods optimal amount of smoothing may be computed, based on the data and the assumed known noise variance. We shall compare our method with the method of Al- Faour [2], over the same highly ill-posed problems and for comparison purposes the results are shown in the tables and the diagrams.