In this thesis spline functions have been used to do data fitting for modeled signals. Optimum splines are obtained based on least squares error for the specific signal and image models. In the case of one-dimensional signal the model is obtained by using the Maximum Entropy Method (MEM). After obtaining the best estimates for the model parameters, the best type of spline is generated based on the source model chosen. For the two-dimensional case a linear least squares technique is used for the estimation of model parameters and then an optimal interpolating spline is used for image reconstruction.