Blind blur identification in video sequences becomes more important. This paper presents a new method for identifying parameters of different blur kernels and image restoration in a weighted double regularized Bayesian learning approach. A proposed prior solution space includes dominant blur point spread functions as prior candidates for Bayesian estimation. The double cost functions are adjusted in a new alternating minimization approach which successfully computes the convergence for a number of parameters. The discussion of choosing regularization parameters for both image and blur function is also presented. The algorithm is robust in that it can handle images that are formed in variational environments with different types of blur. Numerical tests show that the proposed algorithm works effectively and efficiently in practical applications.