Image Deblurring is a very popular area of research in all over the world. It is an illposed problem which still does not have an ideal solution. Therefore, in order to analyse the research problems and to understand the statement of image deblurring we look in to the state-of-the-art methods proposed in various recent publications. Hence, the present study is focused on the overall review of the techniques used in image deblurring and their solutions to tackle the illposed problem using mathematical model. Based on the overall technique simple MAP model falls short in either deriving accurate convergence to the global optimum or computational implementation. Convergence of the algorithm is the most important factor for the effective performance of Lo and L1 norms for regularizers for theoretical applications. The importance of the choice of the correct estimator and the role of various priors in solving the imaging inverse problem using the MAP estimation method is discussed. The consequence of different priors to the rate of convergence of the MAP algorithm and its computational complexity are studied and tabulated.