We propose a relative optimization framework for quasi maximum likelihood blind deconvolution and the relative Newton method as its particular instance. Special Hessian structure allows its fast approximate construction and inversion with complexity comparable to that of gradient methods. The use of rational IIR restoration kernels provides a richer family of filters than the traditionally used FIR kernels. Smoothed absolute value and the smoothed deadzone functions allow accurate and robust deconvolution of super- and sub-Gaussian sources, respectively. Simulation results demonstrate the efficiency of the proposed methods.