The low signal-to-noise ratio and multiplicative speckle noise make edge detection extremely difficult for synthetic aperture radar (SAR) imagery. In this paper a generalized Gaussian (GG) distribution is used as the a prior model for the local mean power, and an optimal estimation for it in the sense of maximum a posterior (MAP) is thus given. A novel ratio-based edge operator for SAR imagery is accordingly developed. The method of log-cumulants (MoLC) based on Mellin transform is employed to estimate the GG distribution parameters, based on which a method of joint and iterative estimation of the local mean power and GG distribution parameters is proposed. The performance of the proposed edge operator is tested using real SAR data, and compared with the ratio of averages (RoA) and ratio of exponentially weighted averages (ROEWA) operators. Experimental results show that the proposed operator can effectively extract edges and suppress speckle noise.