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A fast algorithm for reconstructing the profile of random rough surfaces using electromagnetic scattering data is presented. The algorithm is based on merging a fast forward solver and an efficient optimization technique. The steepest descent fast multipole method is used as the three-dimensional fast forward solver. A rapidly convergent descent method employing a "marching-on" strategy for processing multifrequency and multi-incidence angle data is introduced to minimize an underlying cost function. The cost function represents the error between true (synthetic) and simulated scattered field data. Several key issues that impact the accuracy in reconstructing the rough profile are examined in this work, e.g., the location and number of receivers, the incident and scattered directions, the surface roughness, and details regarding the manner in which sensitivity information is computed in the inversion scheme. The results show that using the multiple-incidence (one angle at a time) and the multifrequency (one frequency at a time) strategies lead to improve the profile reconstruction.