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A new approach for synthetic aperture image formation is presented in this paper. With the presented method image formation is regarded as a signal arrangement that can be described by a matrix. This method integrates the sonar platform motion in the image formation process but more importantly it acknowledges the non ideal data gathering process and implements means to mitigate these shortcomings. This method is illustrated with real data obtained in test mission in the Douro River, Portugaldoi:10.1109/oceans.2008.5151974 fatcat:egfgjwa3fne7nbzselxugvjuhm