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The filtered backprojection algorithm of X-ray tomography and the filtered backpropagation algorithm developed recently by the author for diffraction tomography are tested in computer simulations of ultrasonic tomography of two-dimensional objects for which the Rytov approximation is valid. It is found that the filtered backprojection algorithm gives unsatisfactory results even for wavelengths much smaller than the smallest scale over which the object varies. The filtered back-propogation algorithm yields, in all cases studied, high-quality reconstructions which are simply low-pass filtered versions of the actual object profile. It is shown that the filtered backpropagation algorithm can be approximated by a modified backprojection algorithm having essentially the same computation requirements as filtered backprojection, but yielding considerably higher quality object reconstructions.