A tomographic algorithm believed appropriate for reconstructing the effective index of the refraction structure of bubbly water is developed. The method is optimum in a least-squares sense if the medium can be interpreted as a realization of a Gaussian random process. In contrast to other tomographic algorithms, it can be applied when the number of ray paths is sparse. The measured input may be acoustic travel time, to reconstruct sound speed, or log intensity, to reconstruct attenuation. The data are multiplied by a precalculated matrix that depends on the geometry and the assumed autocorrelation function of the medium. This gives the weights used in the imaging step. To produce an image, the data from each ray are weighted, then backprojected over a smeared region centered about the original ray path. Superimposing the weighted smeared images produces the final reconstruction. The computationally expensive work can be done prior to processing any data, giving the potential to do nearly real-time imaging. The algorithm is tested in numerical simulations of the March 1997 shallow water bubbles experiment. The locations of the sources and receivers are varied. The effects of environmental mismatch are studied.