We present a new approach to improving images in diffusion tomography, involving construction of a linear filter function that converts images of absorption and scattering coefficients back into the original configuration being imaged. In a practical situation the original configuration is not known, so that the filter function is constructed by simulation for a neighboring situation. The algorithm is quite robust, so that the neighboring situation need not be all that close to that of interest. We show how to construct such a filter and give illustrations of how well it solves the problem. In one confirmation shown, this procedure gives a better image than 50 Born iterations. This suggests that the inherent nonlinearity of the problem in diffusion tomography may not be the largest source of error, but that linear errors may be more important. A crucial advantage of the filter procedure is that the filter (or, preferably, library of filters) can be computed before the experiment of interest. It is only inversion of the pattern of detector readings and application of the filter that take place afterward, and both are very fast, leading to enhanced images in what is essentially real time.