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A new emission computed tomographic reconstruction technique has been developed. Each projection is fit with an arbitrary functional form which is constrained in shape by the sharpest response which can be obtained in a tomograph. The image is then reconstructed by backprojecting the best estimate projections which have been filtered by a ramp function in the frequency domain. This procedure reduces the variance in image pixel values while maintaining resolution which is near the intrinsic resolution of the tomograph. This paper presents results for both measured and simulated data from a tomograph designed to measure annihilation photons from the decay of positrons.