In this paper we have discussed what appears to be a superior implementation of the Algebraic Reconstruction Technique (ART). The method is based on 1) simultaneous application of the error correction terms as computed by ART for all rays in a given projection; 2) longitudinal weighting of the correction terms back-distributed along the rays; and 3) using bilinear elements for discrete approximation to the ray integrals of a continuous image. Since this implementation generates a good reconstruction in only one iteration, it also appears to have a computational advantage over the more traditional implementation of ART. Potential applications of this implementation include image reconstruction in conjunction with ray tracing for ultrasound and microwave tomography in which the curved nature of the rays leads to a non-uniform ray density across the image.