An embodiment in accordance with the present invention provides a new SR compensation (SRC) method, using a more efficient conjugate gradient method. In this method, the first and second derivatives are directly calculated analytically. The proposed SRC uses a sinogram restoration approach, integrates the SRF as a part of a forward imaging model, and compensates for the effect of the SR by maximizing the Poisson log-likelihood of measurements. The algorithm can be evaluated using as a simulated fan-beam x-ray CT scanner.