This paper proposes an integral method to achieve a more accurate weighting matrix that makes very positive contributions to the image reconstruction in inertial confinement fusion research. Standard algebraic reconstruction techniques with a positivity constraint included are utilized. The final normalized mean-square error between the simulated and reconstructed projection images is 0.000365%, which is a nearly perfect result, indicating that the weighting matrix is very important. Compared with the error between the simulated and reconstructed phantoms, which is 2.35%, it seems that the improvement of the accuracy of the projection image does not mean the improvement of the phantom. The proposed method can reconstruct a simulated laser-imploded target consisting of 100×100×100 voxels.