One-step Backprojection Algorithm for Computed Tomography

The iterative algorithm can incorporate various physical aspects into its reconstruction process, leading to a more accurate image than the filtered backprojection algorithm. One drawback of the iterative algorithm is that it requires many iterations to produce the final images. In this paper, we show that we can reconstruct the same images as the Landweber iterative method in "one step." We reformulate the iterative procedure into a matrix multiplication, build the matrix and store it on disk. We use this matrix to reconstruct images in one step. The reconstructed images are exactly the same as the ones that are reconstructed by the Landweber iterative method.