Weighting Algorithm and Relaxation Strategies of the Landweber Method for Image Reconstruction

The iterative approach is important for image reconstruction with ill-posed problem, especially for limited angle reconstruction. Most of iterative algorithms can be written in the general Landweber scheme. In this context, appropriate relaxation strategies and appropriately chosen weights are critical to yield reconstructed images of high quality. In this paper, based on reducing the condition number of matrix A(T) A, we find one method of weighting matrices for the general Landweber method to improve the reconstructed results. For high resolution images, the approximate iterative matrix is derived. And the new weighting matrices and corresponding relaxation strategics are proposed for the general Landweber method with large dimensional number. Numerical simulations show that the proposed weighting methods are effective in improving the quality of reconstructed image for both complete projection data and limited angle projection data.