Acceleration of image reconstruction by generalized Landweber's iteration for X-ray cone-beam CT

Low-dose data acquisition is required for the imaging of rapidly moving objects, and the number of projections is usually sparse. In this case, severe artifacts will be introduced by conventional Filtered-backprojection (FBP) method. However, Iterative reconstruction (IR) has been shown to achieve great image quality improvements with the advantage of better noise tolerance and handling of sparse data. The main repellant for using IR in clinical situations was the slow speed. In this paper, we introduce an acceleration procedure based on the generalized Landweber's iteration (GLI) method for X-ray CT image reconstruction from cone-beam projections. Compared to conventional iterative methods, GLI can accelerate the reconstruction of high frequency components and preserve the stability of the solution when the system matrix is illconditioned. Specifically, the relaxation parameter in GLI is selected to be a linear operator, which can shape the response to singular functions of the forward operator. We study various linear operators, and their behavior with respect to speed up the convergence. Basically, we choose the linear operator as polynomials. Compared to conventional iterative methods which updates the image by multiplying a constant to the difference of measured and calculated projections, GLI methods update the image by several reprojection-backprojection of the difference of measured and calculated projections. At last, we compare the performance of using various linear operators by numerical experiments. Computational complexity is also analyzed. While our primary interest is in X-ray CT image reconstruction, it can be applied to radar, acoustic and geophysical imaging, to name a few. (orig.)