Gengsheng L Zeng1. 1. Department of Radiology, University of Utah, Salt Lake City, UT 84108, USA.
Abstract
PURPOSE: In order to eventually develop an analytical algorithm with noise characteristics of an iterative algorithm, this technical note develops a window function for the filtered backprojection (FBP) algorithm in tomography that behaves as an iterative Landweber algorithm. METHODS: Based on the formulation of the iterative Landweber algorithm, a frequency domain window function is derived for each iteration of the Landweber algorithm. The resultant window function has an index k, emulating the characteristics of the Landweber algorithm at the kth iteration. The window function is used to modify the ramp filter in the FBP algorithm. RESULTS: Computer simulations show that the windowed FBP algorithm with window function index k and the iterative Landweber algorithm iteration number k give similar reconstructions in terms of resolution and noise. CONCLUSIONS: Analytical FBP algorithms are able to provide similar results to the iterative Landweber algorithm if the ramp filter in the FBP algorithm is modified by a set of specially designed window functions.
PURPOSE: In order to eventually develop an analytical algorithm with noise characteristics of an iterative algorithm, this technical note develops a window function for the filtered backprojection (FBP) algorithm in tomography that behaves as an iterative Landweber algorithm. METHODS: Based on the formulation of the iterative Landweber algorithm, a frequency domain window function is derived for each iteration of the Landweber algorithm. The resultant window function has an index k, emulating the characteristics of the Landweber algorithm at the kth iteration. The window function is used to modify the ramp filter in the FBP algorithm. RESULTS: Computer simulations show that the windowed FBP algorithm with window function index k and the iterative Landweber algorithm iteration number k give similar reconstructions in terms of resolution and noise. CONCLUSIONS: Analytical FBP algorithms are able to provide similar results to the iterative Landweber algorithm if the ramp filter in the FBP algorithm is modified by a set of specially designed window functions.