一种具有迭代 Landweber 算法特征的滤波反投影算法。
A filtered backprojection algorithm with characteristics of the iterative landweber algorithm.
机构信息
Department of Radiology, University of Utah, Salt Lake City, UT 84108, USA.
出版信息
Med Phys. 2012 Feb;39(2):603-7. doi: 10.1118/1.3673956.
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.
目的
为了最终开发出具有迭代算法噪声特性的分析算法，本技术说明为层析成像中的滤波反投影（FBP）算法开发了一个窗口函数，该函数的行为类似于迭代 Landweber 算法。
方法
基于迭代 Landweber 算法的公式，为 Landweber 算法的每一次迭代推导出一个频域窗口函数。所得的窗口函数具有索引 k，模拟了第 k 次迭代时 Landweber 算法的特性。该窗口函数用于修改 FBP 算法中的斜坡滤波器。
结果
计算机模拟结果表明，在分辨率和噪声方面，具有窗口函数索引 k 的加窗 FBP 算法和迭代 Landweber 算法迭代次数 k 给出了相似的重建结果。
结论
如果 FBP 算法中的斜坡滤波器被一组专门设计的窗口函数修改，则分析 FBP 算法能够提供与迭代 Landweber 算法相似的结果。
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