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Model Based Filtered Backprojection Algorithm: A Tutorial
1Department of Electrical Engineering, Weber State University, Ogden, Utah 84408 USA. Department of Radiology, University of Utah, Salt Lake City, Utah 84108 USA, Tel : +801-626-6864 / Fax : +
Purpose:
People have been wandering for a long time whether a filtered backprojection (FBP) algorithm is able to incorporate measurement noise in image reconstruction. The purpose of this tutorial is to develop such an FBP algorithm that is able to minimize an objective function with an embedded noise model.
Methods:
An objective function is first set up to model measurement noise and to enforce some constraints so that the resultant image has some pre-specified properties. An iterative algorithm is used to minimize the objective function, and then the result of the iterative algorithm is converted into the Fourier domain, which in turn leads to an FBP algorithm. The model based FBP algorithm is almost the same as the conventional FBP algorithm, except for the filtering step.
Results:
The model based FBP algorithm has been applied to low-dose x-ray CT, nuclear medicine, and real-time MRI applications. Compared with the conventional FBP algorithm, the model based FBP algorithm is more effective in reducing noise. Even though an iterative algorithm can achieve the same noise-reducing performance, the model based FBP algorithm is much more computationally efficient.
Conclusions:
The model based FBP algorithm is an efficient and effective image reconstruction tool. In many applications, it can replace the state-of-the-art iterative algorithms, which usually have a heavy computational cost. The model based FBP algorithm is linear and it has advantages over a nonlinear iterative algorithm in parametric image reconstruction and noise analysis.
