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        Model Based Filtered Backprojection Algorithm: A Tutorial

        Gengsheng L. Zeng 대한의용생체공학회 2014 Biomedical Engineering Letters (BMEL) Vol.4 No.1

        Purpose People have been wandering for a long timewhether a filtered backprojection (FBP) algorithm is able toincorporate measurement noise in image reconstruction. Thepurpose of this tutorial is to develop such an FBP algorithmthat is able to minimize an objective function with anembedded noise model. Methods An objective function is first set up to modelmeasurement noise and to enforce some constraints so thatthe resultant image has some pre-specified properties. Aniterative algorithm is used to minimize the objective function,and then the result of the iterative algorithm is converted intothe Fourier domain, which in turn leads to an FBP algorithm. The model based FBP algorithm is almost the same as theconventional FBP algorithm, except for the filtering step. Results The model based FBP algorithm has been applied tolow-dose x-ray CT, nuclear medicine, and real-time MRIapplications. Compared with the conventional FBP algorithm,the model based FBP algorithm is more effective in reducingnoise. Even though an iterative algorithm can achieve thesame noise-reducing performance, the model based FBPalgorithm is much more computationally efficient. Conclusions The model based FBP algorithm is an efficientand effective image reconstruction tool. In many applications,it can replace the state-of-the-art iterative algorithms, whichusually have a heavy computational cost. The model basedFBP algorithm is linear and it has advantages over a nonlineariterative algorithm in parametric image reconstruction andnoise analysis.

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