Abstract
The purpose of this paper is to implement a noise-weighted filtered backprojection (FBP) algorithm in the form of "convolution" backprojection, but this "convolution" has a spatially variant integration kernel. Noise-weighted FBP algorithms have been developed in recent years, with filtering being performed in the Fourier domain. The noise weighting makes the ramp filter in the FBP algorithm shift-varying. It is not efficient to implement shift-varying filtration in the Fourier domain. It is known that Fourier-domain multiplication is equivalent to spatial-domain convolution. An expansion method is suggested in this paper to obtain a closed-form integration kernel. The noise weighted FBP algorithm can now be implemented in the spatial domain efficiently. The total computation cost is less than that of the Fourier domain implementation. Computer simulations are used to show the three-term expansion method to approximate the filter kernel. A clinical study is used to verify the feasibility of the proposed algorithm.
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