Noise-weighted spatial domain FBP algorithm

Abstract

Purpose: 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. Methods: 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. Results: 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. Conclusions: 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. © 2014 American Association of Physicists in Medicine.