Abstract
BackgroundThe Filtered Back-Projection (FBP) algorithm is the most important technique for computerized tomographic (CT) imaging, in which the ramp filter plays a key role. FBP algorithm had been derived using the continuous system model. However, it has to be discretized in practical applications, which necessarily produces distortion in the reconstructed images.MethodsA novel scheme is proposed to design the filters to substitute the standard ramp filter to improve the reconstruction performance for parallel beam tomography. The design scheme is presented under the discrete image model and discrete projection environment. The designs are achieved by constrained optimization procedures. The designed filter can be regarded as the optimal filter for the corresponding parameters in some ways.ResultsSome filters under given parameters (such as image size and scanning angles) have been designed. The performance evaluation of CT reconstruction shows that the designed filters are better than the ramp filter in term of some general criteria.ConclusionsThe 2-D or 3-D FBP algorithms for fan beam tomography used in most CT systems, are obtained by modifying the FBP algorithm for parallel beam tomography. Therefore, the designed filters can be used for fan beam tomography and have potential applications in practical CT systems.
Highlights
The Filtered Back-Projection (FBP) algorithm is the most important technique for computerized tomographic (CT) imaging, in which the ramp filter plays a key role
In order to make the idea behind the design scheme clear, a similar question for 1-D signal is proposed at first, and it is extended to 2-D situations to solve the corresponding question in CT reconstruction
The size of image is selected as N = 256, the projection angles θ =[0o, 3o, · · ·, 177o]
Summary
The reconstruction filter for 1-D signal Suppose a 1-D real signal x(n), n ∈ [0, · · · , N − 1], where N is the length of the signal. (9) and (11) form 2-D DFT and IDFT using the non-uniform frequency sampling, and the non-ignorable distortion will be brought into the reconstructed image. This problem is very similar with the 1-D example in the previous subsection. The objective function is very complicated when the image size is large, and/or the number of projection angles is large
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