Theoretical Investigation on an Unmatched Backprojector for Iterative Reconstruction in Emission Computed Tomography

Lee, Nam Yong; Choi, Yong Min

doi:10.3938/jkps.59.367

Cited by 4 publications

(2 citation statements)

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“…Good results can be obtained by using valid unmatched backprojectors. For example, if the ramp filter is used in the backprojector, the backprojector is valid, the algorithm is fast, but the resultant images are quite noisy [11,12].…”

Section: Introductionmentioning

confidence: 99%

Counter examples for unmatched projector/backprojector in an iterative algorithm

Zeng

2019

Chin J Acad Radiol

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It is rather controversial whether it is justified to use an unmatched projector/backprojector pair in an iterative image reconstruction algorithm. One common concern of using an unmatched projector/backprojector pair is that the optimal solution cannot be reached. This concern is misleading and must be clarified. We define a figure-of-merit in the image domain as the distance between the reconstructed image and the true image, as the normalized mean-squared-error (NMSE). The NMSE is used to determine whether an unmatched matched projector/backprojector pair can provide a better image than a matched projector/backprojector pair. Hot and cold lesion's contrast-to-noise ratio is also used as an alternative secondary figureof-merit for algorithm comparison. Computer-generated counterexamples are used to test the performance for matched and unmatched projection/backprojection pairs for different reconstruction algorithms. The projectors are ray-driven, and the backprojectors are ray-driven and pixel-driven. For the attenuation-free data examples, the unmatched pixel-driven backprojector outperforms the matched ray-driven backprojector. For the attenuated data example, the matched ray-driven backprojector performs better. The ray-driven backprojector can be slightly improved by using an attenuation coefficient that is larger than the true one; in this case the backprojector becomes unmatched. Unmatched projector/backprojector pairs are fairly flexible. If the backprojector is properly chosen, good results can be obtained. However, we have not found a general rule to select a good backprojector.

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Section: Introductionmentioning

confidence: 99%

Counter examples for unmatched projector/backprojector in an iterative algorithm

Zeng

2019

Chin J Acad Radiol

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“…The computational burden can be reduced if an unmatched projector/backprojector strategy is used, where the projector models the axial compression and the backprojector does not. It has been shown that using an unmatched projector/backprojector in the maximum likelihood expectation maximization (MLEM) algorithm is valid under suitable conditions 14,15 and it has been proposed before to reduce the reconstruction times by using a full model in the forward projector and a simpler one in the backprojector. [16][17][18][19] When axial compression is applied, the point spread function (PSF) is extremely shift-variant for high span values.…”

Section: Introductionmentioning

confidence: 99%

Assessment of the impact of modeling axial compression on PET image reconstruction

Belzunce

Reader

2017

Medical Physics

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Purpose: To comprehensively evaluate both the acceleration and image-quality impacts of axial compression and its degree of modeling in fully 3D PET image reconstruction. Method: Despite being used since the very dawn of 3D PET reconstruction, there are still no extensive studies on the impact of axial compression and its degree of modeling during reconstruction on the end-point reconstructed image quality. In this work, an evaluation of the impact of axial compression on the image quality is performed by extensively simulating data with span values from 1 to 121. In addition, two methods for modeling the axial compression in the reconstruction were evaluated. The first method models the axial compression in the system matrix, while the second method uses an unmatched projector/backprojector, where the axial compression is modeled only in the forward projector. The different system matrices were analyzed by computing their singular values and the point response functions for small subregions of the FOV. The two methods were evaluated with simulated and real data for the Biograph mMR scanner. Results: For the simulated data, the axial compression with span values lower than 7 did not show a decrease in the contrast of the reconstructed images. For span 11, the standard sinogram size of the mMR scanner, losses of contrast in the range of 5-10 percentage points were observed when measured for a hot lesion. For higher span values, the spatial resolution was degraded considerably. However, impressively, for all span values of 21 and lower, modeling the axial compression in the system matrix compensated for the spatial resolution degradation and obtained similar contrast values as the span 1 reconstructions. Such approaches have the same processing times as span 1 reconstructions, but they permit significant reduction in storage requirements for the fully 3D sinograms. For higher span values, the system has a large condition number and it is therefore difficult to recover accurately the higher frequencies. Modeling the axial compression also achieved a lower coefficient of variation but with an increase of intervoxel correlations. The unmatched projector/backprojector achieved similar contrast values to the matched version at considerably lower reconstruction times, but at the cost of noisier images. For a line source scan, the reconstructions with modeling of the axial compression achieved similar resolution to the span 1 reconstructions. Conclusions: Axial compression applied to PET sinograms was found to have a negligible impact for span values lower than 7. For span values up to 21, the spatial resolution degradation due to the axial compression can be almost completely compensated for by modeling this effect in the system matrix at the expense of considerably larger processing times and higher intervoxel correlations, while retaining the storage benefit of compressed data. For even higher span values, the resolution loss cannot be completely compensated possibly due to an effective null space in the system. The u...

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Model-Based Guided Wave NDE: The Evolution of Guided Wave NDE from “Magic” to “Physically Based Engineering Tool”

Cho

2012

J Nondestruct Eval

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Theoretical Investigation on an Unmatched Backprojector for Iterative Reconstruction in Emission Computed Tomography

Cited by 4 publications

References 0 publications

Counter examples for unmatched projector/backprojector in an iterative algorithm

Counter examples for unmatched projector/backprojector in an iterative algorithm

Assessment of the impact of modeling axial compression on PET image reconstruction

Model-Based Guided Wave NDE: The Evolution of Guided Wave NDE from “Magic” to “Physically Based Engineering Tool”

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