Advancements to the planogram frequency–distance rebinning algorithm

Champley, Kyle; Raylman, Raymond R.; Kinahan, Paul E.

doi:10.1088/0266-5611/26/4/045008

Cited by 4 publications

(13 citation statements)

References 24 publications

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“…In these cases, resolution can be artificially enhanced when noise amplification in background sources is not also considered. Using analytical reconstruction methods (e.g., filtered back-projection) requires considerable effort (e.g., [26]) and is not a goal of the PET/X project, so it has not been pursued thus far. In Fig.…”

Section: Discussionmentioning

confidence: 99%

Effects of Detector Thickness on Geometric Sensitivity and Event Positioning Errors in the Rectangular PET/X Scanner

MacDonald

Kinahan

Miyaoka

2013

IEEE Trans. Nucl. Sci.

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We used simulations to investigate the relationship between sensitivity and spatial resolution as a function of crystal thickness in a rectangular PET scanner intended for quantitative assessment of breast cancers. The system had two 20 × 15-cm2 and two 10 × 15-cm2 flat detectors forming a box, with the larger detectors separated by 4 or 8 cm. Depth-of-interaction (DOI) resolution was modeled as a function of crystal thickness based on prior measurements. Spatial resolution was evaluated independent of image reconstruction by deriving and validating a surrogate metric from list-mode data (dFWHM). When increasing crystal thickness from 5 to 40 mm, and without using DOI information, the dFWHM for a centered point source increased from 0.72 to 1.6 mm. Including DOI information improved dFWHM by 12% and 27% for 5- and 40-mm-thick crystals, respectively. For a point source in the corner of the FOV, use of DOI information improved dFWHM by 20% (5-mm crystal) and 44% (40-mm crystal). Sensitivity was 7.7% for 10-mm-thick crystals (8-cm object). Increasing crystal thickness on the smaller side detectors from 10 to 20 mm (keeping 10-mm crystals on the larger detectors) boosted sensitivity by 24% (relative) and degraded dFWHM by only ~3%/8% with/without DOI information. The benefits of measuring DOI must be evaluated in terms of the intended clinical task of assessing tracer uptake in small lesions. Increasing crystal thickness on the smaller side detectors provides substantial sensitivity increase with minimal accompanying loss in resolution.

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Section: Discussionmentioning

confidence: 99%

Effects of Detector Thickness on Geometric Sensitivity and Event Positioning Errors in the Rectangular PET/X Scanner

MacDonald

Kinahan

Miyaoka

2013

IEEE Trans. Nucl. Sci.

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“…When the TOF profile h = 1, (7) becomes the non-TOF planogram formulation [5, 6, 7]. Similar to (4), we can use f̂ to represent the Fourier transform p̂ in (5) as…”

Section: Tof-pet Data Formationmentioning

confidence: 99%

“…The full implementations of all the FORCEs are beyond the scope of the paper. For 3D non-TOF planograms, a different rebinning based on the frequency-distance relationship was implemented in [6, 7]. Here, we perform numerical simulations with a generic 2D dual-panel PET system ( r 2 = 0 and υ = 0) with timing resolution of 300 ps FWHM and crystal size of 1.2 mm.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The non-TOF planogram is a 3D extension of the 2D linogram [22, 21], all the LORs passing through a fixed point inside the field of view (FOV) lie on a two-dimensional plane in the four-dimensional space of the non-TOF planograms [5]. For 3D non-TOF planograms, the Fourier rebinning using the frequency-distance relationship was developed by Champley et al [6, 7]. The Fourier rebinning based on John's equation in the local detector coordinates was developed by Defrise and Liu [17], Kao et al [32].…”

Section: Introductionmentioning

confidence: 99%

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Fourier rebinning and consistency equations for time-of-flight PET planograms

Defrise

Matej

et al. 2016

Inverse Problems

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Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF) information can be a promising solution to reduce these artifacts. The TOF planogram is the native data format for dual-panel TOF PET scanners, and the non-TOF planogram is the 3D extension of linogram. The TOF planograms is five-dimensional while the objects are three-dimensional, and there are two degrees of redundancy. In this paper, we derive consistency equations and Fourier-based rebinning algorithms to provide a complete understanding of the rich structure of the fully 3D TOF planograms. We first derive two consistency equations and John's equation for 3D TOF planograms. By taking the Fourier transforms, we obtain two Fourier consistency equations and the Fourier-John equation, which are the duals of the consistency equations and John's equation, respectively. We then solve the Fourier consistency equations and Fourier-John equation using the method of characteristics. The two degrees of entangled redundancy of the 3D TOF data can be explicitly elicited and exploited by the solutions along the characteristic curves. As the special cases of the general solutions, we obtain Fourier rebinning and consistency equations (FORCEs), and thus we obtain a complete scheme to convert among different types of PET planograms: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF planograms. The FORCEs can be used as Fourier-based rebinning algorithms for TOF-PET data reduction, inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. As a byproduct, we show the two consistency equations are necessary and sufficient for 3D TOF planograms. Finally, we give numerical examples of implementation of a fast 2D TOF planogram projector and Fourier-based rebinning for a 2D TOF planograms using the FORCEs to show the efficacy of the Fourier-based solutions.

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“…In Sec. II, we discuss the implementation of a Monte Carlo simulator of the proposed scanner, the experimental determination of the distribution of the dMiCE crystal pair detector signals over depth, description of three different statistical LOR estimation algorithms, and describe the exact planogram frequency distance rebinning 19 ͑PFDRX͒ image reconstruction algorithm and data correction algorithms that are implemented for this scanner. The physical effects modeled by our simulator are summarized in Table I.…”

Section: Introductionmentioning

confidence: 99%