Zhang, Long

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Ghent University Academic Bibliography

Monte Carlo Based Reconstruction Using ARotator for 2-D PET DataLong ZhangSupervisor(s): Stefaan Vandenberghe, Steven StaelensI. INTRODUCTIONAccurate system modeling is normally per-formed through the System Matrix (SM) inPositron Emission Tomography (PET). The SMcan be calculated analytically or by MonteCarlo (MC) methods. MC methods model de-tector response precisely and lead to better im-age quality when used in a statistical recon-struction method[1]. However,for modern hu-man PET scanners, two problems hinder theuse this method. The first problem lies in thestorage of the huge SM. The second problemis the intensive computational load in simulat-ing the SM. We used a Gaussian rotator [2] tosolve these problems. With the rotator, both theSM storage and SM simulation requirement isgreatly reduced (proportional to the number ofscanner blocks) without loss of image quality.II. METHODS AND MATERIALSA. SymmetriesThe rotator facilitates the utilization of all thein-plane rotational symmetry of a PET scan-ner. In Fig. 1, this symmetry is illustrated. Thevoxel in the rotated grids (in black) contributesthe same to the system matrix element as theone in the original grids (in grey). This resultsin a reduction factor given by the number of de-tector blocks in contrast to a fixed factor of 8 [3]in a non-rotator case. In 3-D case, other sym-metries (i.e. axial translational symmetry [3])remains.—————————————————–L. Zhang is with the ELIS Department, GhentUniversity (UGent), Gent, Belgium. E-mail:Lonzhang.Zhang@UGent.be .Figure 1. Rotational symmetry. The black grid is therotated object grid. The grey grid is the originalone. The contributions to the green LORs fromthe red voxels in both grids are identical, if alldetector blocks are identical.B. System Matrix: Calculation & storageWe used the rotational symmetry for the SMcalculation and storage. When using the sym-metry, any coincidence detection that does notfall into the base SM is rotated to the base SM.In this way the statistics of the SM is improved,thus reducing the total number of coincidencesrequired. In addition, the EGSnrc based codeegs pet is used for SM calculations, which hasbeen reported to be at least two orders of mag-nitude faster than GATE [4]. Only the basesymmetry system matrix is stored. A SM el-ement is represented by a 4 bytes unsigned in-teger, including the SM index and SM value.This leads to a system matrix storage of around4 × Nnon zero bytes, where Nnon zero is thenumber of non-zero elements in the base sym-metry system matrix.C. Image quality evaluationTo evaluate the image quality, we performeda simulation based study. The image qual-0 0.2 0.4 0.6 0.8 10.20.30.40.50.60.70.80.91CRC vs Noise − HotNoiseContrast  Siddon 9.89 mmSiddon 12.43 mmMC 9.89 mmMC 12.43 mmFigure 2. CRC curve for the smallest two hot spots.ity phantom consists of 4 hot lesions (9.89,12.43, 15.43, 19.79 mm in diameter) with 5:1ratio to background, 2 cold lesions (25.4, 31.27mm in diameter) and a background of 204 mm(in diameter). We evaluate the contrast re-covery coefficient characteristics of this algo-rithm. The contrast recovery is measured us-ing the ratio between the mean in the RegionOf Interest (ROI) of the lesions and in the ROIof the background. For hot lesions, it is ex-pressed as Ccontrast = C × HROI/BROI ,where C is the true ratio of hot lesions to thebackground, HROI is the mean in a hot le-sion ROI, BROI is the mean in the backgroundROI. For the cold lesions, it is expressed as:Ccontrast =1−CROIBROI, where CROI is themean in the cold lesion ROI. The noise is eval-uated using the standard deviation in the ROI ofthe background. The results are compared withstandard MLEM using a multi-ray ray-tracing(5 rays) projector.III. RESULTS AND DISCUSSIONSA. Evaluation resultsThe CRC (Contrast Recovery Coefficient)curves of 2-D reconstructions are plotted ver-sus noise (Fig. 2 and Fig. 3). The improve-ment for both hot spots and cold spots is greaterthan 30%. Moreover, In our method, the CRCreaches to its plateau at lower noise level, espe-cially for hot spots (Fig. 2).B. DiscussionThis rotator based algorithm enables the useof rotational symmetries. The symmetries con-0 0.2 0.4 0.6 0.8 100.20.40.60.81CRC vs Noise − ColdNoiseContrast  Siddon 25.4 mmSiddon 31.8 mmMC 25.4 mmMC 31.8 mmFigure 3. CRC curve for the cold spots.tribute the a reduction factor of 28 for both stor-age and simulation time of the SM. The im-age quality evaluation result indicates that theMC based SM is superior to the ray-tracing sys-tem model. However, these improvements areachieved at the cost of significant increase inmemory usage and computational time.IV. CONCLUSION & FUTURE WORKThis proposed methods show superior imagequality with regard to standard MLEM. The useof additional rotational symmetries give thismethod the potential of solving both the SM’sstorage and calculation problem in 3-D modernhuman PET reconstruction. Thus, reconstruc-tion based on MC calculated SM for modernhuman PET systems is achievable. In the fu-ture, this algorithm will be extended into fully3-D reconstruction. Better image qualities canbe expected.REFERENCES[1] M. Rafecas, et al, Use of a Monte Carlo-BasedProbability Matrix for 3-D Iterative Reconstruc-tion of MADPET-II Data, IEEE TNS, vol. 51, no.5, pp. 2597-2605, 2004[2] J. W. Wallis, T. R. Miller, An Optimal Rotator forIterative Reconstruction, IEEE TMI, vol. 16, no.1, pp. 118-123, Feb. 1997[3] C. A. Johnson, et al, A System for the 3D Re-construction of Retracted-Septa PET Data Usingthe EM Algorithm, IEEE TNS, vol. 42, no. 4, pp.1223-1227, Aug. 1995[4] I. Kawrakow, et al, Using EGSnrc within GATE toimprove the efficiency of positron emission tomog-raphy simulations, AAPM 50th Annual Meeting,2008

Monte Carlo based reconstruction using a rotator for 2-D PET data

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Monte Carlo based reconstruction using a rotator for 2-D PET data

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