Crystal Identification in Dual-Layer-Offset DOI-PET Detectors Using Stratified Peak Tracking Based on SVD and Mean-Shift Algorithm

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1 2502 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 63, NO. 5, OCTOBER 2016 Crystal Identification in Dual-Layer-Offset DOI-PET Detectors Using Stratified Peak Tracking Based on SVD and Mean-Shift Algorithm Qingyang Wei, Tiantian Dai, Tianyu Ma, Yaqiang Liu, and Yu Gu Abstract An Anger-logic based pixelated PET detector block requires a crystal position map (CPM) to assign the position of each detected event to a most probable crystal index. Accurate assignments are crucial to PET imaging performance. In this paper, we present a novel automatic approach to generate the CPMs for dual-layer offset (DLO) PET detectors using a stratified peak tracking method. In which, the top and bottom layers are distinguished by their intensity difference and the peaks of the top and bottom layers are tracked based on a singular value decomposition (SVD) and mean-shift algorithm in succession. The CPM is created by classifying each pixel to its nearest peak and assigning the pixel with the crystal index of that peak. A Matlabbased graphical user interface program was developed including the automatic algorithm and a manual interaction procedure. The algorithm was tested for three DLO PET detector blocks. Results show that the proposed method exhibits good performance as well as robustness for all the three blocks. Compared to the existing methods, our approach can directly distinguish the layer and crystal indices using the information of intensity and offset grid pattern. Index Terms Crystal position map, DOI-PET detector, mean-shift, peak tracking, singular value decomposition (SVD). I. INTRODUCTION SILICON photomultipliers (SiPMs) have many advantages, including magnetic-field insensitivity, compact size, high gain, high quantum efficiency, low working voltage and good timing performance [1], [2]. They are promising sensors for positron emission tomography (PET) systems. Our group is developing a SiPM based brain-pet system which is planned to be inserted into a 3T clinical magnetic resonance imaging (MRI) system. The brain-pet insert scanner should have a smaller ring diameter than a stand-alone brain-pet system due to the limited space of the MRI s patient port. Manuscript received March 11, 2016; revised June 1, 2016; accepted July 5, Date of publication July 12, 2016; date of current version October 11, This work was supported in part by Fundamental Research Funds for the Central Universities (No. FRF-TP A1),NationalNatural Science Foundation of China (No ), National Natural Science Foundation of China (No ), and Tsinghua University Initiative Scientific Research Program (No ). Q. Wei and Y. Gu are with the School of Automatic and Electrical Engineering, University of Science and Technology Beijing, Beijing , China ( weiqy@ustb.edu.cn; guyu@ustb.edu.cn). T. Dai is with the Department of Radiation Oncology, China-Japan Friendship Hospital, Beijing , China. T. Ma and Y. Liu are with the Key Laboratory of Particle & Radiation Imaging, Ministry of Education and Department of Engineering Physics, Tsinghua University, Beijing , China. Digital Object Identifier /TNS The restricted geometry design leads to high probability of obliquely incident gamma-rays which increases the parallax error. Therefore, the depth-of-interaction (DOI) encoding ability of the detectors is critical for highperformanceimaging. DOI information can be obtained by multiple ways such as light sharing technique [3], dual-end readout [4] and pulse shape discrimination [5], [6], etc. In our project, we have developed DOI detector blocks using dual-layer offset (DLO) design, which is a kind of light sharing technique [7]. The DLO design has better sampling density than the conventional design and would achieve better image performance for a whole system [8]. One traditional way for PET detectors to decode the positions is using the Anger-logic. Each event has a coordinate (x, y) whichisapseudo-positionofthegammainteraction [9]. A crystal position map (CPM) also called look up table (LUT) should be pre-generated from the detector s flood histogram to assign each (x, y) toaspecificcrystalindex. The accuracy of the CPMs is crucial to the detector s intrinsic spatial resolution. The most primitive method to generate the CPM is manual segmentation. However, it is not accurate enough and time consuming, especially for a whole system consisting of thousands and thousands of crystals. Several automatic or semiautomatic approaches were proposed to perform an appropriate segmentation of the flood histograms. A statistical model based on likelihood boundaries of Gaussian mixture models (GMMs) was presented by Stonger [10] and Yoshida [11]. Approaches based on neural networks were implemented by Hu [12] and Wang [13]. A Fourier template and non-rigid registration based method was proposed by Chaudhari [14], [15]. Moreover, aprincipalcomponentanalysisbasedalgorithm[16]anda probabilistic graphical model based algorithm [17] were also proposed to build CPMs. We also developed a neighborhood standard deviation based algorithm [18] for an animal PET system [19]. However, most of these methods were geared to non-doi detectors. Dealing with DLO detectors, the layers distinction and crystal indices generation would be a problem for these methods. The GMM-based method has been employed for DOI-PET detectors by Yoshida [11]. However, it is time-consuming and impractical for large dimension position histograms, because a large number of parameters for the GMMs must be estimated. In this paper, a novel method using stratified peak tracking is proposed IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 WEI et al.: CRYSTALIDENTIFICATIONINDUAL-LAYER-OFFSETDOI-PETDETECTORS USING STRATIFIED PEAK TRACKING 2503 Fig. 2. One flood histogram of a DLO DOI detector (denoted as I 0, size ). Fig. 1. (a) & (b) One home-made DLO-LYSO array (a top layer and a bottom layer); (c) Schematic illustration of the DLO detector; (d) A home-made SiPM array with two separated 8 8arrays. II. MATERIAL AND METHODS A. The DLO Detector & Flood Histogram One of the home-made DLO-LYSO array is shown in Fig. 1(a) & (b). The crystal with all surfaces polished has a size of mm 3 (SIPAT, China). The top layer (15 15 array, size mm 3 )wasplaced half crystal offset in two dimensions on the bottom layer (16 16 array, size mm 3 )asshowninfig.1(c). Enhanced specular reflector (ESR, 3M) was used between the crystals to achieve high crystal discrimination. The bottom layer was coupled to an 8 8 SiPMarrayasshowninFig.1(d). The SiPM pixel (MicroFB SMT, SensL Inc.) consists of 4774 of µm 2 microcells with a size of 4 4mm 2 and a sensitive area of mm 2.TheSiPMarray has an overall dimension of mm 2 with 0.2 mm gaps between adjacent SiPM elements. The output channels of the SiPM array were directly fed to a front-end ASIC called EXYT [20] and multiplexed by on-chip resistor networks to generate 3 analog outputs including an energy (E) and two positions (X and Y). Two 8 8SiPMarrayswerefabricated on a same printed circuit board to share a same 8 channel ADC chip (AD9637). In this study, only one of them was used. The detector was covered by a light-tight box and worked at room temperature (about 25 C) without cooling and with Fig. 3. Method flowchart description. avoltageof28.5vforsipms.a 22 Na point source with an activity of about 3 µci was placed at about 3 cm from the top of the detector block. Fig. 2 shows the flood histogram with ahalf-houracquisition.thecrystals are clearly distinguished except for a small amount of crystals overlapping at the edges of the block. The crystals in the top layer have more counts than the crystals in the bottom layer due to the gamma-ray attenuation effect. B. Method Flowchart Description AnovelautomaticmethodtogeneratetheCPMsforthe DLO detectors using a stratified peak tracking was developed. The flowchart of the method is described in Fig. 3. The peaks of the top layer are tracked firstly using the following

3 2504 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 63, NO. 5, OCTOBER 2016 Fig. 4. Image I 1,squareofI 0. Fig. 5. Image I 2 :theprincipalcomponentimageofthetoplayer. procedure: 1) the original flood histogram (I 0 ) is squared, the result is denoted as I 1 ;2)theimageI 1 is decomposed using a singular value decomposition (SVD) algorithm, and then a principal component image (PCI) of the top layer is generated using the largest eigenvalue denoted as I 3 ;3) average horizontal and vertical peaks of the projections of the PCI are determined and employed as the initial peaks of the top layer; 4) true peaks of the top layer are tracked by the mean-shift algorithm [21]. Then, the peaks of the bottom layer are tracked as below: 1) a template image of the top layer is created using the peaks of the top layerandagaussiankernel denoted as I 3 ;2)imageI 3 is subtracted from I 0,theresultis denoted as I 4 ;3)initialpeaksofthebottomlayerarecreated using the peaks of the top layer; 4) true peaks of the bottom layer are tracked by the mean-shift algorithm. At last, the CPM is generated using all the peaks with a distance-based method. C. Details of the Program To simplify the description of the following algorithms, we use the specific numbers that the DLO block consists of a array in the top layer and a array in the bottom layer and the flood histogram I 0 with size of pixels. The first step is to increase distinction between the top and bottom layers. The square image I 1 is generated, i.e. I 1 = I 0. I 0.AnexampleofI 1 is shown in Fig. 4, which gives prominence to the top layer. Singular value decomposition and only keeping some components with large eigenvalues has been used in image compression. In this paper, SVD is employed to create a principal component image (PCI) of the top layer. The SVD of I 1 is shown in equation (1). I 1 = U V (1) where, U/V is an matrix formed by the normalized eigenvectors of I 1 I 1 (I 1 I 1 ) associated with the eigenvalues Fig. 6. Projection profiles of I 2 along the X and Y directions. λ 1 λ 2... λ 512,and =diag[σ 1, σ 2...,σ 512 ]is adiagonalmatrix(σ i = λ i ). A new diagonal matrix ( ) only with the largest eigenvalue and the other eigenvalues set to 0 is created, i.e. =diag[σ 1, 0...,0]. ThePCIimageof the top layer I 2 can be created by equation (2). I 2 = U V (2) AtypicalresultofimageI 2,asshowninFig.5,hasaneat lattice, indeed, highlights theaverageverticaland horizontal grid lines of the top layer. Then, the projection profiles of I 2 along the X and Y directions are obtained as shown in Fig. 6. A local maximum identification method is used to find 15 peaks individually from these one-dimensional projections. The method is described as follows: I) the index of the maximum value of the projection is determined; II) the projection around the index is assigned to 0; III) go to step I until finding 15 indices. After all the peak locations are determined, the initial peaks of the top layer are created. An example is shown in Fig. 7. The mean-shift algorithm has been proposed as a method for cluster analysis, which is an iterative procedure that shifts each data point to the centroid position of data points in its neighborhood [21]. There are different kinds of kernels can

4 WEI et al.: CRYSTALIDENTIFICATIONINDUAL-LAYER-OFFSETDOI-PETDETECTORS USING STRATIFIED PEAK TRACKING 2505 Fig. 7. The crosses represent the initial peaks of the top layer. be employed for the mean-shift algorithm. In this paper, the simplest one so-called flat kernel is used. Let K be a flat kernel that is the characteristic function of the λ-ball as shown in equation (3) (λ = 6inthefollowingcalculation): { 1 if x λ K (x) = (3) 0 if x >λ The sample mean at point x is calculated by equation (4): K (s x)i 1 (s)s s S m(x) = (4) K (s x)i 1 (s) s S where, s is any point position in the 2D coordinate set S, and I 1 (s) is the intensity at point s. Thedatapointx is moved to its sample mean m(x), i.e.x is updated by m(x). Thismovement is repeated until convergence. To increase the robustness of the algorithm, an average mean-shift is performed in advance. The initial peaks are divided into 3 3groupswith5 5initialpeaksineach group. The center position of each group is iterated using equation (5), and the initial peak positions of each group are iteratively updated using equation (5): c j = i=1 25 x i, j m(c j ) = 1 m(x i, j ) 25 i=1 x i, j = x i, j + (m(c j ) c j ), i = 1 25; j = 1 9 (5) where, c j is the center position of group j, andx i, j (i = 1-25) are the peak positions of group j. After this step, all the peak positions are continually iterated by mean-shift algorithm individually until convergence. At last, each initial peak of the top layer is moved to its true peak position. Fig. 8(a) shows the mean-shift procedure and Fig. 8. (a) The mean-shift procedure, initial peaks were converged after several iterations. (b) Identification of the true peaks of the top layer using the mean-shift algorithm. Fig. 8(b) shows the mean-shift result of the example flood histogram. A binary image with an intensity of 1 at the true top-peak locations and 0 otherwise is created. The binary image is convolved with a 2D spatial Gaussian filter. The convolved image is denoted as I 3 as shown in Fig. 9(a). The intensity of I 3 is adjusted to 70% of I 0.Then,anewimagedenotedasI 4 is obtained by subtracting I 3 from I 0,whichmainlyincludes the responses of the bottom layer as shown in Fig. 9 (b). If the peaks of image I 4 are clearly distinguished, the same process can be used for assigning the initial peaks of the bottom layer. As the crystal responses at the edges of the bottom layer cannot be well distinguished, a more robust method is introduced using the peaks of the top layer to locate the initial peaks of the bottom layer. Due to the half crystal offset design, the crystal responses in the top and bottom layers are in a staggered arrangement. Based on this prior knowledge,

5 2506 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 63, NO. 5, OCTOBER 2016 Fig. 9. (a) Convolved image I 3 with a 2D Gaussian filter; (b) Image I 4 which equals to I 0 -I 3. the algorithm is developed as follows: 1) the center of each adjacent four true peaks of the top layer is assigned as one initial peak of the bottom layer. From this, initial peaks of the bottom layer could be created as shown in the dotted box in Fig. 10(a). 2) The initial peaks at the edges are then determined and extrapolated from the coordinate information of the newly generated peak-matrix. For example, for the upper edge peaks in the first row, their column coordinates are assigned as those of the second row and the row coordinates are subtracted 20 from the second row. The results of the initial peaks of the bottom layer are shown in Fig. 10(a). The meanshift algorithm is also employed to identify the true peaks of the bottom layer, as shown in Fig. 10(b). After this step, all the peaks of the crystal responses are tracked and each peak includes the information of the layer, Fig. 10. (a) Initial peaks of the bottom layer (black cross showed in I 4, center peaks are shown in the dotted box); (b)true peaks of the bottom layer using mean-shift (black cross showed in I 4 ). column and row number. To generate the CPM, distances from each pixel in the flood histogram to the peaks are calculated. Each pixel is assigned to a unique crystal with the minimum distance value. To speed up the algorithm, a rough estimation process is proposed. For the pixel (i, j), its estimated peak index is [round(i 15/512), round( j 15/512)] in the top layer and [round(i 16/512), round( j 16/512)] in the bottom layer. Only the distances for a 5 5peakarraywiththecenterof the estimated peak are calculated in the top and bottom layers. D. Manual Correction None of the automatic segmentation methods can completely succeed for all flood histograms. Manual correction should be added for minor modification of the incorrect

6 WEI et al.: CRYSTALIDENTIFICATIONINDUAL-LAYER-OFFSETDOI-PETDETECTORS USING STRATIFIED PEAK TRACKING 2507 parts. In our automatic methods, the peaks of the top layer and the bottom layer may converge to an error position in the situation of flood histogram with serious distortion. In this work, an easily operable graphical user interface (GUI) program including the automatic algorithm and the manual correction procedure was developed based on Matlab2012a. There are two interaction steps in the manual correction procedure: 1) after the true peaks of the top layer are tracked, the flood histogram with the identified peaks (displayed as crosses) is visually inspected by the operator. If any of them is uncorrected, the operator only needs to click on the point near the crystal response without peak (cross) on the flood histogram with the mouse, the nearest initial peak to the clicked point will be replaced with the click point. Then, the mean-shift algorithm is carried out to move this point to its desired location; 2) the same process is carried out to the bottom layer. A. Crystal Position Maps III. RESULTS The proposed method was tested for 3 home-made DLO PET detector blocks with energy resolutions around 15%. All the CPMs could be generated automatically. The average computation time for generating a CPM is 55.6 s on a Lenovo laptop computer (Intel(R) Core(TM) 8.0 GB RAM), and only 0.74 s is expended for the stratified peak tracking. Fig. 11 shows the segmentation results of the three detector blocks. The segmentation boundaries surrounding the peaks display the pixels with the equivalent distances to its two closest peaks. The segmentation results were checked visually, and 100% could be accepted without further manual modification. IV. DISCUSSIONS In this paper, an automatic crystal position map generating approach was proposed using a stratified peak tracking method based on the SVD decomposition and mean-shift algorithm. AsimpleGUIprogramincludingtheautomaticalgorithmand the manual correction procedure was developed. Compared to the other methods, our approach is an optimal design for duallayer offset PET detectors, which can directly distinguish the layer information and crystal indices by using the intensity difference and offset grid pattern. The algorithm procedure presented here is a practical implementation for our built-up DLO detectors with same length crystals for both layers (7 mm), which leads to the count distinction between the two layers. Some groups have provided DLO detectors with longer bottom crystals than top crystals to get similar crystal efficiency for both layers [22]. For this design, the layers cannot be separated in the flood histogram with the source irradiating from the top of detectors. Thus the algorithm will fail. However, since Lutetium based scintillators are the most widely used materials in PET detectors, and the Lutetium intrinsic radiation could be used as an approximate flood source [23], our algorithm could work with a minor modification. The bottom layer has a higher Lutetium background sensitivity than the top layer, thus the bottom peaks can be Fig. 11. Segmentation results of the three detector blocks. tracked firstly. Even for a non Lu-based detector module, the algorithm will also be workable by irradiating a source from the bottom side.

7 2508 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 63, NO. 5, OCTOBER 2016 Moreover, the presented program can also be employed to generate CPMs for single layer detectors by using one time of SVD and mean-shift procedure. V. CONCLUSIONS In conclusion, we developed an optimal algorithm for the DLO PET detectors. The algorithm produced accurate delineation of crystals from flood histograms obtained from three DLO PET detectors developed in our lab. The proposed method is promising and expected to be applied easily to DLO PET detectors and potentially should facilitate accurate system characterization. More tests will be carried out in the future. REFERENCES [1] E. Roncali and S. R. Cherry, Application of silicon photomultipliers to positron emission tomography, Ann. Biomed. Eng., vol. 39, no. 4, pp , Apr [2] H. S. Yoon et al., InitialresultsofsimultaneousPET/MRIexperiments with an MRI-compatible silicon photomultiplier PET scanner, J. Nucl. Med., vol.53,no.4,pp ,2012. [3] N. Zhang, C. J. Thompson, D. Togane, F. Cayouette, and K. Q. Nguyen, Anode position and last dynode timing circuits for dual-layer BGO scintillator with PS-PMT based modular PET detectors, IEEE Trans. Nucl. Sci., vol.49,no.5,pp ,Oct [4] A. Kishimoto et al., Development of a dual-sided readout DOI-PET module using large-area monolithic MPPC-arrays, IEEE Trans. Nucl. Sci., vol.60,no.1,pp.38 43,Feb [5] C. M. Pepin et al., PropertiesofLYSOandrecentLSOscintillators for phoswich PET detectors, IEEE Trans. Nucl. Sci., vol. 51, no. 3, pp , Jun [6] K. Wienhard et al., The ECAT HRRT: Performance and first clinical application of the new high resolution research tomograph, IEEE Trans. Nucl. Sci., vol.49,no.1,pp ,Feb [7] Q. Wei, S. Wang, T. Xu, Y. Gao, Y. Liu, and T. Ma, Development of an MR-compatible DOI-PET detector module, EJNMMI Phys., vol. 2, p. A4, Dec [8] X. Zhang et al., DevelopmentandevaluationofaLOR-basedimage reconstruction with 3D system response modeling for a PET insert with dual-layer offset crystal design, Phys. Med. Biol., vol. 58, no. 23, p. 8379, [9] Q. Wei et al., Influencefactorsoftwodimensionalpositionmapon photomultiplier detector block designed by quadrant sharing technique, Nucl. Sci. Technol., vol.22,pp ,2011. [10] K. A. Stonger and M. T. Johnson, Optimal calibration of PET crystal position maps using Gaussian mixture models, IEEE Trans. Nucl. Sci., vol. 51, no. 1, pp , Feb [11] E. Yoshida, Y. Kimura, K. Kitamura, and H. Murayama, Calibration procedure for a DOI detector of high resolution PET through a Gaussian mixture model, IEEE Trans. Nucl. Sci., vol.51,no.5,pp , Oct [12] D. Hu, B. E. Atkins, M. W. Lenox, B. Castleberry, and S. B. Siegel, A neural network based algorithm for building crystal look-up table of PET block detector, in Proc. IEEE Nucl. Sci. Symp. Conf. Rec., vol.4. Oct./Nov. 2006, pp [13] Y. Wang, D. Li, X. Lu, X. Cheng, and L. Wang, Self-organizing map neural network-based nearest neighbor position estimation scheme for continuous crystal PET detectors, IEEE Trans. Nucl. Sci., vol. 61, no. 5, pp , Oct [14] A. J. Chaudhari, A. A. Joshi, S. L. Bowen,R.M.Leahy,S.R.Cherry, and R. D. Badawi, Crystal identification in positron emission tomography using nonrigid registration to a Fourier-based template, Phys. Med. Biol., vol.53,no.18,p.5011,2008. [15] A. J. Chaudhari, A. A. Joshi, Y. Wu, R. M. Leahy, S. R. Cherry, and R. D. Badawi, Spatial distortion correction and crystal identification for MRI-compatible position-sensitive avalanche photodiode-based PET scanners, IEEE Trans. Nucl. Sci., vol. 56, no. 3, pp , Jun [16] J. Breuer and K. Wienhard, PCA-based algorithm for generation of crystal lookup tables for PET block detectors, IEEE Trans. Nucl. Sci., vol. 56, no. 3, pp , Jun [17] D. B. Keator and A. Ihler, Crystal identification in positron emission tomography using probabilistic graphical models, IEEE Trans. Nucl. Sci., vol.62,no.5,pp ,Oct [18] Q. Wei et al., Aneighborhoodstandarddeviationbasedalgorithmfor generating PET crystal position maps, in Proc. IEEE Nucl. Sci. Symp. Med. Imag. Conf. Rec., Oct./Nov.2013,pp.1 4. [19] Q. Wei et al., PerformanceevaluationofacompactPET/SPECT/CTtrimodality system for small animal imaging applications, Nucl. Instrum. Methods Phys. Res. A, vol.786,pp ,Jun [20] X. Zhu, Z. Deng, Y. Chen, Y. Liu, and Y. Liu, Development of a 64-channel readout ASIC for an 8 8 SSPM array for PET and TOF-PET applications, IEEE Trans. Nucl. Sci., vol. 63, no. 3, pp , Jun [21] Y. Cheng, Mean shift, mode seeking, and clustering, IEEE Trans. Pattern Anal. Mach. Intell., vol.17,no.8,pp ,Aug [22] C. Thompson et al., Comparison of single and dual layer detector blocks for pre-clinical MRI PET, Nucl. Instrum. Methods Phys. Res. A, vol.702,pp.56 58,Feb [23] Q. Wei, T. Ma, S. Wang, R. Yao, and Y. Liu, Measure PET detector performance with the intrinsic radioactivity of scintillator, in Proc. IEEE Nucl. Sci. Symp. Med. Imag. Conf. Rec., Oct./Nov.2012, pp