Preamble

Development and performance evaluation of a 4 -FoV Compton camera based on spherical detector system with hybrid imaging capabilities Huai-Zhong Gao, 1, 2, 3, 4, 5 Li-Ye Liu, 3, 4, 5 San-Qiang Xia, 3, 4, 5 Chong-Yang Wang, 3, 4, 5 Xiao-Long Wang, 3, 4, 5 Heng-Guan Yi, 3, 4, 5 Hua Li, 3, 4, 5 Fa-Guo Chen, 3, 4, 5 and Ming Zeng 1, 2, 1 Key Laboratory of Particle and Radiation Imaging (Tsinghua University), Ministry of Education, Beijing 100084, China Department of Engineering Physics, Tsinghua University, Beijing 100084, China China Institute for Radiation Proctection, Shanxi, Taiyuan 030006, China Shanxi Provincial Key Laboratory for Radiation Safety and Protection, Shanxi, Taiyuan 030006, China CNNC Key Laboratory for Radiation Protection Technology, Shanxi, Taiyuan 030006, China Gamma-ray imaging plays a crucial role in source-term monitoring and consequence management of nuclear power plants. These applications typically involve mapping of spatial radiation distributions consisting of var- ious isotopes. This requires the imaging equipment to achieve not only an 4 field-of-view (FoV), but also an isotropic response within the FoV across a wide energy range. To resolve these issues, we designed and im- plemented a spherical detector system with complete readout electronics to function as a Compton camera with an isotropic FoV and active coded aperture imaging capabilities. This camera system adopts Cerium-doped (Ce:GAGG) scintillator detectors and a multichannel electronics system utilizing application specific integrated circuit (ASIC). Besides Compton imaging, a modified hybrid gamma-ray imaging approach is developed to combine Compton and active coded aperture imaging capabilities, which was not fully explored in previous research. Through systematic evaluations of Compton, coded aperture and hybrid imaging, we have verified that the modified hybrid imaging method can provide enhanced image quality and sensitivity, along with an extended energy range. By applying the modified hybrid imaging technique, the developed camera system achieves fine imaging performance in single- and double-point source imaging scenarios which makes a promising candidate future application in free-moving 3-D radiation imaging to realize the mapping of complex distributions and coverage of large areas

Keywords

FoV, Spherical detector configuration, Compton camera, Active coded aperture imaging, Hybrid gamma-ray imaging

INTRODUCTION

Gamma-ray imaging has been applied in various industries such as nuclear safety and security [ ], nuclear medicine ] and astrophysics [ ]. Two commonly adpoted imag- ing methods are coded aperture imaging [ ] and Comp- ton imaging [ ]. Coded aperture imaging utilizes the photon attenuation of patterned coded masks, making it excel

at low energy ( < 500 keV) [ 40 ]. However, its effectiveness 8

diminishes at higher energies due to the increased penetra- 9

tion of the gamma-ray photons. On the other hand, Comp- ton imaging is advantageous at higher energies (500 keV– a few MeV) due to a relatively higher cross section of the Compton scattering process [ There are also previous studies indicating a good performance of Compton imag- ing within the energy range of 140–500 keV [ makes Compton imaging suitable for scenarios like source-

term monitoring [ 21 , 22 ], decommissioning [ 4 , 23 ], contami- 17

nation remediation and consequence management of nuclear power plants (NPPs) [ ] where typical radioactive nu- clides emit gamma-rays of energies within the energy range of several hundred of keV to several MeV [ ]. Never- theless, these scenarios often require precise localization of radioactive sources within vast areas and mapping possibly

Supported by the National Natural Science Foundation of China (Grant No. 12405223) and Tsinghua University Initiative Scientific Research Pro-

intricate spatial distributions of radioactivity. These distri- butions may either originate from complex spatial distribu- tion of radioactive substances or caused by complex shielding structures [ ]. The integration of contextual sensors and scene data fusion approach provides a viable solution. This advancement leads to the development of gamma-ray imaging systems that are capable of mapping the 3D radiation distribu- tion in real time while moving through the scene [ The utilization of free-moving measurement approach and the mapping of complex source distributions both imply that the gamma-rays may enter the imager from various angles. Thus, the conventional imaging systems with planar configurations

encounter significant limitations in terms of imaging perfor- 36

mance in these scenarios [ ]. Additionally, there is evidence indicating the presence of radioactive isotopes with charac- teristic gamma-ray energies below the effective energy range

of Compton imaging ( > 250 keV) in scenarios like source 40

term monitoring during maintenance and consequence man- 41

agement in NPPs [ 34 – 36 ]. Therefore, apart from attaining an 42

isotropic 4 field of view (FoV) for complex radiation dis- tribution mapping and free-moving measurement, achieving a fine imaging performance across a broad energy range is crucial for the future development of gamma cameras in the aforementioned applications.

In order to enhance the performance of gamma-ray imag- ing in free-moving measurements or mapping complex dis- tributions, Hellfeld et al developed an active coded mask imaging system based on spherical detector configuration ]. Although the detector configuration is optimized to achieve an isotropic 4 FoV, the resulting configuration

is not unique. The system also adopted CdZnTe detectors, 54

which is may not be the most cost-effective choice of de- tection material compared with some novel heavy scintilla- tor materials such as Ce-doped Gd (Ce:GAGG).

Moreover, the Compton imaging capability of this system is not exploited, which leaves the issue of effective imaging across a wide energy range unaddressed.

Kitayama et al also developed coded aperture imager with 4 FoV based on a cost-effective 3-D configuration utilizing Ce:GAGG detectors

and lead cubes [ 38 ]. Nontheless, the uniformity of the system 63

response across the FoV has not been examined, and the ap- plicable energy range of the imager remains undetermined.

To address the aforementioned issues, Liang et al conducted a simulation study on the coded aperture and Compton imag-

ing performance of a more uniformly distributed spherical de- 68

tector configuration with Ce:GAGG sensors [ Unlike the conventional dual-layer configuration with distinct scatter and absorber layers, the spherical configuration enables Comp- ton imaging through the coincidence detection of the detector

units. Additionally, active coded aperture imaging can be per- 73

formed in such configuration through the collimation pattern

formed by the gamma-ray attenuation of the detector units. 75

The isotropic dual-mode imaging capability of such design is verified through Monte Carlo simulations, which enables the capability for gamma-ray imaging in a broad energy range.

However, this design still faces challenges in the limited an- gular resolution of Compton imaging, which can affect the image quality when employed in free-moving 3D distribution mapping.

For gamma-ray imagers with dual-mode imaging capabil- ities like the aforementioned spherical configuration, a great portion of gamma-ray photons are captured via direct pho- toelectric absorption apart from Compton scattering in the energy range of approximately 300 keV to 1 MeV. Along- side the multiple interaction Compton events, the utilization of these single photon interaction events can provide addi- tional information for image reconstruction to achieve hybrid gamma imaging [ ]. This method can be beneficial in im- proving both the angular resolution and the sensitivity of the gamma-ray imager, while enabling imaging at energies be- 250 keV. Previous studies have demonstrated the effec- tiveness of such hybrid imaging method on Compton imagers equipped with passive [ ] or active coded masks [ suggesting that it can achieve a better angular resolution than both single-mode imaging methods. Xu applied this method to a gamma camera with multi-layer planar configuration that possesses 4 FoV for both Compton and active coded aper- ture imaging [ ]. The 4 hybrid imaging capability is val- idated through Monte Carlo simulation [ ]. While method can effectively enhance the imaging performance of Comp- ton imagers with multi-layer configuration while preserving the 4 FoV, it has not yet been tested on a detector config- uration with isotropic 4 FoV. Furthermore, this method has some issues related the convergence in iterative image recon- struction, which will be discussed in sec. . The imperative remains to develop a dedicated and theoretically sound hy-

brid imaging technique for dual-mode gamma cameras with 110

isotropic 4 In this paper, we present the development of a Compton camera based on the spherical detector configuration simi- lar to the one proposed by Liang et al [ , and exploita- tion of hybrid imaging capabilities with the developed cam- . A spherical detector array comprised of Ce:GAGG de-

tector units and a custom multichannel signal processing sys- 117

tem are developed, with slight refinements to the structure of the previously reported configuration to enhance Compton imaging performance. Compton and active coded aperture imaging tests are performed on this camera to evaluate its dual-mode imaging performance. Finally, a modified hybrid gamma-ray imaging method that aligns more closely with the dual-mode hybrid imaging model is developed based on pre- vious research and applied to the developed Compton camera.

This method proves to be effective in enhancing the imag- ing performance of the camera with improved image quality Using this hybrid imaging method, high-resolution and high- sensitivity gamma-ray imaging with isotropic 4 FoV across a wide energy range is achieved on the developed Compton camera.

MATERIALS AND METHODS Imaging system design The imaging system reported in this paper consists of a detector system based on spherical configuration, a multi-

channel frontend electronics system based on application spe- 136

cific integrated circuit (ASIC) and a backend electronics sys- 137

tem that employs field programmable gate array (FPGA). A schematic illustration of the system composition is given in Unit 1 Signal transferring module Unit 2 Detector unit (8 units total)

Frontend electronics based on ASIC

Backend electronics based on FPGA

Scintillator (Ce:GAGG) processing software Unit 1 Signal transferring module Unit 2 (8 units total) (10 modules total)

The detector system consists of 80 detector units arranged 141

in a configuration similar to the design proposed by Liang

et al [ 37 ]. The positioning of each detector unit is derived 143

with the same strategy as Liang et al, with minor adjustments

in the orientation of each unit for convenience in the design 145

of mechanical supporting structure. Since the geometry of 146

the system and the spatial resolution of the detector unit can 147

significantly influence the angular uncertainty of Compton 148

measurements [ ], the configuration of the detector array is

slightly adjusted to ensure a good intrinsic Compton imag-

ing performance . This process involves fine-tuning of the key 151

structural parameters, including sphere radius and crystal based on their impact on the imaging performance of the Compton camera as well as the engineering constraint for future expansion to free-moving 3-D imaging A constrained camera weight is demanded for such applications that require handheld measurements [ ] or drone-mounting operations ], thereby limiting the total weight of the crystals. How- ever, an overly limited crystal mass leads to reduced detection efficiency due to the small crystal size. Following the designs of Compton cameras in previous studies [ ], a weight limit of 1 kg for the crystals is established, which corresponds to

a crystal size of l c = 12 mm. On the other hand, the sphere 163

radius influences both angular resolution and detection effi- ciency of the Compton camera. While the angular resolu- tion is directly determined by the sphere radius and is not subject to further optimization once is fixed, the detection efficiency can be further enhanced by adding additional de-

tector units to fill the interval in the setup after determining 169

. Since this study focuses on the development of a first- generation prototype, imaging resolution is selected as the principal metric for the refinement of structural parameters.

An upper limit of ARM UL = 20 ◦ is adopted for the angular 173

resolution measure (ARM) based on prior studies [ Additionally, a larger sphere radius necessitates a heavier sup- porting structure and casing, thereby impacting the weight of

the camera. Thus, an upper limit of r d ≤ 15 cm is applied 177

in reference to existing studies [ ]. With the selection criteria and engineering constraints established, Monte Carlo simulations of the detector system are performed using the Geant4 toolkit [ ] to evaluate the angular resolution and de- tection efficiency for Compton imaging across various values of the sphere radius, ranging from 7 cm (determined by the geometric constraint) to 15 cm with a step size of 1 cm. The results are displayed in Fig. . Considering that the detection

efficiency decreases with increasing radius, the minimum ra- 186

dius that satisfies ARM+ σ ARM ≤ ARM UL is selected as the 187

final value, with representing the standard deviation of the ARM values. Such selection criteria give the result of

r d = 10 cm, which specifies the refined structure values along 190

with the previously determined crystal size of l c = 12 mm . 191

This specific configuration is expected to achieve an angular resolution of ˜14 when measuring the 662 keV gamma-ray emitted from a point source.

Based on the refined configuration, the detector system is

fabricated. Each detector unit comprises a 12 × 12 × 12 mm 3 196

Ce:GAGG crystal coupled to a 6 mm silicon photomultiplier (SiPM, ONSEMI MicroFJ-60035-TSV) mounted on a circuit board and an aluminum shell securing the crystal to the SiPM circuit board. The average energy resolution of the detector

units is (7 . 96 ± 0 . 27) % at 662 keV with the best single- 201

channel resolution of 7.29 % and the worst value of 8.94 %

as depicted in Fig. 3 [FIGURE:3] . Additionally, a plastic mechanical frame 203

is designed and implemented to precisely position and orient

each of the 80 detector units according to the refined config- 205

uration. The detector units are divided into 10 groups, and 206

the SiPM high voltage (HV) input and signal output wiring (Color online) The variation of (a) ARM and (b) detection efficiency against sphere radius derived from the Monte Carlo simulations.

of the 8 adjacent units in each group are connect to a des- 208

ignated signal transferring unit. These connections are then 209

consolidated into a single cable that connects to the electron- ics system, effectively preventing any potential wiring con- gestion that could arise from numerous input and output chan- nels. The developed spherical detector system is depicted in

In order to handle the signals from the 80 detector units, 215

a multichannel signal processing frontend electronics system 216

is developed. The system is composed of three 32-channel ASICs, with 80 channels for signal processing along with 16 redundant channels for backup. Each channel is processes and digitizes the input signal independently to acquire both the amplitude and the generation time of the signal. Subse-

quently, the data is relayed to the backend electronics sys- 222

tem based on FPGA. At the backend electronics, a global 223

timestamp is added to the data in order to identify coinci- dent events. The processed data is packaged for transmission to the on-board computer to check for temporal coincidence, and perform Compton event reconstruction as well as image

reconstruction. The developed electronics system is depicted 228

in Fig.

Imaging methods The primary imaging modality of the developed gamma camera is Compton imaging. Additionally, the feasibility of applying active coded aperture imaging on the adopted spher- ical configuration has been proved by Hellfeld et al [ ] and Liang et al [ ]. Therefore, the capability to perform active coded aperture imaging is also validated for the developed Compton camera. Moreover, a modified hybrid gamma imag- ing method is devised to further enhance the imaging perfor- mance of the camera. Based on the methods from previous re- searches, this method effectively combines the Compton and active coded aperture imaging modalities in order to achieve high-quality imaging across a wide energy range ( 59.5 keV-

1.3 MeV)

Compton imaging. Compton imaging has diverse appli- cations in fields such as astrophysics, medical imaging, radi- ation protection and nuclear security. It utilizes the Comp- ton scattering process to capture direction information of the gamma-ray photons, which enables image reconstruction through back-projection. When an incident photon of energy

E 0 undergoes Compton scattering in a detector unit, it cre- 250

ates a Compton event by depositing an amount of energy,

in that unit, with the remaining energy fully collected by one 252

or a few other detector units. With these energy depositions 253

recorded by the detector units, the scatter angle, θ , of the inci- 254

dent photon can be determined using the well-known Comp- ton scattering formula,

cos( θ ) = 1 + m e c 2

where is the rest mass energy of an electron. The scattering angle indicates the angle between the directions of the incident and the scattered photons. While the direction of the scattered photon can be determined from the relative

displacement of the detector units that recorded the first and 262

second interactions, the direction of the incident photon can- not be pinpointed with the obtained information. Instead, the possible directions of the incident photon are described with

a conical surface, referred to as the Compton cone. After ac- 266

cumulating a sufficient number of Compton events, the corre- sponding Compton cones are then back-projected onto the 4 spherical image space surrounding the camera. The intersect- ing point of these cones denotes the position of the radioactive source.

Since the difference in occurring times between the inter- actions of a Compton event amounts to around 120–670 coseconds in the adopted configuration, directly establishing the order of these interactions via the time-of-flight method requires specifically designed camera systems, as exempli- fied by TOF-PET systems that utilize GAGG or GFAG scin-

tillators and customized electronics with timing resolutions 278

of 300–400 ps [ ]. However, such direct determination can- not be achieved with the developed camera system, as the slow output channel of the SiPM is utilized to achieve bet- ter energy resolution, which reduces the slope of the rising edge in the signal . Thus, the order of interaction is deter- mined using the methods proposed by Boggs et al [ ], with distinct methods for the determination of two-interaction and multiple-interaction sequences.

Verification tests with Monte Carlo simulations indicates that such methods can achieve a correct-sequence rate of 67.5 % for two-interaction events, and 54.3 % for multiple-interaction events that only accounts for ˜3 % of total events.

With the ordering of the interactions determined, the Compton events can be used for image reconstruction. For the

reported camera, the list mode-maximum likelihood expecta- tion maximization (LM ML-EM) algorithm [ ] is adopted,

λ ( l +1) j = λ ( l ) j s C j

denoting the estimated intensity of source pixel

j on the 4 π spherical image space after iteration l , j = 297

, ..., M being the sensitivity matrix element which represents the probability that a photon emitted from source pixel is detected anywhere in the camera in the form of Compton events, being the angular measurement uncer-

tainty of Compton event i , i = { 1 , 2 , ..., N } , and t C ij being the 302

system matrix element that describes the probability of pro- ducing event (assuming that the first interaction is recorded

by detector unit p) given an photon emitted from source pixel 305

. The system matrix element is derived with [

t C ij = ε C ij ∥ d pj ∥ 2 · K ( β | E 0 ) · 1 �

where is the probability of a photon emitted from source

pixel j being detected by detector unit p via Compton scatter- 309

is the distance between source pixel and detec-

tor unit p , β is the corresponding scatter angle for a photon 311

emitted from source pixel to generate event the Klein-Nishina formula describing the Compton scattering cross section [ ], while are the angular measurement uncertainties caused by detector energy resolu-

tion, doppler broadening of Ce:GAGG and detector spatial 316

resolution, respectively. These angular uncertainties are de- termined using the method reported in Wu et al [ Coded aperture imaging.

The coded aperture imaging

technique relies on the mutual attenuation of photons among 320

detector units to form effective patterned projections that is 321

essential for image formation. These projections, determined by the system response of the configuration, are crucial for the image reconstruction process. To accurately determine the system response, Monte Carlo simulations of the devel- oped camera are conducted using the Geant4 toolkit. A total of 5762 directional points on the 4 image space are selected following the same strategy reported by Liang et al [ ensure a fine precision in the derived system response.

strategy is achieved by adding points uniformly to the icosa- 330

hedron structure. It is accomplished through two distinct op- erations: a ”bisector point addition” step that adds the bisec- tor points of the arcs formed by projecting the triangle edges onto the spherical surface, and a ”trisector point addition” that adds trisector points of these arcs. The required point set for the simulation is generated by performing three consecutive bisector point addition steps followed by one trisector point addition step. This results in a precision of 2.64 for the simulated system response matrix, which is defined by the angular distance in the neighboring directional points in the set. To facilitate future extension to 3-D imaging applications that require near-field image reconstruction, the simulations are performed using near-field point sources as opposed to the commonly used far-field sources.

Near-field point sources with various energies are placed at each selected point at spec-

ified distances to record the count of each detector unit in the 346

simulation. A depiction of the obtained system response is portrayed in Fig.

It should be noted that the detection effi- ciency in Fig. is derived by first summing the total number

of full-energy absorption events over the 80 detector units, 350

then dividing the obtained total number of full-energy events by the total number of incident photons.

With the full system response generated, the coded aperture image reconstruction can be performed. ML-EM algorithm is also employed for the coded aperture imaging,

λ ( l +1) j = λ ( l ) j s A j

where P denotes the total number of detector units, s A j = 357 � P p =1 ε A pj is the absorption sensitivity matrix element that de- 358

notes the probability that a photon emitted from source pixel is detected anywhere in the camera in the form of single- interaction events, is the system response matrix element derived from the simulation, and is the single-interaction

full-energy event count of detector unit p . In practice, the full- 363

energy events are picked out by performing Gaussian fits on the full-energy peaks in the spectra collected by each detec-

tor unit to obtain its center µ p and standard deviation σ p , and 366

setting the energy window for event selection to [

µ p + 3 σ p ] for each detector unit. This energy cut also serves 368

as the background subtraction method for the camera.

Hybrid imaging. To further enhance the imaging perfor- mance and extract additional physical information by effec-

tively combining the Compton and coded aperture data, a hy- 372

brid gamma imaging method is developed. Lee et al initially 373

introduced an approach for the imaging reconstruction of hy- brid imaging data based on the ML-EM algorithm [

λ ( l +1) j = λ ( l ) j s A j + s C j

ε A pj C A p � M k =1 ε A pj λ ( l ) j

t C ij � M k =1 t C ij λ ( l ) j

This approach has been successfully applied to a dual- mode camera with a coded mask. However, its applicability to cameras that utilizes active masks is limited. This is due to the coded aperture image requiring a greater number of it- erations to converge compared to the Compton image in such

camera setups [ 42 , 51 ]. Thus, synchronized iteration between 382

the two modalities may not be appropriate. Apart from the issue with the rate of convergence, the algorithm described in Eq. essentially combines the two images that are cor- rected based on the Compton and coded aperture data, with

(a) 60 keV, (b) 356 keV, (c) 662 keV and (d) 1274 keV gamma-rays generated via simulation. the weighting factor determined by the detection efficiency of the corresponding modality,

λ ( l +1) j = s A j s A j + s C j · λ ( l ) j s A j

ε A pj C A p � M k =1 ε A pj λ ( l ) j

t C ij � M k =1 t C ij λ ( l ) j ,

In dual-model cameras utilizing active masks, the detection efficiency of single-interaction typically surpasses the Comp-

ton efficiency significantly. This causes the image derived us- 392

ing Eq. to closely resemble the image reconstructed solely with coded aperture data, failing to effectively combine the data from both modalities. To address these issues, Xu in- troduced a hybrid imaging method for cameras that equipped solely with active masks [ ]. Instead of simultaneously in- corporating data from both modalities in each iteration for image correction, this method involves correcting the image with coded aperture data multiple times within each itera- tion step. This additional iterations for image correction (re- ferred to as ”sub-iteration” from here on) aims to align the convergence rate of the two modalities. Apart from the sub- iterations, the algorithm substitutes the weighting factors of the corrected images with an adjustable parameter. The itera- tive process of the algorithm can be expressed as Algorithm The parameter represents the total iterations for the recon- struction, denotes the number of sub-iterations conducted in each iteration step, and denotes the adjustable weighting

factor. Additionally, the initial value λ (0) j can be set as either 410

the image reconstructed using simple back projection algo-

rithm or uniform across the image space. Although the fea- 412

Algorithm 1: Iteration process of hybrid imaging Begin sub-iteration;

λ A , ( r ) j = λ A , ( r − 1) j

sibility of the aforementioned algorithm for dual-mode imag- ing systems with active masks has verified via Monte Carlo simulations [ ], a substantial drawback of the algorithm is identified in the coded aperture sub-iterations. Despite tak- ing the weighted average of the Compton and coded aper- ture images to compensate for the discrepancies between the two modalities, the coded aperture sub-iterations adopted the same iteration formula as the single modality case. This for- mula is derived from the single modality measurement model for coded aperture imaging. It focuses solely on optimiz- ing the logarithmic likelihood of the coded aperture measure- ments rather than the combined log-likelihood of both coded aperture and Compton measurements. The oversight of ad- ditional information brought by the Compton dataset during the sub-iterations leads to a divergence from the intended search direction derived from the dual-modality measurement model. This deviation accumulates with each sub-iteration and results in the failure to optimize the dual-modality log- likelihood, which serves as the objective function for the op-

timization. It may even lead to a decreasing value of the ob- jective function during the sub-iterations. Consequently, the existing hybrid imaging method can perform poorly in some circumstances, exhibiting inferior results in terms of image quality compared to coded aperture imaging on the developed camera, as can be seen from the results in sec.

In order to address the issues with the existing hybrid imag- ing method in image quality , a modified algorithm is devel- oped based on the existing framework. Aimed at achieving a better applicability in a wide energy range (300 keV–1 MeV) and for various camera configurations, we focus on improv- ing the compatibility of the coded aperture sub-iterations with the dual-modality measurement model. The imaging model can be expressed with the combined possibility of acquiring two independent sets of measurements both subject to Pois- son statistics. These measurements involves the full-energy

event counts X in each detector unit and list-mode Compton 448

events with corresponding counts , from a given source distribution Hybrid Coded Compton

j =1 z ij p ( A i ) t C ij λ j � M k =1 s C k λ k

· ( T � M k =1 s C k λ k ) N

N ! e − T � M k =1 s C k λ k , (7) 451

where denotes the number of photons emitted from

source pixel j and contribute to the counts in detector unit 453

denotes the contribution of the photons emitted from source pixel to event is the measurement time, is a likelihood term derived when applying Bayes’ rule and is irrelevant to the iteration formula [ ]. From this model, the log-likelihood can be derived ) = ln( Hybrid

j =1 X pj ln( t A pj λ j )

j =1 z ij ln( t C ij λ j ) −

j =1 ( s A j + s C j ) λ j ,

Note that the terms that remain constant during the itera- tions are discarded. Then the E-step of the ML-EM algorithm is applied by replacing the variables with their ex- pected values under the reconstructed source distribution at the current iteration

j =1 E ( X pj | λ ( l ) ) ln( t A pj λ j )

j =1 E ( z ij | λ ( l ) ) ln( t C ij λ j )

j =1 ( s A j + s C j ) λ j ,

The iteration formula can then be derived by setting the gradient of the objective function to 0, which leads to Eq. . Based on this hybrid imaging model, the iteration formula of the sub-iterations in Algorithm can be modified accordingly. Given that only the coded aperture estimation of the source distribution is updated during the sub-iterations, while the Compton estimates remain unchanged, the expected values of utilized at the E-step should correspond to the es- timated source distribution before applying the sub-iterations, . With this modification, the objective function for the sub-iterations can be expressed as

Q ( λ | λ ( l ) , λ A , ( r − 1) ) =

) ln(

j =1 E ( z ij | λ ( l ) ) ln( t C ij λ j )

j =1 ( s A j + s C j ) λ j ,

The modified iteration formula can then be derived by set- ting the gradient of Eq. to 0,

t C ij (∆ θ i ) − 1 � M k =1 t C ij λ ( l ) j

Finally, the modified hybrid image reconstruction algo- rithm is given by substituting the formula of the sub-iterations in Algorithm with Eq. . It should be noted that the modi-

fied algorithm may not perform well in the initial stages of the 484

reconstruction process (i.e. the first few iterations) since the Compton estimation of the source distribution may undergo rapid changes. This may cause the coded aperture estimates to be corrected to inaccurate values when applying Eq.

Thus, the original formula in Algorithm is retained in the first iteration.

RESULTS

The dual-mode and hybrid imaging performance of the de- veloped Compton camera is evaluated using various radioac- tive isotopes with gamma-ray energies ranging from 60 keV to 1.274 MeV. A list of radioactive sources used for the per- formance evaluation is provided in Table For brevity, re- sults from the 511 keV line of the isotope are excluded to avoid redundancy with the of the 662 keV gamma-ray data.

Data is collected under two distinctive scenarios: one involv- ing measurements with a single point-like radioactive source

and the other combining the data from two measurements of 501

the same point-like radioactive source placed at different lo-

cations with a predetermined opening angle. The single point 503

source data serves to validate the core functionality of the de- veloped camera to perform Compton, active coded aperture and hybrid imaging, as well as to assess the sensitivity of dif- ferent imaging methods. On the other hand, the double point source data is adopted for the systematic evaluation of the imaging resolution of the two single-modality imaging meth- ods and for comparing image quality between the proposed

modified hybrid imaging technique and existing methods. 511

The verification of basic functionality for the developed camera is conducted with single point sources listed in Ta- to ensure that Compton, active coded aperture and hy- perform image reconstruction with different imaging meth- are performed for the corresponding isotopes with identical distances to verify the theoretical validity of the modified hy- in Fig. , with detailed information of the measured data pro- dergo 30 iterations for reconstruction, while the iterations (or total sub-iterations) required for the coded aperture data vary across different isotopes as indicated in the figure captions.

The stopping criteria for the image reconstruction process is defined the completion of the preset number of iterations. For

241 Am

data, hybrid and modified hybrid imaging results are effectively equivalent to coded aperture imaging, due to the negligible amount of Compton events collected as a result of low interaction cross-section at such energies. An illustration of the imaging errors for different methods during the itera- tion process is depicted in Fig. , which is plotted according to the measured data. Note that the imaging error is measured in normalized root mean squared error (NRMSE) ] between the reconstructed images, , and the reference source distributions,

1 M

� M j =1 ( λ r − λ T ) 2

NRMSE ( λ r | λ T ) =

To roughly estimate the imaging resolution, 2-dimensional Gaussian fits are performed on the hotspots of the images to determine their full width at half maximum (FWHM) values ), which are defined by the quadratic mean of the standard deviations from the 2-D Gaussian fit,

σ FWHM =

where σ max and σ min are the maximum and minimum stan- 552

dard deviations of the 2-D Gaussian functions. The fitted FWHM values are listed in Table , and more systematic de- termination of the imaging resolution is given in sec.

III C These results suggest that the modified imaging method can achieve better angular resolutions than Compton imaging and existing hybrid imaging methods.

Although the modified imaging method exhibit a slightly larger FWHM value (by less than 5 %) than coded aperture imaging in the simula- tions, with a decreasing difference at higher energies, it still outperforms coded aperture imaging in the measured data. A mismatch between the measured and simulated images and FWHM values can also be found in Fig. and Table investigate the cause of the mismatches between the simu- lated and measured results, a comparison between the single- channel spectra from both datasets are displayed in Fig.

Although the spectra in Fig. reveal no evident discrepan- cies from detector calibration and energy window mismatch, a slightly elevated scattering component is observed in the measured spectrum. This suggests that the discrepancies most likely originate from environmental factors such as scatter- ing and shielding, which are not accounted for in the sim- ulations.

Another contributing factor is discrepancies be- tween the simulated and actual detector response, or physi- cal model. This includes the unmodeled components, such as internal cabling, or mismatch in material density for the Ce:GAGG crystals and supporting structures. Therefore, the modified hybrid imaging method demonstrates superior esti- mated imaging resolution in practical applications compared to coded aperture imaging, although the discrepancies re- vealed by the simulated results indicates potential for further improvement in its theoretical model.

This indicates that the proposed method has great potential in enhancing the imaging performance of the camera, which will be further analyzed in III D

, respectively. The true positions of the sources are marked with dashed red lines.

Detailed information of the measured data. The estimated background only includes the single-interaction natural background events within the full-energy range instead of scattering contribution or multiple-interaction background events.

Radioactive Measurement Source Total Full-energy Compton Estimated isotope time (s) distance (m) collected events events

background

events counts To evaluate the sensitivity of the developed camera in Compton and coded aperture imaging, an additional measure-

Reconstructed FWHM ( Radioactive Coded Compton Hybrid Modified isotope aperture imaging imaging hybrid imaging imaging

133 Ba

simulated measured

137 Cs

simulated measured

22 Na

simulated measured (Color online) The variation of imaging errors for different methods during the iteration process of image reconstruction, plotted according to the measured data. The total iteration counts are 30 for Compton imaging, 450 for coded aperture imaging, and 30 main iterations and 450 coded aperture sub-iterations for both hybrid imaging methods. specified in Table approximately 7.5 meters away from the camera, with the angular position of the sources being (0 ), to acquire coded aperture and Compton data, respec-

tively. The sensitivity is measured as the minimum time re- 594

quired to localize the single point sources, which is consis- tent with previous researches [ ]. However, the criteria for

successful localization vary significantly across different ap- 597

plications. For instance, scenarios like contamination detec- tion often employ a low decision threshold for source inten- sity to avoid omissions of potential radiation hotspots [ while nuclear security applications demand higher thresholds to suppress false positives [ ]. Due to the absence of a stan- dard to establish the localization criteria, a specific set of cri- teria is chosen for this study. The selected criteria require the peak image value in the hotspot area near the source, , and the fluctuation of background image values out-

side the hotspot area, σ bkg , to satisfy H peak ≥ 3 σ bkg , while 607

the peak image value of the artifacts in the background region, (Color online) The comparison between the single-channel spectra from simulated and measured data of

H artifact , should satisfy H artifact ≤ 0 . 5 H peak to achieve suc- 609

cessful localization. The camera is capable of localizing the

241 Am

source through coded aperture imaging within

onds of data collection, obtaining a total of 754 full-energy 612

events. However, a decrease in sensitivity is observed for the

137 Cs

source compared to low energies. A total of seconds is required to localize the source using collected full-energy events. depicts the variation in localization error for coded aperture imaging of obtained under dif- ferent acquisition times, with the localization error defined as the angular distance between the image centroid and the actual source direction.

Nonetheless, Compton imaging dis- play slightly better sensitivity at such energies, being capable of localizing the source within 15 seconds. The re- sulting count rate for full-energy Compton events is 3.47 cps (52 events collected within 15 seconds), corresponding to a detection efficiency of 91.32 cps/( Sv/h) under the dose rate of Sv/h established by the setup. Additionally, in order to compare the sensitivity of hybrid imaging with the two single- modality imaging methods, the same measure- ment with the source is performed using hybrid and

modified hybrid imaging. Both hybrid imaging methods are capable of localizing the within 10 seconds. This in- dicates that hybrid imaging can effectively improve the sen- sitivity of the developed camera. The aforementioned results given by the time required to localize the sources with differ- ent methods are summarized in Table (Color online) The in localization for coded aperture imaging of measured data under different data acquisition times.

Time required for localization (s) Radioactive Coded Compton Hybrid Modified isotope aperture imaging imaging hybrid imaging imaging The enhanced sensitivity of the hybrid imaging method can be attributed to its excellent capability of extracting physi- cal information. Although the coded aperture and Compton imaging data collected within a very short period both con- tain numerous artifacts, these artifacts typically do not coin- cide spatially between the two modalities. In addition, the hotspot can be reconstructed at the position of the source in both images despite the presence of high-intensity artifacts.

Through the weighed summation employed in the hybrid im- age reconstruction process, the intensity of the source pixels

in the vicinity of the radioactive source is amplified, while the 646

artifacts are suppressed. In order to systematically evaluate the angular resolution of Compton and active coded aperture imaging with the devel- oped camera, the Rayleigh criterion [ ] is employed. This from two measurements with the same point source placed at different positions, which is performed for multiple iso- topes.

Although this pseudo-double source method of mea- surement differs from actual double source measurements, the sources utilized for the measurement have relatively low activities under the experimental setup. This leads to low pho- ton intensities in the sensitive volume of the camera relative to the coincidence time window chosen for Compton event selection, which is set to 50 ns. Thus, effects such as acci- dental coincidences, overlapping contributions and count-rate dependence can be neglected.

The results of coded aperture imaging are illustrated in Fig. 10 FIGURE:10 10(b)

137 Cs

sources. These results reveal that while the two

sources can be distinguished at an opening angle of 5 ◦ , dif- 666

ferentiation between the two sources is only achievable

when the opening angle reaches 10 ◦ . These findings indi- 668

cate that the angular resolution of the developed camera in coded aperture imaging can reach 5 at a few tens of keV, but degrades at higher energies. On the other hand, the re- sults of Compton imaging for sources shown in Fig. 10(c) 10(d) suggest an angular resolution slightly better than 15 at the energies of 662 keV and 1274 keV.

In order to more systematically analyze the imaging reso- lutions of the camera, the center-cross profiles of the double source images are fitted with double Gaussian functions as performed in previous studies [ ]. The fitting results are dis- played in Fig. . The imaging resolution is derived from the average FWHM value of the two Gaussian peaks, which are also given in Fig. . This result suggest that the developed camera can reach an angular resolution of with Compton imaging when measuring 662 keV gamma rays, and with active coded aperture imag- ing when measuring 60 keV gamma rays.

Evaluation of hybrid imaging performance To evaluate the effectiveness of the modified hybrid imag- ing method, imaging data obtained with two identical point sources are reconstructed using both hybrid and single- modality imaging methods.

Corresponding double-source simulations are also performed with the measured isotopes at the same measurement distances for theoretical verification of the comparison in imaging performance between different methods.

The hybrid imaging method previously proposed by Xu [ ] is also utilized for comparison. It should be noted that for each set of data, the iterations required for image re- construction are consistent across different imaging methods for both simulated and measured data , with the iterations for coded aperture imaging matching the total sub-iterations for hybrid imaging. In order to compare the results from differ- ent imaging methods, a reference source distribution is gen- erated by applying 2-D blurring to the true source distribution to simulate data acquired with high-resolution cameras such as conventional coded aperture cameras [ ], using a Gaus- sian filter with a standard deviation of 2 . Subsequently, im- age quality is evaluated with the NRMSE between the recon- structed images and the reference source distributions given

sources (59.5 keV) with opening angle of 5 placed 2 m from the camera and (b) sources (662 keV) with opening angle of 10 placed 3 m away , as well as Compton imaging results of two (c) sources placed 3 m away and (d) sources (1274 keV) placed 1 m away both with opening angles of 15 . The true positions of the sources are marked with dashed red lines. by Eq.

The imaging results are depicted in Fig. , with the corre- sponding NRMSE values detailed in Table . Through com- parison, it is evident that the hybrid imaging method outper- forms both single-modality imaging methods and the previ-

ously proposed hybrid imaging technique in terms of image 713

quality for both simulated and measured data . Such advan- tage enables the extraction of additional physical informa- tion regarding the spatial distribution of radioactive sources, thereby leading to enhanced gamma-ray imaging capabilities.

NRMSE Radioactive Coded Compton Hybrid Modified isotope aperture imaging imaging hybrid imaging imaging

CONCLUSION

In situations such as source-term monitoring and conse- 719

quence management in NPPs, an isotropic FoV for free- moving measurement of complex source distribution and compatibility across a wide energy range is typically required for gamma-ray imaging devices. In this article, we present the development and performance evaluation of a Compton camera based on spherical detector array , and the application of hybrid gamma-ray imaging to the developed camera . The

camera consists of 80 GAGG detector units, with the config- 727

uration optimized for Compton imaging, along with a mul-

tichannel electronics system based on ASIC. To achieve ef- 729

fective imaging across a wide energy range, the active coded aperture imaging capabilities of the developed camera is also tested. The imaging evaluation of the camera reveals a good performance for both modalities, achieving angular resolu- tions of for Compton imaging at 662 keV and up to for coded aperture imaging at 60 keV. The camera is capable of localizing a 765.9

137 Cs

placed 7.5 meters away (corresponding to the dose rate of Sv/h) within 15 seconds through Compton imaging. For coded aperture imaging, the localization of the

137 Cs

source requires seconds, whereas the localization of a 478.5 source at the same distance can be accomplished in seconds. Additionally, a modified hybrid imaging method that combines Compton and coded aperture

(Color online) Fitting results of the center-cross profiles of the double source images (Fig. ), including the coded aperture images of (a) and (b) , and the Compton images of (c) and (d) . The fitted FWHM values ( ) of each image are given in the corresponding figure titles. data is devised based on existing methods and applied to the camera to further enhance the imaging performance. Through measurements involving various radioactive isotopes, it has been verified that the modified hybrid imaging method ex- hibits improved imaging sensitivity compared with Compton coded aperture imaging, as well as better image quality than both single-modality imaging and previously proposed hybrid imaging methods. With the modified hybrid imag- ing method applied, the developed camera can achieve high sensitivity and fine resolution for gamma-ray imaging across a wide energy range (59.5 keV–1.3 MeV) with isotropic 4 excellent imaging performance achieved using the de- veloped Compton camera in junction with the modified hy- C.G. Wahl, W. Kaye, W. Wang et al., Polaris-H measure- ments and performance. Paper presented at IEEE Nuclear Sci- ence Symposuim & Medical Imaging Conference, Seattle, WA, USA, 8 November - 15 November, 2014.

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K. Vetter, Multi-sensor radiation detection, imaging, and fu- sion. Nucl. Instrum. Methods Phys. Res. A , 127–134 (2016). brid imaging method makes it promising for application to free-moving 3-D mapping of radioactive sources across broad energy ranges. This process involves integrating the cam- era with a simultaneous localization and mapping (SLAM) system to obtain 3-D scene data, and then employing the scene data fusion approach through 3-D image reconstruction method based on the acquired data.

Such method enables the quick coverage of vast areas.

Currently we have conducted preliminary tests on a prototype of such system by combin- ing the Compton imaging capability of the developed camera with a SLAM system, which yield promising results. Fur- ther testing and enhancements of the system are in progress.

Subsequent progress and results will be detailed in upcoming reports.

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