Maximum Likelihood Expectation Maximization Research Articles

On the Choice and Evaluation of Regularization Priors for CT/ PET Image Reconstruction

Computed Tomography and Positron Emission Tomography (CT/PET) are primary imaging tools for the clinical diagnosis. The main objective of the imaging tool is to minimize the radiation dose without sacrificing the quality of CT/PET images. To achieve this goal, a suitable regularization prior is incorporated with the iterative reconstruction method. The proposed model is a fusion of Maximum Likelihood Expectation Maximization (MLEM) with partial differential equation based anisotropic diffusion (AD) filter. The proposed method is capable enough to minimize the radiation dose, removing the staircase effects as well as handle the ill-posed issue. To check the validation of the proposed method, both qualitative and quantitative results are presented using the simulated and real test phantoms. The results shown that the proposed methods outperform the state-of-the-art methods.

Nonlocal total variation based dynamic PET image reconstruction with low-rank constraints

Faced with the low signal-to-noise ratio of measurements due to the short data acquisition time between adjacent frames, reconstruction techniques for dynamic positron emission tomography (dPET) images have been under development for decades. In this paper, a novel reconstruction method of dPET is presented. We first enforce a joint low-rank model to simultaneously exploit the spatiotemporal priors. Considering that PET images suffer from noise actually, a nonlocal total variation (TV) constraint is incorporated in the low-rank framework because it is able to preserve fine structures and remove the staircase effect by using image redundancies. We solve the objective function by using the augmented Lagrangian multiplier method with variable splitting. We then validate the effectiveness of the proposed method with Monte Carlo-simulated datasets and real patient data. The proposed approach gives superior reconstruction results compared with the maximum likelihood-expectation maximization and low-rank TV methods.

Examining an image reconstruction method in infrared emission tomography

We present and evaluate the application of the “Reconstructed Image from Simulations Ensemble” (RISE), a novel tomographic image reconstruction method, in infrared tomography. We demonstrate that established methods of photon emission tomography, widely used with penetrating ionizing radiation, are applicable to infrared radiation. RISE, the method of choice, employs statistical physics concepts and utilizes Monte Carlo techniques to construct the imaged object from its infrared planar projections. The validity of the InfraRed Emission Tomographic (IRET) method is demonstrated, and the efficacy of RISE is evaluated with (A) simulated data and (B) experimental sets of infrared projections obtained from a thermal phantom with an infrared camera. For the simulation studies presented, the reconstructed images obtained with RISE and the well - known Algebraic Reconstruction Technique (ART) and Maximum Likelihood Expectation Maximization (MLEM) method were evaluated using well-established metrics.

Tomographic Cherenkov-excited luminescence scanned imaging with multiple pinhole beams recovered via back-projection reconstruction.

Cherenkov-excited luminescence scanned imaging (CELSI) is achieved with a clinical linear accelerator during external beam radiotherapy to map out molecular luminescence intensity or lifetime in tissue. In order to realize a deeper imaging depth with a reasonable spatial resolution in CELSI, we optimized the original scanning procedure to complete this in a way similar to x-ray computed tomography and with image reconstruction from maximum-likelihood expectation maximization and multi-pinhole irradiation for parallelization. Resolution phantom studies showed that a 0.3mm diameter capillary tube containing 0.01nM luminescent nanospheres could be recognized at a depth of 21mm into tissue-like media. Small animal imaging with a 1mm diameter cylindrical target demonstrated that fast 3D data acquisition can be achieved by this multi-pinhole collimator approach to image high-resolution luminescence through a whole animal.

Radiation measurement and imaging using 3D position sensitive pixelated CZT detector

Abstract In this study, we evaluated the performance of a commercial pixelated cadmium zinc telluride (CZT) detector for spectroscopy and identified its feasibility as a Compton camera for radiation monitoring in a nuclear power plant. The detection system consisted of a 20 mm × 20 mm × 5 mm CZT crystal with 8 × 8 pixelated anodes and a common cathode, in addition to an application specific integrated circuit. The performance of the various radioisotopes 57Co, 133Ba, 22Na, and 137Cs was evaluated. In general, the amplitude of the induced signal in a CZT crystal depends on the interaction position and material non-uniformity. To minimize this dependency, a drift time correction was applied. The depth of each interaction was calculated by the drift time and the positional dependency of the signal amplitude was corrected based on the depth information. After the correction, the Compton regions of each spectrum were reduced, and energy resolutions of 122 keV, 356 keV, 511 keV, and 662 keV peaks were improved from 13.59%, 9.56%, 6.08%, and 5%–4.61%, 2.94%, 2.08%, and 2.2%, respectively. For the Compton imaging, simulations and experiments using one 137Cs source with various angular positions and two 137Cs sources were performed. Individual and multiple sources of 133Ba, 22Na, and 137Cs were also measured. The images were successfully reconstructed by weighted list-mode maximum likelihood expectation maximization method. The angular resolutions and intrinsic efficiency of the 137Cs experiments were approximately 7°–9° and 5 × 10−4–7 × 10−4, respectively. The distortions of the source distribution were proportional to the offset angle.

Computed tomography reconstruction on distributed storage using hybrid regularization approach

Computed Tomography (CT) is considered as a significant imaging tool for clinical diagnoses. Due to low-dose radiation in CT, the projection data is highly affected by Gaussian noise which may lead to blurred images, staircase effect, loss of basic fine structure and detailed information. Therefore, there is a demand for an approach that can eliminate noise and can provide high-quality images. To achieve this objective, this paper presents a new statistical image reconstruction method by proposing a suitable regularization approach. The proposed regularization is a hybrid approach of Complex Diffusion and Shock filter as a prior term. To handle the problem of prominent Gaussian noise as well as ill-posedness, the proposed hybrid regularization is further combined with the standard Maximum Likelihood Expectation Maximization (MLEM) reconstruction algorithm in an iterative manner and has been referred to as the proposed CT-Reconstruction (CT-R) algorithm here after. Besides, considering the large sizes of image data sets for medical imaging, distributed storage for images have been employed on Hadoop Distributed File System (HDFS) and the proposed MLEM algorithms have been deployed for improved performance.The proposed method has been evaluated on both the simulated and real test phantoms. The final results are compared with the other standard methods and it is observed that the proposed method has many desirable properties such as better noise robustness, less computational cost and enhanced denoising effect.

Simultaneous estimation and segmentation from projection data in dynamic PET.

Dynamic positron emission tomography (PET) is known for its ability to extract spatiotemporal information of a radio tracer in living tissue. Information of different functional regions based on an accurate reconstruction of the activity images and kinetic parametric images has been widely studied and can be useful in research and clinical setting for diagnosis and other quantitative tasks. In this paper, our purpose is to present a novel framework for estimating the kinetic parametric images directly from the raw measurement data together with a simultaneous segmentation accomplished through kinetic parameters clustering. An iterative framework is proposed to estimate the kinetic parameter image, activity map and do the segmentation simultaneously from the complete dynamic PET projection data. The clustering process is applied to the kinetic parameter variable rather than to the traditional activity distribution so as to achieve accurate discrimination between different functional areas. Prior information such as total variation regularization is incorporated to reduce the noise in the PET images and a sparseness constraint is integrated to guarantee the solution for kinetic parameters due to the over complete dictionary. Alternating direction method of multipliers (ADMM) method is used to solve the optimization problem. The proposed algorithm was validated with experiments on Monte Carlo-simulated phantoms and real patient data. Symbol error rate (SER) was defined to evaluate the performance of clustering. Bias and variance of the reconstruction activity images were calculated based on ground truth. Relative mean square error (MSE) was used to evaluate parametric results quantitatively. In brain phantom experiment, when counting rate is 1×106 , the bias (variance) of our method is 0.1270 (0.0281), which is lower than maximum likelihood expectation maximization (MLEM) 0.1637 (0.0410) and direct estimation without segmentation (DE) 0.1511 (0.0326). In the Zubal phantom experiment, our method has the lowest bias (variance) 0.1559 (0.0354) with 1×105 counting rate, compared with DE 0.1820 (0.0435) and MLEM 0.3043 (0.0644). As for classification, the SER of our method is 18.87% which is the lowest among MLEM+k-means, DE+k-means, and kinetic spectral clustering (KSC). Brain data with MR reference and real patient results also show that the proposed method can get images with clear structure by visual inspection. In this paper, we presented a joint reconstruction framework for simultaneously estimating the activity distribution, parametric images, and parameter-based segmentation of the ROIs into different functional areas. Total variation regularization is performed on the activity distribution domain to suppress noise and preserve the edges between ROIs. An over complete dictionary for time activity curve basis is constructed. SER, bias, variance, and MSE were calculated to show the effectiveness of the proposed method.

Compton-based prompt gamma imaging using ordered origin ensemble algorithm with resolution recovery in proton therapy

Prompt gamma ray (PG) imaging based on Compton camera (CC) is promising to realize in vivo verification during the proton therapy. However, the finite spatial and energy resolution of current CC, as well as the Doppler broaden effect, degrade the quality and resolution of PG images. In addition, due to the inherent geometrical complexity of Compton camera data, PG imaging can be time-consuming and difficult to reconstruct in real-time, while using standard techniques such as filtered back-projection or maximum likelihood-expectation maximization. In this paper, we propose three modifications of origin ensembles with resolution recovery (OE-RR) algorithm based on Markov chains to accelerate the convergence to equilibrium of OE-RR algorithm and improve the image quality. For evaluation, we performed a Monte Carlo simulation of a three-stage CZT Compton camera with resolution loss to detect the PG produced by a proton beam in a water phantom, and evaluate image quality of the gamma rays emitted during proton irradiation. The results show that our ordered OE-RR algorithm realized a good resolution recovery and accurate estimation of the position, including the peak and the distal falloff of the PG emission with remarkably faster reconstruction, thus demonstrating the feasibility of this new method in non-idealized PG-based proton range verification.

Performance of compressed sensing-based iterative reconstruction for single-photon emission computed tomography from undersampled projection data: a simulation study in 123I-N-ω-fluoropropyl-2β-carbomethoxy-3β-(4-iodophenyl)nortropane imaging.

The aim of this study was to investigate the efficacy of compressed sensing (CS)-based iterative reconstruction (CS-IR) from undersampled projection data in I-N-ω-fluoropropyl-2β-carbomethoxy-3β-(4-iodophenyl)nortropane single-photon emission computed tomography (SPECT). We used the cylinder/sphere and the striatal digital phantom models. The number of projections was set at 120, 90, 60, 40, and 30 projections. SPECT images were reconstructed using filtered back-projection (FBP), maximum likelihood-expectation maximization (ML-EM), and CS-IR. The total-variation transform with local image gradient in L1-norm was adopted in our CS algorithm. The efficacy of CS-IR was examined in terms of the spatial resolution, recovery coefficient, aspect ratio (ASR), activity concentration linearity, percent coefficient of variation (%CV), and specific binding ratio. As the number of projections decreased, the following results were observed. No differences of the spatial resolution and activity concentration linearity were observed between reconstruction methods. However, ASR for FBP slightly increased in contrast to ML-EM and CS-IR for which ASR remained constant. There were not any clear differences between recovery coefficients obtained from each reconstruction. The %CV obtained by CS-IR was significantly superior to that obtained by other reconstructions at all number of projections: for example, the %CV obtained by 60 projection CS-IR was equivalent to that obtained by 120 projection FBP and ML-EM. The specific binding ratio did not change with the number of projections, and there were no significant differences between FBP, ML-EM, and CS-IR. We have demonstrated that CS-IR with decreased number of projections can provide a good image quality compared with commonly used SPECT reconstruction methods. This CS could help to reduce overall acquisition time in I-N-ω-fluoropropyl-2β-carbomethoxy-3β-(4-iodophenyl)nortropane SPECT, particularly.

Prototype of an array SiPM-based scintillator Compton camera for radioactive materials detection

The Compton camera, which visualizes the distribution of gamma-ray sources based on the kinematics of Compton scattering, has advantage of wide field of view, broad range of energy and compact structure. In this study, we proposed a prototype of Compton camera, which included array silicon photomultiplier (SiPM)-based position-sensitive detectors, data acquisition (DAQ) system and image reconstruction system. The detectors were composed of Ce-doped Gd3Al2Ga3O12 scintillator arrays and pixel Si-PM arrays. In DAQ system, symmetric charge division circuit, impedance bridge circuit and the delay coincidence algorithm were designed to record coincidence events. Simple back-projection algorithm and list-mode maximum likelihood expectation maximization algorithm were adopted for image reconstruction. The coordinate of longitude and latitude was used for image fusion. The performance of this Compton camera prototype system was evaluated. The results indicated that this system was able to locate a 137Cs point source within 20 s with the corresponding radiation dose of ~ 1.0 μSv/h. The angular resolution of point source was ~ 7° (FWHM), and the total energy resolution of 662 keV was 7.2%. Furthermore, we succeeded in separating two point sources of different energy [22Na (511 keV), 137Cs (662 keV)] in laboratory test. This prototype of scintillator Compton camera offers capabilities for applications like source term investigation and radioactive materials detection.

Evaluation of an emission path length computation model applied at different resolutions in Tomographic Gamma Scanning

Tomographic Gamma Scanning (TGS) is a non-destructive technique used to assay and characterize low-level and mediate-level (LL & ML) radioactive waste drums qualitatively and quantitatively without opening waste drums. The ideal voxelized TGS model used in this paper is based on the assumption that matrices are uniformly distributed and radioactivity from gamma emitting radioactive sources is concentrated at the mass centroid of each voxel. An “point-detector (PD)” model in which the germanium crystal surface of High Purity Germanium (HPGe) detector is divided into different pixels are taken into account to compute the average emission path length of every gamma-ray through each voxel in the drum. Different from the previously described transmission PD model that treats the transmission source as the only “point”, this emission PD model treats the mass centroid of each voxel in the drum as an independent “point” and the finite field of views (FOVs) of the collimated High Purity Germanium (HPGe) detector must be carefully considered. The difference among this emission PD model applied at different resolutions is that the germanium crystal surface of HPGe detector is divided into different numbers of pixels respectively. Algebraic Reconstruction Technique (ART) with the non-negativity constraint and Maximum Likelihood Expectation Maximization (MLEM) are respectively used as the emission reconstruction algorithm. In order to compare these different emission path length computation models and emission reconstruction algorithms, three different series of waste drums are established, allowing to calculate the count distribution for various point source positions and different matrix configurations. Results show that ART algorithm is superior to MLEM algorithm to assay high-density drums. The more pixels the germanium crystal surface of HPGe detector is divided into, the better the emission-reconstructed results when using ART to assay high-density drums.

FPGA as a Hardware Accelerator for Computation Intensive Maximum Likelihood Expectation Maximization Medical Image Reconstruction Algorithm

The major requirements of a good tomographic reconstruction algorithm are a reduction in radiation dosage, accurate reconstruction, detail enhancement, and rapid reconstruction time. Some of these factors are covered by many algorithms but are not collectively addressed in one. While the Maximum Likelihood Expectation Maximization (MLEM) algorithm fares well on many of these factors, it is difficult to apply this algorithm in real-time due to its long execution time. Our predetermined goal is to reduce the execution time to a large extent so that the MLEM’s advantages can be leveraged by using hardware accelerators such as Field Programmable Gate Arrays (FPGA). The FPGAs are becoming especially popular as hardware accelerators and are well known for their programmability, configurability, and massive parallelism through a large number of Configurable Logic Blocks (CLBs). Although FPGAs are extremely versatile, they require complex languages like Verilog or VHDL to program them, incorporating changes in the design level at a later stage in FPGAs demands increased effort. Here, in this paper, for the first time, we present a parallel structure for hardware acceleration of the MLEM on the mammoth Virtex 7 $VC$ 709 FPGA. Using available tools, we also present a programming flow to design the algorithmic acceleration hardware architecture. The proposed flow does not require prior knowledge of the traditionally cumbersome Hardware Description Languages (HDLs) and this makes post design changes very easy to incorporate and validate. The parallel architecture is implemented on an FPGA operating at 220 MHz and we have achieved a $288\times $ performance compared to an optimized software execution on an Intel Xeon workstation with 12-cores 3.1 GHz 32 GB RAM and 12 MB Cache architecture.

Scattering Noise Model Enhanced EM-TV Algorithm for Benchtop X-ray Fluorescence Computed Tomography Image Reconstruction

Current benchtop x-ray fluorescence computed tomography (XFCT) devices, which use x-ray tubes to stimulate x-ray fluorescence (XRF) photons, suffer from the contamination of Compton scatter background produced by the polychromatic incident beam. The conventional maximum-likelihood expectation-maximization (ML-EM) algorithm only considers the noise model of the XRF signal, which results in high statistical noise in reconstructed images caused by scattered photons. In this study, we proposed a scattering noise model enhanced EM-TV algorithm for benchtop XFCT image reconstruction in order to reduce the noise of scatter background and improve the sensitivity of XFCT images. The statistical noise of scattered photons was considered in the likelihood function and the EM iteration step was modified correspondingly to suppress the statistical noise caused by Compton scattered photons. The robustness of the EM iteration was improved by applying the reweighted total variation (TV) norm as the penalty function. Numerical simulations and imaging experiments of a PMMA phantom consisting of gadolinium (Gd) solutions were performed to validate the proposed algorithm. The phantom was irradiated by a cone-beam polychromatic source and the projection was recorded by a linear-array photon counting detector. For comparison, the XFCT images of Gd were reconstructed using different algorithms. Results indicate that compared with the conventional ML-EM algorithm, the proposed algorithm can obtain XFCT images with lower background noise and higher contrast, which may further improve the sensitivity and image performance of current benchtop XFCT systems.

Novel muon imaging techniques.

Owing to the high penetrating power of high-energy cosmic ray muons, muon imaging techniques can be used to image large bulky objects, especially objects with heavy shielding. Muon imaging systems work just like CT scanners in the medical imaging field-that is, they can reveal information inside of a target. There are two forms of muon imaging techniques: muon absorption imaging and muon multiple scattering imaging. The former is based on the flux attenuation of muons, and the latter is based on the multiple scattering of muons in matter. The muon absorption imaging technique is capable of imaging very large objects such as volcanoes and large buildings, and also smaller objects like spent fuel casks; the muon multiple scattering imaging technique is best suited to inspect smaller objects such as nuclear waste containers. Muon imaging techniques can be applied in a broad variety of fields, i.e. from measuring the magma thickness of volcanoes to searching for secret cavities in pyramids, and from monitoring the borders of countries checking for special nuclear materials to monitoring the spent fuel casks for nuclear safeguards applications. In this paper, the principles of muon imaging are reviewed. Image reconstruction algorithms such as Filtered Back Projection and Maximum Likelihood Expectation Maximization are discussed. The capability of muon imaging techniques is demonstrated through a Geant4 simulation study for imaging a nuclear spent fuel cask.This article is part of the Theo Murphy meeting issue 'Cosmic-ray muography'.

PET Reconstruction of the Posterior Image Probability, Including Multimodal Images

In PET image reconstruction, it would be useful to obtain the entire posterior probability distribution of the image, because it allows for both estimating image intensity and assessing the uncertainty of the estimation, thus leading to more reliable interpretation. We propose a new entirely probabilistic model: the prior is a distribution over possible smooth regions (distance-driven Chinese restaurant process), and the posterior distribution is estimated using a Gibbs Markov chain Monte Carlo sampler. Data from other modalities (here one or several MR images) are introduced into the model as additional observed data, providing side information about likely smooth regions in the image. The reconstructed image is the posterior mean, and the uncertainty is presented as an image of the size of 95% posterior intervals. The reconstruction was compared with the maximum-likelihood expectation-maximization and OSEM algorithms, with and without post-smoothing, and with a penalized ML or MAP method that also uses additional images from other modalities. Qualitative and quantitative tests were performed on realistic simulated data with statistical replicates and on several clinical examinations presenting pathologies. The proposed method presents appealing properties in terms of obtained bias, variance, spatial regularization, and use of multimodal data, and produces, in addition, potentially valuable uncertainty information.

Muography of different structures using muon scattering and absorption algorithms.

In recent decades, muon imaging has found a plethora of applications in many fields. This technique succeeds to infer the density distribution of big inaccessible structures where conventional techniques cannot be used. The requirements of different applications demand specific implementations of image reconstruction algorithms for either multiple scattering or absorption-transmission data analysis, as well as noise-suppression filters and muon momentum estimators. This paper presents successful results of image reconstruction techniques applied to simulated data of some representative applications. In addition to well-known reconstruction methods, a novel approach, the so-called μCT, is proposed for the inspection of spent nuclear fuel canisters. Results obtained based on both μCT and the maximum-likelihood expectation maximization reconstruction algorithms are presented.This article is part of the Theo Murphy meeting issue 'Cosmic-ray muography'.

Monte Carlo-based SPECT reconstruction within the SIMIND framework

This paper presents the development and validation of a Monte Carlo-based singe photon emission computed tomography reconstruction program for parallel-hole collimation contained within the SIMIND Monte Carlo framework. The Monte Carlo code is used as an accurate forward-projector and is combined with a simplified back-projector to perform iterative tomographic reconstruction using the Maximum Likelihood Expectation Maximization and Ordered Subsets Expectation Maximization algorithms, together forming a program called SIMREC. The Monte Carlo simulation transforms the estimated source distribution directly from activity to counts in its projections. Hence, the reconstructed image is expressed in activity without reference to an external calibration. The program is tested using phantom measurements of spheres filled with 99mTc, 177Lu and 131I placed in air and centrally and peripherally in a water-filled elliptical phantom. The feasibility of applying the reconstruction to patients is also demonstrated for a range of radiopharmaceuticals. The deviation in total activity in the spheres ranged between −4.1% and 6.2% compared with the activity determined when preparing the phantom. The SIMREC program was found to be accurate with respect to activity estimation and to reconstruct visually acceptable images within a few hours when applied to patient examples.

Precise System Models using Crystal Penetration Error Compensation for Iterative Image Reconstruction of Preclinical Quad-Head PET

A-PET is a quad-head PET scanner developed for use in small-animal imaging. The dimensions of its volumetric field of view (FOV) are 46.1 × 46.1 × 46.1 mm3 and the gap between the detector modules has been minimized in order to provide a highly sensitive system. However, such a small FOV together with the quad-head geometry causes image quality degradation. The main factor related to image degradation for the quad-head PET is the mispositioning of events caused by the penetration effect in the detector. In this paper, we propose a precise method for modelling the system at the high spatial resolution of the A-PET using a LOR (line of response) based ML-EM (maximum likelihood expectation maximization) that allows for penetration effects. The proposed system model provides the detection probability of every possible ray-path via crystal sampling methods. For the ray-path sampling, the sub-LORs are defined by connecting the sampling points of the crystal pair. We incorporate the detection probability of each sub-LOR into the model by calculating the penetration effect. For comparison, we used a standard LOR-based model and a Monte Carlo-based modeling approach, and evaluated the reconstructed images using both the National Electrical Manufacturers Association NU 4–2008 standards and the Geant4 Application for Tomographic Emission simulation toolkit (GATE). An average full width at half maximum (FWHM) at different locations of 1.77 mm and 1.79 mm are obtained using the proposed system model and standard LOR system model, which does not include penetration effects, respectively. The standard deviation of the uniform region in the NEMA image quality phantom is 2.14% for the proposed method and 14.3% for the LOR system model, indicating that the proposed model out-performs the standard LOR-based model.

Accurate modeling of event-by-event backprojection for a germanium semiconductor Compton camera for system response evaluation in the LM-ML-EM image reconstruction method

We develop an image reconstruction method, considering the physical phenomenon in the measurement process of a Compton camera. The image quality is improved by applying an accurate error model of the Compton scattering angle. The angular error has two properties: an error distribution function specific to the detector material and the variation of its function parameters, depending on each measurement event. We incorporate these factors into the backprojection of the list-mode maximum-likelihood expectation-maximization method as the system response function. We apply our image reconstruction method to simulated data assumed to be measured by a Ge-semiconductor Compton camera GREI, and the imaging data of a tumor-bearing live mouse obtained using GREI. This method is evaluated by comparing an image with variable angular error with that having fixed angular error. The consideration of the variable angle estimation error improves the spatial resolution and reduces image roughness.

Optimization of a table-top x-ray fluorescence computed tomography (XFCT) system

Pencil beam x-ray fluorescence computed tomography (XFCT) has typically used a single spectrometer and prohibitively long scan times. However, detecting backscattered fluorescent x-rays from gold nanoparticles (AuNPs) using multiple spectrometers greatly reduces image noise and scan time. The arrangement of eight spectrometers for combined K-shell and L-shell XFCT was investigated along with a variety of conditions. A 2.5 cm-diameter cylindrical water phantom containing 4 mm-diameter vials with 0.1%–2% AuNP concentrations by weight was modeled by TOPAS, a GEANT4-based Monte Carlo software. The phantom was irradiated to 30 mGy by a 0.5 mm Pb-filtered 120 kVp and 1 mm Al-filtered 30 kVp 1 mm2 x-ray pencil beam to yield respective Au K-shell and L-shell fluorescent x-rays, with 50 0.5 mm translation and 2-degree rotation steps. Eight CdTe and silicon drift detector (SDD) spectrometers were placed 2.25 cm away from the isocentre. The respective energy resolution was applied to the detected energy spectra and the spectra were corrected for detector response before extracting the fluorescence signal. Three CdTe and SDD spectrometer configurations (isotropic/backscattered grid/backscattered row arrangements), two CdTe crystal sizes (9 mm2/25 mm2), two scanning techniques (moving/stationary spectrometers) and five vial-edge depths (0–4 mm) were considered in optimizing the contrast-to-noise ratio (CNR) for each XFCT image reconstructed with a maximum-likelihood expectation maximization (MLEM) algorithm. The isotropic spectrometer arrangement had AuNP detection sensitivities of 0.106% for K-shell and 0.132% for L-shell XFCT at 4 mm depth. Comparatively, the backscattered grid arrangement had the best AuNP sensitivity of 0.055% and 0.095%. The highest K-shell (0.044%) and L-shell (0.004%) AuNP sensitivities were found for vials at 0 mm depth. Using stationary spectrometers or the 9 mm2 CdTe crystal compromised the CNR. For the best-case arrangement, L-shell XFCT is superior at vial-edge depths less than 3.0 mm. This work demonstrated the importance of spectrometer arrangement and vial depth for improving AuNP sensitivity and will guide the design for our table-top XFCT system.