Maximum Likelihood Expectation Maximization Method Research Articles

Development of a compact fast-neutron spectrometer for nuclear emergency response applications

We have developed a Compact Fast Neutron Spectrometer (CFNS) for passive assay of special nuclear material (SNM) through the observation of fast neutrons. The CFNS consists of eight organic glass scintillators (OGS) coupled to silicon photomultipliers and a waveform digitizer, which are integrated within a human-portable box. The CFNS determines the neutron energy profile by spectrum unfolding using the Maximum-Likelihood Expectation Maximization method. The detector acquisition system was optimized to have a dynamic range of up to 10 MeV neutron energy. Bulk special nuclear material (SNM) measurements from the National Criticality Experiments Research Center were analyzed for SNM validation/examination. The results show that the CFNS can be used to distinguish between fission and (α, n) neutron emitters, regardless of intervening material type (Cu and polyethylene) and thickness, by taking the ratio of neutron counts at different regions in the unfolded energy spectrum. Additionally, by fitting an exponential curve to the unfolded energy spectrum of PuO2 and Pu neutron emitters, the CFNS showed the ability of distinguishing between pure Pu oxide, pure Pu metal and mixed oxide-metal configurations.

A novel coded aperture for [formula omitted]-ray imaging based on compressed sensing

High spatial resolution is of great significance for the γ-ray imaging technique, whose performance is mainly limited by the spatial resolution of position sensitive detectors (PSDs). In this work, the compressive coded aperture is introduced in γ-ray imaging as the basic pattern, and enlarged with the “mosaic” method to increase the Fully Coded Field of View (FCFV) of the PSDs. In order to demonstrate the performance of the compressive coded aperture, Monte-Carlo simulations of the encoding process have been performed for the mosaiced compressive coded aperture as well as the Modified Uniformly Redundant Arrays (MURA) coded aperture. The encoded image of the compressive coded aperture is reconstructed using the sparse reconstruction algorithm based on interior point method, with Discrete Cosine Transform (DCT) basis, Haar wavelet basis and Discrete Fourier Transform (DFT) basis respectively, and the encoded image of the MURA coded aperture is reconstructed respectively with the sparse method and the Maximum-Likelihood, Expectation-Maximization (MLEM) algorithm. In comparison with the MURA coded aperture reconstructed with the MLEM method, higher resolution images can be obtained from lower resolution detectors with both compressive coded aperture and MURA coded aperture using the sparse method. However, with the sparse method, the compressive coded aperture leads to higher quality images than the MURA coded aperture does.

Multi GPU parallelization of maximum likelihood expectation maximization method for digital rock tomography data

Digital rock is an emerging area of rock physics, which involves scanning reservoir rocks using X-ray micro computed tomography (XCT) scanners and using it for various petrophysical computations and evaluations. The acquired micro CT projections are used to reconstruct the X-ray attenuation maps of the rock. The image reconstruction problem can be solved by utilization of analytical (such as Feldkamp–Davis–Kress (FDK) algorithm) or iterative methods. Analytical schemes are typically computationally more efficient and hence preferred for large datasets such as digital rocks. Iterative schemes like maximum likelihood expectation maximization (MLEM) are known to generate accurate image representation over analytical scheme in limited data (and/or noisy) situations, however iterative schemes are computationally expensive. In this work, we have parallelized the forward and inverse operators used in the MLEM algorithm on multiple graphics processing units (multi-GPU) platforms. The multi-GPU implementation involves dividing the rock volumes and detector geometry into smaller modules (along with overlap regions). Each of the module was passed onto different GPU to enable computation of forward and inverse operations. We observed an acceleration of sim 30 times using our multi-GPU approach compared to the multi-core CPU implementation. Further multi-GPU based MLEM obtained superior reconstruction compared to traditional FDK algorithm.

Scintillating fibre based beta spectrometer: Proof of concept by Monte-Carlo simulation and first experimental assessment

We developed a new beta measurement method based on scintillating fibres, able to discriminate incident beta particles based on their energy, using various cladding thicknesses, which could find useful applications in the field of nuclear decommissioning and dismantling (D&D). Indeed, thanks to Monte Carlo simulations, we found that high-energy beta particles were less affected by thicker cladding than medium-energy beta particles. Therefore, combining different cladding thicknesses and a deconvolution method, we were able to identify and quantify convoluted beta spectra in a simulated scenario. In this paper, we describe the Monte Carlo simulations combined with the deconvolution algorithm based on the Maximum Likelihood-ExpectationMaximization method (ML-EM), and the associated experimental setup. We demonstrated the feasibility of such a method, using both simulated and experimental data, by deconvoluting 36Cl and 90Sr–90Y spectra, considering 36Cl as a medium-energy beta emitter and 90Sr-90Y as a high-energy beta emitter. Using fibres with only one thickness of cladding, we found that we could not estimate both contributions correctly, with errors reaching up to 71% of the actual activities. However, using two different acquisitions of fibres each one with a different cladding thickness, we were able to estimate both contributions with an error of 26% for 36Cl and 10% for 90Sr-90Y. Study of the improvement of these performances is presented and could help to fine-tune activities estimated. The next step of this work would consist in designing a beta spectrometer, based on scintillating fibres, and assess its performances. Taking advantage of both deformability capacity of scintillating fibres and their potential lengths up to a few metres, we expect that such a detection system will be well adapted to the radiological characterization of large surfaces, and suitable for deployment on uneven surfaces.

APPLICATION OF POSITION-SENSITIVE DETECTORS FOR ANALYZING THE ENERGY SPECTRA OF PHOTON RADIATION

Monitoring the spectral composition of photon radiation from generating sources and emitting objects is the most informative way to analyze the radiation fields created by them. However, it is impossible to study the radiation characteristics of radiation fields of ultra short duration and high intensity using direct measurement methods. This work considers a method for reconstructing the spectral distributions of photon radiation from the profile of the secondary radiation fields recorded by a position-sensitive detector. To implement a new method of measurement in the primary beam of radiation is an extended scattering body of homogeneous material. Outside the field of the primary beam, a position-sensitive detector is placed along the generatrix of the scattering body, which records the photons of the secondary radiation and the coordinates of their emission. The spectral composition of the primary radiation beam is restored from the shape of the spatial distribution obtained. To find a quasi-solution describing the energy spectrum of the primary radiation beam, it is proposed to use the maximum likelihood expectation maximization method. The possibility of switching to measurements in secondary radiation fields having a lower intensity is confirmed by the experimental results. To form secondary radiation fields, we used a composite phantom containing three scattering bodies in the form of rectangular parallelepipeds made of graphite, aluminum, and titanium. The secondary radiation fields were recorded by a radiographic sensor. Using an X-ray source operating in a pulsed mode, images were obtained and profiles of the secondary radiation fields were formed. It is experimentally shown that the secondary radiation fields have a gradient structure and can be used to analyze the energy spectra of the radiation beams generating them. The method for reconstructing spectral distributions proposed in this work allows one to measure the energy spectra of photons using position-sensitive detectors and can be used in solving problems of diagnostics of pulsed high-intensity radiation beams.

Performance of neutron spectrum unfolding using deuterated liquid scintillator

The performance of the maximum likelihood expectation maximization method for unfolding neutron energy spectra using deuterated liquid scintillator is evaluated for future utilization with rare isotope beams. High-resolution neutron energy spectra as well as the detector response matrix were measured at the Edwards Accelerator Laboratory at Ohio University. Maximum-likelihood expectation maximization (MLEM) unfolded neutron spectra are compared with spectra from neutron time-of-flight. The effects of the MLEM stopping criteria and spectrum statistics are also investigated.

Feasibility study on image reconstruction for single-photon emission computed tomography with limited projections by neural networks

This study investigated the feasibility of using a neural network for single-photon emission computed tomography (SPECT) in boron neutron capture therapy (BNCT) with limited projection data. In order to determine the therapeutic dose for use in BNCT under neutron irradiation, a real-time reconstruction method is required. However, BNCT-SPECT has limitations related to the projection angle range and number of projection points. It is not easy to reconstruct an image under these projection limitations using a conventional filtered back-projection (FBP) method. Therefore, a convolutional neural network (CNN) was adopted to reconstruct radioactivity distribution images using the responses from radiation detectors arranged to surround a system. An original dataset of radioactivity distribution images with specific conditions was prepared, and the CNN was trained using the training data. The performances of the CNN for BNCT-SPECT with the limited projections were evaluated. The conditions were the limitations on the number of projections in 180° and on the projection angle range at a constant step angle. The results were compared with those of the FBP method and maximum likelihood-expectation maximization (ML-EM) method. The CNN could be used to estimate radioactivity distributions for BNCT-SPECT with a limited projection angle range. Under the condition of only five projection angles in 180°, the CNN and ML-EM methods could reconstruct images more accurately than the FBP method. In the case of the limitation on the projection angle range, the tolerance of the projection angle range with a step angle of 5° for CNNs was greater than approximately 45°.

Quantitative X-ray fluorescence imaging of gold nanoparticles using joint L1 and total variation regularized reconstruction.

This work proposed a joint L1 and total variation (TV) regularized reconstruction method for X-ray fluorescence tomography (XFT), and investigated the performance of this method in quantitative imaging of gold nanoparticles (GNPs). We developed a dual-modality XFT/CT imaging system which consisted of a benchtop X-ray source, a translation/rotation stage, a silicon drift detector for X-ray fluorescence (XRF) detection, and a flat panel detector for transmission X-ray detection. A pencil-beam collimator was 3D printed with steel and employed in sample excitation. The sensitivity of the XFT imaging system was determined by imaging water phantoms with multiple inserts containing GNP solutions of various concentrations (0.02-0.16 wt.%). A joint L1 and total variation (TV) regularized algorithm was developed for XFT reconstruction, where the L1 regularization was used to reduce image artifacts and the TV regularization was used to preserve the shape of targets. Nonlinear conjugate gradient (NCG) descent algorithm with backtracking line search was adopted to solve the reconstruction problem. We compared the L1 + TV regularization method with filtered back projection (FBP), maximum likelihood expectation maximization (ML-EM), L1 regularization, and TV regularization methods. Contrast-to-noise ratio (CNR), Dice similarity coefficient (DSC) and localization error (LE) metrics were used to compare the performance of different methods. The CT and XFT imaging doses were also measured using EBT2 radiochromic films. The 3D printed pencil-beam collimator shaped an excitation beam with a 2 mm full width at half maximum at the imaging isocenter. Based on the phantom imaging experiments, the joint L1 and TV regularization method performed better than FBP, ML-EM, L1 regularization and TV regularization methods, with higher localization accuracy (offset <0.6 mm), CNR and DSC values. Compared with CT, XFT with L1 + TV regularized reconstruction demonstrated higher sensitivity in GNP imaging, and could detect GNP at a concentration of 0.02 wt.% or lower. Moreover, there existed a significant linear correlation (R2>0.99) between the reconstructed and true GNP concentration. The estimated XFT imaging dose is about 41.22 cGy under current setting. The joint L1 + TV regularized reconstruction algorithm performed better in noise suppression and shape preservation. Using the L1 + TV regularized reconstruction, the XFT system is able to localize GNP targets with submillimeter accuracy and quantify GNP distribution at a concentration of 0.02 wt.% or lower.

Development of the Hemispherical Rotational Modulation Collimator Imaging System

A rotational modulation collimator (RMC) imager consists of two collimator masks rotating ahead of a non-position-sensitive detector. It requires fewer detectors than other radiation imagers, which offers the possibility of reducing the instrument complexity and cost. A hemispherical RMC (H-RMC) is capable of imaging radiation with a significantly better field of view (FOV) than conventional RMCs with cylindrical geometry. In this study, a novel hemispherical collimator design was developed in order to extend the FOV to nearly $2\pi $ . We designed the hemispherical mask considering several parameters, demonstrated the measured performance of the instrument, and showed the two-dimensional (2-D) reconstructed images of radiation distribution. The H-RMC imager described herein featured a symmetric design that leads to degenerate reconstruction of two possible source locations for a single true source location. Nevertheless, it has been possible to establish that the maximum likelihood expectation maximization (MLEM) approach with regularization technique significantly reduced the artifact of misestimated source positions and improved the values of signal-to-noise ratio (SNR) and the structural similarity (SSIM) index compared to the conventional MLEM method.

Studies on unfolding energy spectra of neutrons using maximum-likelihood expectation–maximization method

Energy spectra of neutrons are important for identification of unknown neutron sources and for determination of the equivalent dose. Although standard energy spectra of neutrons are available in some situations, e.g., for some radiotherapy treatment machines, they are unknown in other cases, e.g., for photoneutrons created in radiotherapy rooms and neutrons generated in nuclear reactors. In situations where neutron energy spectra need to be determined, unfolding the required neutron energy spectra using the Bonner sphere spectrometer (BSS) and nested neutron spectrometer (NNS) has been found promising. However, without any prior knowledge on the spectra, the unfolding process has remained a tedious task. In this work, a standalone numerical tool named “NRUunfold” was developed which could satisfactorily unfold neutron spectra for BSS or NNS, or any other systems using similar detection methodology. A generic and versatile algorithm based on maximum-likelihood expectation–maximization method was developed and benchmarked against the widely used STAY’SL algorithm which was based on the least squares method. The present method could output decent results in the absence of precisely calculated initial guess, although it was also remarked that employment of exceptionally bizarre initial spectra could lead to some unreasonable output spectra. The neutron count rates computed using the manufacturer’s response functions were used for sensitivity studies. The present NRUunfold code could be useful for neutron energy spectrum unfolding for BSS or NNS applications in the absence of a precisely calculated initial guess.

APPLICATION OF THE FOREST SHIELDING FACTOR TO THE MAXIMUM-LIKELIHOOD EXPECTATION MAXIMIZATION METHOD FOR AIRBORNE RADIATION MONITORING.

The maximum-likelihood expectation maximization (ML-EM) method is expected to improve the accuracy of airborne radiation monitoring using an unmanned aerial vehicle. The accuracy of the ML-EM method depends on various parameters, including detector efficiency, attenuation factor, and shielding factor. In this study, we evaluate the shielding factor of trees based on several field radiation measurements. From the actual measurement, the shielding factors were well correlated with the heights of the trees. The evaluated shielding factors were applied to the ML-EM method in conjunction with the measured data obtained from above the Fukushima forest. Compared with the conventional methods used for calculating the dose rate, the proposed method is found to be more reliable.

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.

Inverse estimation methods of unknown radioactive source for fuel debris search

To identify the distribution of fuel debris remaining in the reactor vessel and/or the containment vessel of Fukushima Daiichi NPS, we focused on the inverse estimation of radioactive source distribution using the measured radiation counts. The Maximum Likelihood-Expectation Maximization (ML-EM) and the Moore-Penrose Matrix Inverse (MPMI) methods are examined. The ML-EM method has been used for the image reconstruction of computed tomography, and the MPMI method is one of the solution methods for simultaneous linear equations with the underdetermined condition. A simple calculation model simulating a containment vessel was constructed including detectors and radiation sources. In an actual situation, a sufficient number of radiation measurement positions would not be available owing to the complexity of structures inside the containment vessel. Thus, the number of radiation measurement points (number of constraints) is smaller than that of radiation source positions. It means that an underdetermined inverse problem should be solved. The detection probability of radiation (neutron or photon) is calculated by the adjoint transport calculation since the detection probability is used as the coupling coefficient between radiation counts at a detector and a radioactive source. The result of estimation using the ML-EM or the MPMI method indicates that the accuracy of estimation depends on the distance between a radiation source and a detector, and measurement positions of radiation count. The ML-EM and the MPMI methods show different prediction accuracy depending on the prediction condition. It is found that reasonable prediction accuracy would be obtained when the detectors are placed at the vicinity of radiation sources of interest.

Scalable gamma-ray camera for wide-area search based on silicon photomultipliers array.

Portable coded-aperture imaging systems based on scintillators and semiconductors have found use in a variety of radiological applications. For stand-off detection of weakly emitting materials, large volume detectors can facilitate the rapid localization of emitting materials. We describe a scalable coded-aperture imaging system based on 5.02 × 5.02 cm2 CsI(Tl) scintillator modules, each partitioned into 4 × 4 × 20 mm3 pixels that are optically coupled to 12 × 12 pixel silicon photo-multiplier (SiPM) arrays. The 144 pixels per module are read-out with a resistor-based charge-division circuit that reduces the readout outputs from 144 to four signals per module, from which the interaction position and total deposited energy can be extracted. All 144 CsI(Tl) pixels are readily distinguishable with an average energy resolution, at 662 keV, of 13.7% FWHM, a peak-to-valley ratio of 8.2, and a peak-to-Compton ratio of 2.9. The detector module is composed of a SiPM array coupled with a 2 cm thick scintillator and modified uniformly redundant array mask. For the image reconstruction, cross correlation and maximum likelihood expectation maximization methods are used. The system shows a field of view of 45° and an angular resolution of 4.7° FWHM.

Improvement of Dose Calculation with Scattered Photon-Corrected kV Cone-Beam CT Image Using the Kernel Deconvolution Method

Intensity modulated radiation therapy (IMRT) and stereotactic body radiation therapy (SBRT) has to be accomplished with a dose distribution in terms of changes in the tumor size and position for minimizing adverse effects on neighboring organs. If cone-beam computed tomography (CBCT) would facilitate dose calculation attached to the IMRT or SBRT apparatus, we could use the CBCT-based adaptive radiation therapy (ART). However, a CBCT image cannot achieve quantitative electron density values owing to scattered photons; thus, we cannot use it directly for dose calculation. In this study, we calculated the distribution of scattered photons in CBCT images using the Monte Carlo (MC) method and corrected the scattered photon effect with scatter kernels in the process of image reconstruction with the maximum likelihood expectation maximization (MLEM) method. Moreover, we investigated the accuracy of dose calculation by this segmented region method in comparison with typical methods by replacing CBCT values with ideal density values. We calculated the distribution of scattered photons with slab phantoms using the MC method and acquired scattered kernels of three materials (bone, water, and lungs) having different thicknesses until 20 cm every 0.1 cm. These kernels were used in the MLEM method for correcting scattered photons in lung and pelvis CBCT images. Next, we segmented CBCT and multislice CT (MSCT) images into three regions (lungs, bones, and soft tissues) and compared segmentation accuracy between MSCT and scatter-corrected CBCT images. Moreover, we evaluated the effectiveness of dose calculation by CBCT images. In the CBCT to density conversion method, we converted the CBCT value using individual three tables in each organ, and in the density overriding method, we observed calculated doses on accurate organ-segmented images using γ and dose–volume histogram (DVH) analyses. Segmentation results showed that the threshold value of bone and soft tissue separation was similar to the ideal threshold value used in MSCT images; the segmentation error ratio improved (w/o: 63.0%, w/: 4.7%). Similarly, segmentation error ratios for lungs and soft tissues improved by 8.6% compared with those observed on the original CBCT image. In the CBCT to density conversion method, differences in target doses of MSCT and CBCT with scatter corrections were small in the DVH analysis. In the density overriding method, γ analysis results showed that the calculated dose distributions with scatter-corrected images were similar to those seen in MSCT; the pass rate was significantly higher with an accurate segmentation effect (w/o: 70.1%, w/: 95.9%). We evaluated the effectiveness of scattered photon-corrected CBCT image using the kernel deconvolution method for organ segmentation and the effect of this contribution on dose calculation. Improvement of the segmentation accuracy with scattered photon correction can be observed using CBCT dose calculation for ART.

A proposal of Fourier-Bessel expansion with optimized ensembles of bases to analyse two dimensional image.

It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.

Double-Layered CZT Compton Imager

In this paper, we propose a double-layered cadmium zinc telluride Compton camera using the weighted list-mode maximum likelihood expectation maximization (MLEM) method. We performed a Monte Carlo simulation of the performance. The detection system comprised two detector arrays arranged in parallel. Each array consisted of $6 \times 6$ crystals with a 7.5 mm pixel pitch. The dimension of a single crystal was $6 \times 6 \times 15$ mm. For Compton imaging, the 137Cs activity was set to 78 kBq and the acquisition time was set to 2 hours. By applying the weighted MLEM method, the events with small angular uncertainty were more emphasized than those with large angular uncertainty. Each angular uncertainty was calculated based on the energy and geometry uncertainties of each event. We compared the traditional list-mode MLEM and the weighted list-mode MLEM for single and double detector arrays. The results showed that the combination of a double-layered imager with the weighted MLEM method represented the best image performance compared to other combinations. The sources at the offset positions were also simulated to estimate the directional dependency of the camera system.

An inner-crystal neutron-scatter camera: Monte carlo simulation

Neutron energy emitted from special nuclear materials (SNMs) can be measured by using neutronproton scattering; also, the scattering angle can be calculated from the ratio of the scattered energy to the incident energy. By using position and energy information, we can image the original source position by using the backprojection and list-mode maximum-likelihood expectation maximization (MLEM) method. In this paper, we propose an inner-crystal neutron scatter camera system in which the detectors are not separated to obtain interactions at a variety of scatter angles; based on this system, we analyzed the characteristics of the corresponding neutron-scattering camera. The factors that affected the neutron-scatter image were the neutron velocity after scattering, the cut-off level of the time of flight (ToF), and the width of the cones used for image reconstruction. To determine the optimal point for the reconstruction of an image, we estimated the performance of the system by using the figure of merit (FoM). The optimal neutron-velocity (d/ToF) was ~0.3 × 107 m/s according to our simulation result, while the optimal cut-off level of the ToF was 4 ns as the latter minimized the noise while maintaining the required efficiency. The widths of the cones (e) also affected the full width at half maximum (FWHM) and the noise of the image. In terms of a simple source-geometry, whereby concepts such as “point source” were used, a large e value was suitable to achieve noise reduction; however, regarding the complicated source geometry, a small e value was favorable for precise reconstruction of the original source geometry for both the backprojection and the list-mode MLEM methods.

Event reconstruction in NEXT using the ML-EM algorithm

The NEXT collaboration aims to find the neutrinoless double beta decay in 136Xe. The rareness of this decay demands an exceptional background rejection. This can be obtained with an excellent energy resolution, which has been already demonstrated in the NEXT prototypes. In addition to this, the ββ0ν decay in gas produces a characteristic topological signal which could be an extremely useful extra handle to avoid background events.The need for a satisfactory topology reconstruction has led the NEXT Collaboration to implement the Maximum Likelihood Expectation Maximization method (ML-EM) in the data processing scheme. ML-EM is a generic iterative algorithm for many kinds of inverse problems. Although this method is well known in medical imaging and has been used widely in Positron Emission Tomography, it has never been applied to a time projection chamber. First results and studies of the performance of the method will be presented in this poster.

Particle induced X-ray emission-computed tomography analysis of an adsorbent for extraction chromatography

Nd, which simulates minor actinides (MAs), was used for investigating residual minor actinides produced during the extraction chromatography separation of spent fuel from fast neutron reactors. A cross-sectional distribution of Nd in a minute globular adsorbent having diameter less than 50μm was obtained using particle induced X-ray emission-computed tomography with a 3-MeV proton microbeam. The measurement area was 150×150μm2 corresponding to 128×128 imaging pixels in projection images with 9° resolution, image reconstruction was carried out by a modified ML-EM (maximum likelihood expectation maximization) method. As a result, the cross-sectional distribution of Nd in the adsorbent was successfully obtained, and it was first revealed that Nd existed both in the central region and on the outer surface even after an elution. This implies that the internal structure of the adsorbent must be modified for improving of the recovery of MAs.