Reducing negativity artifacts in emission tomography: post-processing filtered backprojection solutions

Non-destructive 3D imaging method using muonic X-rays and a CdTe double-sided strip detector

Elemental analysis based on muonic X-rays resulting from muon irradiation provides information about bulk material composition without causing damage, which is essential in the case of precious or otherwise unreachable samples, such as in archeology and planetary science. We developed a three-dimensional (3D) elemental analysis technique by combining the elemental analysis method based on negative muons with an imaging cadmium telluride double-sided strip detector (CdTe-DSD) designed for the hard X-ray and soft \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}γ-ray observation. A muon irradiation experiment using spherical plastic samples was conducted at the Japan Proton Accelerator Research Complex (J-PARC); a set of projection images was taken by the CdTe-DSD, equipped with a pinhole collimator, for different sample rotation angles. The projection images measured by the CdTe-DSD were utilized to obtain a 3D volumetric phantom by using the maximum likelihood expectation maximization algorithm. The reconstructed phantom successfully revealed the 3D distribution of carbon in the bulk samples and the stopping depth of the muons. This result demonstrated the feasibility of the proposed non-destructive 3D elemental analysis method for bulk material analysis based on muonic X-rays.

Reconstruction of Preclinical PET Images via Chebyshev Polynomial Approximation of the Sinogram

Over the last decades, there has been an increasing interest in dedicated preclinical imaging modalities for research in biomedicine. Especially in the case of positron emission tomography (PET), reconstructed images provide useful information of the morphology and function of an internal organ. PET data, stored as sinograms, involve the Radon transform of the image under investigation. The analytical approach to PET image reconstruction incorporates the derivative of the Hilbert transform of the sinogram. In this direction, in the present work we present a novel numerical algorithm for the inversion of the Radon transform based on Chebyshev polynomials of the first kind. By employing these polynomials, the computation of the derivative of the Hilbert transform of the sinogram is significantly simplified. Extending the mathematical setting of previous research based on Chebyshev polynomials, we are able to efficiently apply our new Chebyshev inversion scheme for the case of analytic preclinical PET image reconstruction. We evaluated our reconstruction algorithm on projection data from a small-animal image quality (IQ) simulated phantom study, in accordance with the NEMA NU 4-2008 standards protocol. In particular, we quantified our reconstructions via the image quality metrics of percentage standard deviation, recovery coefficient, and spill-over ratio. The projection data employed were acquired for three different Poisson noise levels: 100% (NL1), 50% (NL2), and 20% (NL3) of the total counts, respectively. In the uniform region of the IQ phantom, Chebyshev reconstructions were consistently improved over filtered backprojection (FBP), in terms of percentage standard deviation (up to 29% lower, depending on the noise level). For all rods, we measured the contrast-to-noise-ratio, indicating an improvement of up to 68% depending on the noise level. In order to compare our reconstruction method with FBP, at equal noise levels, plots of recovery coefficient and spill-over ratio as functions of the percentage standard deviation were generated, after smoothing the NL3 reconstructions with three different Gaussian filters. When post-smoothing was applied, Chebyshev demonstrated recovery coefficient values up to 14% and 42% higher, for rods 1–3 mm and 4–5 mm, respectively, compared to FBP, depending on the smoothing sigma values. Our results indicate that our Chebyshev-based analytic reconstruction method may provide PET reconstructions that are comparable to FBP, thus yielding a good alternative to standard analytic preclinical PET reconstruction methods.

Development and evaluation of a prototype detector for an intraoperative laparoscopic coincidence imaging system with PET tracers

PURPOSE

Conventional positron emission tomography can be used only preoperatively to identify lymph node metastases, and hence, these growths are difficult to locate intraoperatively. Previously, an intraoperative laparoscopic coincidence imaging system, with an external fixed detector array and a detector probe that can be moved and inserted into the stomach, was proposed to identify lymph node metastases during stomach cancer surgery. This paper proposes a prototype detector for this system.

METHODS

GAGG:Ce (Gd₃Al₂Ga₃O₁₂:Ce) scintillator crystals, one to one coupled with silicon photomultipliers (SiPMs), were used to identify 511 keV photons. An optical tracking system followed the position and orientation of the movable detector. SiPM outputs were read out by time-over-threshold (TOT)-based application-specific integrated circuits, which converted the electrical charges into digital pulses. To identify the arrival time, channel number, and pulse width, which indicate the energy information of each TOT output, a data acquisition system was developed based on a field-programmable gate array.

RESULTS

The spatial resolution of the reconstructed images in lateral direction was better than 7 mm, but that of depth direction was limited, owing to inadequate projections. The prototype successfully reconstructed 44 kBq ¹⁸F-fluorodeoxyglucose sources during a 2-min scan.

CONCLUSION

We developed a prototype detector for an intraoperative laparoscopic coincidence imaging system. The prototype detector was evaluated successfully, and the produced images were similar to those obtained in the simulation results, thereby suggesting that this method offers a new possibility of imaging lymph node metastases intraoperatively.

Efficient Bandwidth Estimation in 2D Filtered Backprojection Reconstruction

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in 2D filtered backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form, derives results on eigendecomposition of symmetric 2D circulant matrices, and applies them to make bandwidth estimation a computationally efficient operation within the context of standard backprojected filtering reconstruction. Performance evaluations on a range of simulated emission tomography experiments give promising results. The superior performance holds at both low and high total expected counts, pointing to the method's applicability even in weak signal-to-noise-ratio situations. The approach also applies to the more general class of elliptically symmetric filters, with the reconstructed estimate's performance often better than even that obtained with the true optimal radially symmetric filter.

Selection Criteria for Determination of Optimal Reconstruction Method for Cu-64 Trastuzumab Dosimetry on Siemens Inveon PET Scanner

The goal of this study was to suggest criteria for the determination of the optimal image reconstruction algorithm for image-based dosimetry of Cu-64 trastuzumab PET in a mouse model. Image qualities, such as recovery coefficient (RC), spill-over ratio (SOR), and non-uniformity (NU), were measured according to National Electrical Manufacturers Association (NEMA) NU4-2008. Mice bearing a subcutaneous tumor ( 200 &nbsp; mm 3 , HER2 NCI N87) were injected with monoclonal antibodies (trastuzumab) with Cu-64. Preclinical mouse PET images were acquired at 4 time points after injection (2, 15, 40 and 64 h). Phantom and Cu-64 trastuzumab PET images were reconstructed using various reconstruction algorithms (filtered back projection (FBP), 3D reprojection algorithm (FBP-3DRP), 2D ordered subset expectation maximization (OSEM 2D), and OSEM 3D maximum a posteriori (OSEM3D-MAP)) and filters. The absorbed dose for the tumor and the effective dose for organs for Cu-64 trastuzumab PET were calculated using the OLINDA/EXM program with various reconstruction algorithms. Absorbed dose for the tumor ranged from 923 mGy/MBq to 1830 mGy/MBq with application of reconstruction algorithms and filters. When OSEM2D was used, the effective osteogenic dose increased from 0.0031 to 0.0245 with an increase in the iteration number (1 to 10). In the region of kidney, the effective dose increased from 0.1870 to 1.4100 when OSEM2D was used with iteration number 1 to 10. To determine the optimal reconstruction algorithms and filters, a correlation between RC and NU was plotted and selection criteria (0.9 < RC < 1.0 and < 10% of NU) were suggested. According to the selection criteria, OSEM2D (iteration 1) was chosen for the optimal reconstruction algorithm. OSEM2D (iteration 10) provided 154.7% overestimated effective dose and FBP with a Butterworth filter provided 20.9% underestimated effective dose. We suggested OSEM2D (iteration 1) for the calculation of the effective dose of Cu-64 trastuzumab on an Inveon PET scanner.

Comparison of a noise-weighted filtered backprojection algorithm with the Standard MLEM algorithm for poisson noise

Iterative maximum-likelihood expectation maximization and ordered-subset expectation maximization algorithms are excellent for image reconstruction and usually provide better images than filtered backprojection (FBP). Recently, an FBP algorithm able to incorporate noise weighting during reconstruction was developed. This paper compares the performance of the noise-weighted FBP algorithm and the iterative maximum-likelihood expectation maximization algorithm with Poisson noise-corrupted emission data generated by computer simulations and a SPECT experimental study. The results show comparable performance for these 2 algorithms.

Molecular-frame 3D photoelectron momentum distributions by tomographic reconstruction

Naphthalene molecules are fixed in space by a laser field and rotated, in 2° steps, over 180°. For each orientation, they are ionized by an intense, circularly polarized femtosecond laser pulse, and the 2D projection of the photoelectron momentum distribution is recorded. The molecular-frame 3D momentum distribution is obtained by tomographic reconstruction from all 90 projections. It reveals an anisotropic electron distribution, angularly shifted in the polarization plane, that is not accessible by the 2D momentum images. Our theoretical analysis shows that the magnitude of the angular shift is very sensitive to the exact form of the laser-modified molecular potential.

Filtered Backprojection Algorithm Can Outperform Iterative Maximum Likelihood Expectation-Maximization Algorithm

The iterative maximum-likelihood expectation-maximization (ML-EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML-EM in certain occasions, when the least-squared difference from the true image, that is, the least-squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML-EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML-EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML-EM images. For the noiseless projections, the FBP algorithms outperform the ML-EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML-EM algorithm.

RMDP: a dedicated package for 131I SPECT quantification, registration and patient-specific dosimetry

The limitations of traditional targeted radionuclide therapy (TRT) dosimetry can be overcome by using voxel-based techniques. All dosimetry techniques are reliant on a sequence of quantitative emission and transmission data. The use of (131)I, for example, with NaI or mIBG, presents additional quantification challenges beyond those encountered in low-energy NM diagnostic imaging, including dead-time correction and additional photon scatter and penetration in the camera head. The Royal Marsden Dosimetry Package (RMDP) offers a complete package for the accurate processing and analysis of raw emission and transmission patient data. Quantitative SPECT reconstruction is possible using either FBP or OS-EM algorithms. Manual, marker- or voxel-based registration can be used to register images from different modalities and the sequence of SPECT studies required for 3-D dosimetry calculations. The 3-D patient-specific dosimetry routines, using either a beta-kernel or voxel S-factor, are included. Phase-fitting each voxel's activity series enables more robust maps to be generated in the presence of imaging noise, such as is encountered during late, low-count scans or when there is significant redistribution within the VOI between scans. Error analysis can be applied to each generated dose-map. Patients receiving (131)I-mIBG, (131)I-NaI, and (186)Re-HEDP therapies have been analyzed using RMDP. A Monte-Carlo package, developed specifically to address the problems of (131)I quantification by including full photon interactions in a hexagonal-hole collimator and the gamma camera crystal, has been included in the dosimetry package. It is hoped that the addition of this code will lead to improved (131)I image quantification and will contribute towards more accurate 3-D dosimetry.

[Analysis of the convergence relation of reconstructed algorithms disregarding local and global visual evaluations]

Tomographic reconstruction methods used in positron emission tomography are classified in two major groups: the traditionally and still widely applied filtered backprojection, and the iterative methods based on statistical models. This study focused on the objective comparison of different reconstruction algorithms, excluding criteria based on pure visual evaluation. The evaluation criteria were mathematically defined parameters, i.e., mean square error, standard deviation, signal-to-noise ratio and contrast recovery. The methods used for comparison were the classical filtered backprojection, the maximum likelihood expectation maximization algorithm, the maximum a-posteriori reconstruction model based on the Bayes Theorem, as well as the acceleration algorithms based on ordered subsets and high over-relaxation. These algorithms were evaluated by means of a mathematical brain phantom and of a physical spherical phantom. In terms of the applied parameters, the majority of the experiments showed a quantifiable superiority of the iterative methods compared the filtered backprojection.

Theoretical study of lesion detectability of MAP reconstruction using computer observers

The low signal-to-noise ratio (SNR) in emission data has stimulated the development of statistical image reconstruction methods based on the maximum a posteriori (MAP) principle. Experimental examples have shown that statistical methods improve image quality compared to the conventional filtered backprojection (FBP) method. However, these results depend on isolated data sets. Here we study the lesion detectability of MAP reconstruction theoretically, using computer observers. These theoretical results can be applied to different object structures. They show that for a quadratic smoothing prior, the lesion detectability using the prewhitening observer is independent of the smoothing parameter and the neighborhood of the prior, while the nonprewhitening observer exhibits an optimum smoothing point. We also compare the results to those of FBP reconstruction. The comparison shows that for ideal positron emission tomography (PET) systems (where data are true line integrals of the tracer distribution) the MAP reconstruction has a higher SNR for lesion detection than FBP reconstruction due to the modeling of the Poisson noise. For realistic systems, MAP reconstruction further benefits from accurately modeling the physical photon detection process in PET.