Algebraic Reconstruction Technique Method Research Articles

Voxel-free neural volume reconstruction technique for volumetric flame reconstructions

Volumetric reconstructions of transparent or translucent mediums are critical for various applications. For instance, successful reconstructions of transient and turbulent flames will assist in understanding the complex combustion mechanisms during combustion and advanced burner design. The most common method for volumetric flame combustion diagnosis is the tomographic reconstruction technique. Originating from computed tomography for medical diagnosis purposes, computed tomography of chemiluminescence (CTC) is a volumetric flame diagnostic method that utilizes two-dimensional projections of flame under limited viewing angles to reconstruct three-dimensional information of the combustion field. Typical flame reconstructions use discrete volumetric voxels to represent the flame luminosities at different spatial locations. However, this approach increases the computation costs in both weight matrix calculations and tomographic iterations. This investigation proposes a neural volume reconstruction technique (NVRT) that uses a neural network to represent the continuous flame luminosity implicitly. Besides, this investigation adopts the differentiable volume rendering (DVR) technique to train the network based on two-dimensional flame projections and does not require 3D supervision. We use both simulated flames and experimental flames to verify the capability of the proposed NVRT method against the traditional algebraic reconstruction technique (ART). Results show that the NVRT method is superior to the ART method in reconstruction fidelity, resistance to noise, and computational cost (especially RAM usage) for flame reconstructions.

Estimation of a Fission Product Concentration Distribution in a Spherical Body from Surface Release Measurements

The diffusion of fission products (FPs) in reactor materials affects the nuclear source term. The diffusion coefficient itself is measured through various techniques. In the release method, it is of interest to know the initial distribution of the FPs in nuclear graphite or other materials from an exterior measurement like mass surface flux or cumulative mass release. In this paper, a Fredholm integral of the first kind is considered, relating the initial distribution to the cumulative release fraction of a diffusant from a spherically symmetric body. The Tikhonov regularization, conjugate gradient least-squares (CGLS) method, and algebraic reconstruction technique (ART) with nonnegativity and conserved mass constraints were compared to fractional release data from a simulated linear profile using data for Cs diffusion in a 0.32-cm sphere NBG-18 at 1090 K. The Tikhonov regularization was shown to provide a better estimation of the initial linear distribution than the CGLS and ART methods. The performance of the Tikhonov regularization was further examined with simulated constant, quartic, and exponential initial distributions. The Tikhonov regularization provided a reasonable recovery of the exponential profile, while the estimation of the linear, constant, and quartic profiles suffers from several issues.

An improved ART algorithm for attenuation coefficient reconstruction of tomographic gamma scanners

A method of reconstructing the attenuation coefficient in the case of tomographic gamma scanning (TGS) imaging of nuclear waste tanks is proposed. The method was developed on the basis of the algebraic reconstruction technique (ART) method and is called the simultaneous iterative reconstruction techniques diagonally relaxed orthogonal projections (SIRT-DROP) method. To evaluate the accuracy of the method, a multi-layer model was designed. Each layer consisted of 25 (5 × 5) voxels, and each pixel measured 12 ×12× 12 cm. Results indicated that a maximum uncertainty of 34.88% and an average uncertainty of 14% were obtained when applying the ART method, while a maximum uncertainty of 16.11% and an average uncertainty of 9.96% were obtained when applying the proposed SIRT-DROP method. By performing linear regression in a C-language program on the energy–mass attenuation coefficient, the maximum and average uncertainties of the energy–mass attenuation coefficient were 35.32% and 15.67%, respectively, when the ART method was applied. When the SIRT-DROP method was applied, the maximum and average uncertainties of the energy–mass attenuation coefficient were lowered to 22.43% and 8.01%, respectively. Monte Carlo simulation results verified the capability of the proposed method, and the reconstructed attenuation coefficient was in an agreement with the pre-set value.

Adaptive weight matrix and phantom intensity learning for computed tomography of chemiluminescence.

Classic algebraic reconstruction technique (ART) for computed tomography requires pre-determined weights of the voxels for the projected pixel values to build the equations. However, such weights cannot be accurately obtained in the application of chemiluminescence measurements due to the high physical complexity and computation resources required. Moreover, streaks arise in the results from ART method especially with imperfect projections. In this study, we propose a semi-case-wise learning-based method named Weight Encode Reconstruction Network (WERNet) to co-learn the target phantom intensities and the adaptive weight matrix of the case without labeling the target voxel set and thus offers a more applicable solution for computed tomography problems. Both numerical and experimental validations were conducted to evaluate the algorithm. In the numerical test, with the help of gradient normalization, the WERNet reconstructed voxel set with a high accuracy and showed a higher capability of denoising compared to the classic ART methods. In the experimental test, WERNet produces comparable results to the ART method while having a better performance in avoiding the streaks. Furthermore, with the adaptive weight matrix, WERNet is not sensitive to the ensemble intensity of the projection which shows much better robustness than ART method.

Optimization of Reconstruction Accuracy of Anomaly Position Based on Stacked Auto-Encoder Neural Networks

The diffuse optical tomography (DOT) technique which uses the traditional linear iterative algorithm has the problems of slow calculation speed and low reconstruction imaging accuracy in the inverse problem reconstruction, which limits its clinical application and development. This paper proposes an inverse-problem solving technology based on a stacked auto-encoder (SAE) network to improve the reconstruction accuracy of anomaly position, size and absorption coefficient in tissues. The reconstruction accuracy of anomaly position, size and absorption coefficient obtained by the traditional algebraic reconstruction technique (ART) method and the SAE based method are experimentally compared. The experimental results show that the SAE based method achieves the prediction accuracy of anomaly position of 96.25%, thus improving the accuracy and shortening the reconstruction time compared with the traditional ART method. Accordingly, the proposed method provides a better solution to the problem of the inaccurate reconstruction of the position and size of the rapid DOT based positioning of anomalies.

Cloud tomography applied to sky images: A virtual testbed

Two tomographic techniques are applied to two simulated sets of sky images with different cloud fraction. The Algebraic Reconstruction Technique (ART) is applied to optical depth maps from sky images to reconstruct 3-D cloud extinction coefficients without considering multiple scattering effects. Reconstruction accuracy is explored for different products, including surface irradiance and extinction coefficients, and as a function of the number of available sky imagers and setup distance. Increasing the number of imagers improves the accuracy of the 3-D reconstruction: for surface irradiance, the error decreases significantly up to four imagers at which point the improvements become marginal. But using nine imagers gives more robust results in practical situations in which the circumsolar region of images has to be excluded due to poor cloud detection. The ideal distance between imagers was also explored: for a cloud height of 1 km, increasing distance up to 3 km (the domain length) improved the 3-D reconstruction. An iterative reconstruction technique that iteratively updated the source function improved the results of the ART by minimizing the error between input red radiance images and reconstructed red radiance simulations. For the best case of a nine-imager deployment, the ART and iterative method resulted in 53.4% and 33.6% relative mean absolute error for the extinction coefficients, respectively.

Investigation of various reconstruction parameters for algebraic reconstruction technique in a newly developed chest digital tomosynthesis

Chest digital tomosynthesis (CDT) is a promising new modality that provides 3D information by reconstructing limited projection views. CDT systems have been developed to improve the limitations of conventional radiography such as image degradation and low sensitivity. However, the development of reconstruction methods is challenging because of the limited projection views within various angular ranges. Optimization of reconstruction parameters for various reconsturction methods in CDT system also is needed. The purpose of this study was to investigate the feasibility of algebraic reconstruction technique (ART) method, and to evaluate the effect of the reconstruction parameters for our newly developed CDT system. We designed ART method with 41 projection views over an angular range of ±20°. To investigate the effect of reconstruction parameters, we measured the contrast-to-noise ratio (CNR), artifact spread function (ASF), and quality factor (QF) using LUNGMAN phantom included tumors. We found that the proper choice of reconstruction parameters such as relaxation parameter, initial guess, and number of iterations improved the quality of reconstructed images from the same projection views. Optimal values of ART relaxation parameter with uniform (UI) and back-projection (BP) initial guesses were 0.4 and 0.6, respectively. BP initial guess improved image quality in comparison with UI initial guess, in terms of providing a higher CNR and QF values with a faster speed. CNR and QF values improved with increasing number of iteration. Particularly, ART method with BP initial guess (when β = 0.6) after 3-terations provide satisfactory reconstructed image. In conclusion, the use of ART method with proper reconstruction parameters provided better image quality than FBP method as well as conventional radiography. These results indicated that the ART method with optimal reconstruction parameters could improve image quality for nodule detection using the CDT system.

Two-Phase Flow Regime Identification Based on Cross-Entropy and Information Extension Methods for Computerized Tomography

Computerized tomography (CT) is applied to multiphase flow measurements in recent years. A new approach based on the cross-entropy and information extension methods is proposed for two-phase flow regime identification in this paper. Two minimum cross-entropy methods, namely, maximum a posteriori and simultaneous multiplicative algebraic reconstruction technique (ART), are presented. This paper discusses the selection of parameters and prior smoothing operator. An information extension method is proposed based on the geometrical model of the CT system to reduce ill condition and modify the edge shape of reconstruction. Both simulation and experiments were carried out for typical flow regimes, indicating that the proposed method can reduce the computation time and improve the resolution of the reconstructed images compared with the ART method.

X-Ray Image Reconstruction of Solder Joints by Using Several Algebraic Reconstruction Techniques

In this study, several Algebraic Reconstruction Technique (ART) algorithms are used to construct the 3 D sliced images from several transparent X-ray images. The speed and quality of image reconstruction are two important requirements when doing the inspection in a printed circuit board (PCB) assembly line. . To fulfill the requirements, several methodologies are discussed. The image qualities of regular ART method, binary ART method and Mixed ART method are developed and compared. The binary ART method uses the property of x-ray absorb rate of metal, silicon and other non- metal material are extremely different. The absorb rates of non-metal part are assumed to be zero and metal parts are assumed to be a single value. By using this method the quality of image reconstruction is improved. The mixed ART method is the combination of the tradition ART method and binary ART. Due to the X-ray sensor’s framing time, a method to improve the image reconstruction quality due to effect of X-ray sensor framing time is also discussed. Finally, the best solution algorithm is found to be mixed binary steering ART when consider the signal noise of X-ray detector.

Algebraic reconstruction techniques for spectral reconstruction in diffuse optical tomography

Reconstruction in diffuse optical tomography (DOT) necessitates solving the diffusion equation, which is nonlinear with respect to the parameters that have to be reconstructed. Currently applied solving methods are based on the linearization of the equation. For spectral three-dimensional reconstruction, the emerging equation system is too large for direct inversion, but the application of iterative methods is feasible. Computational effort and speed of convergence of these iterative methods are crucial since they determine the computation time of the reconstruction. In this paper, the iterative methods algebraic reconstruction technique (ART) and conjugated gradients (CGs) as well as a new modified ART method are investigated for spectral DOT reconstruction. The aim of the modified ART scheme is to speed up the convergence by considering the specific conditions of spectral reconstruction. As a result, it converges much faster to favorable results than conventional ART and CG methods.

Simulations of an Optical Tactile Sensor Based on Computer Tomography

In order to create a robotic tactile sensor of thin shape, a new optical tactile sensor is developed by applying a CT (Computer Tomography) algorithm. The present tactile sensor is comprised of infrared emitting diode arrays, receiving phototransistor arrays and a transparent acrylic plate and a black rubber sheet with projections. Infrared rays emitted from the diode array are directed into one end of the plate and their intensity distribution is measured by the phototransistor array mounted on the other end. If the CT algorithm is directly applied to the tactile sensor, there are two shortcomings: the shape of the sensing area is limited to a circular region and there is a long calculation time. Thus, a new CT algorithm oriented to tactile sensing is proposed for overcoming these problems. In the present algorithm, a square sensing area is divided into an N-by-N array and algebraic equations are derived from the relationship between the input and output light intensities on the assumed light projections. Several reconstruction methods are considered for obtaining pressure values caused in the squares. In the present study, the ART (Algebraic Reconstruction Technique) and LU decomposition methods were employed, and these methods were compared to select the best reconstruction method. In a series of simulations, it was found that the LU decomposition method held an advantage for the present type of tactile sensor because of its robustness against disturbance and short calculation time.

Implementation of uniform and simultaneous ART for 3-D reconstruction in an X-ray imaging system

The authors propose a 3-D volume reconstruction method using X-ray images with a calibration method to implement it in an X-ray imaging system. Previously the authors have proposed an advanced 3-D reconstruction algorithm based on an algebraic reconstruction technique (ART), called a uniform and simultaneous ART (USART). In practice, however, there are two main issues in implementing it in a realised X-ray imaging system. The first one is the huge computation time and memory required in achieving 3-D volume, which is a common limitation in most ART methods. The second issue is the system calibration for determining the geometry of the X-ray imaging conditions needed for the ART method. These two critical problems are addressed. A fast computing model of USART is proposed, where spherical voxel elements are employed in computation to reduce the computation time and memory. Then, a calibration method is proposed to identify the X-ray imaging geometry based on a cone beam projection model. For this purpose, a set of X-ray images of a reference grid pattern is used and the X-ray source positions are determined from the analysis of the image features, the centres of the grid points in the X-ray images. The validity of the proposed 3-D reconstruction method is investigated using a series of experiments.

An extended algebraic reconstruction technique (ART) for density-gradient projections: laser speckle photographic tomography

An extended algebraic reconstruction technique (ART) is presented for tomographic image reconstruction from the density-gradient projections, such as laser speckle photography. The essence of the extended ART is that the density-gradient projection data of speckle photography (Eq. (1)) are first numerically integrated to the algebraic representation of interferometric fringe number data (Eq. (12)), which ART can readily reconstruct into the cross-sectional field. The extended ART is numerically examined by using two computer synthesized phantom fields, and experimentally by using asymmetric single and double helium jets in air. The experimentally reconstructed images were also compared with the direct measurements of helium concentration using an oxygen analyzing probe. The extended ART method shows an improved accuracy and is proposed to use to tomographically reconstruct the density-gradient projections over the previous Fourier convolution (FC) method (Liu et al. 1989).

A high resolution EPR-CT microscope using cavity-resonators equipped with small field gradient coils

Cylindrical cavity resonators equipped with field gradient coils were developed for two-dimensional EPR-CT microscope systems. The field gradient coils lie in four (or six) thin metal tubes placed along the direction of the microwave magnetic field in the cavity to minimize impact on the resonator's quality factor. Two pairs of the tubes carry a 100 kHz current for magnetic field modulation. This cavity has high spin-detection sensitivity and can provide EPR images with submillimeter resolution. In order to reconstruct better images from fewer projections, we used an algebraic reconstruction technique (ART) for the two-dimensional image reconstruction. The ART method may be suitable for not only spectral-spatial two-dimensional EPR imaging, but also spatio-temporal EPR imaging in dynamic spin systems.

Implementation and experimental evaluation of the constrained ART algorithm on a multicomputer system

Truly three-dimensional reconstruction from projections can be carried out by the well-known ART (algebraic reconstruction technique) methods. In this work we present the implementation of an additive ART algorithm based on the theory of projections onto convex sets. It takes advantage of the high sparsity of the coefficient matrix allowing for an efficient parallelization. The solution has been conceived for a multiprocessor system using the SPMD (single program multiple data) programming model and our practical evaluation has been realized on an i860 based multiprocessor system.

A comparison of transform and iterative reconstruction techniques for a volume-imaging PET scanner with a large axial acceptance angle

The authors present the results of comparing 3-D transform and iterative reconstruction methods with measured PET data from the HEAD PENN-PET scanner, which has a very large axial acceptance angle of 27/spl deg/. The algorithms compared are the 3-D-reprojection (3DRP) method, the iterative algebraic reconstruction technique (ART), and the maximum likelihood (ML-EM) algorithm. For the iterative methods, alternatives to the cubic voxel basis functions are also implemented. The comparisons are based on a series of figures of merit, including the point-spread function, the contrast recovery coefficient, and signal-to-noise ratios (SNR). The results show that the ART method implemented with the new basis functions requires only one cycle through the data to produce images with measured SNR values comparable to or better than the 3DRP method. The ML-EM method was run for 10 iterations and produced images with lower SNR values for the test phantom used. With the exception of the ML-EM results, these are in agreement with the authors' previous simulation studies.