Simultaneous Multiplicative Algebraic Reconstruction Technique Research Articles

Estimation of pollutant source using source-receptor response matrix from maximum-length sequence pulse technique

Accurate estimation of pollutant sources in built environments is crucial for monitoring air quality and preventing harm to health and property. This study presented an improved method for estimating the dynamical pollutant source strength using the concentration signal monitored at the receptor point. We employed a built environment system subjected to a pollutant pulse signal in accordance with the maximum-length sequence (m-sequence) to acquire response concentration. Subsequently, the source-receptor response matrix was inversely identified based on the known pulse signal and the response concentration. Then, the unknown source release rate was inversely estimated by the monitored concentration signal and previously identified response matrix. In addition, the performances of different inverse algorithms and m-sequence orders were also analyzed. Here both simulation and application to a real experiment of a wind duct were implemented, and the results demonstrated the higher-order m-sequence method exhibited better noise resistance compared to the traditional unit pulse method. In both simulation and experiment, the m-sequence pulse method reduced the root mean square error (RMSE) by 39.9 % and 70.7 %, respectively, compared to the unit pulse method. In experiment, the simultaneous multiplicative algebraic reconstruction technique (SMART) combined with the Tikhonov regularization (TR) method showed relatively stable performance.

Image Reconstruction Algorithm Using Weighted Mean of Ordered-Subsets EM and MART for Computed Tomography

Iterative image reconstruction algorithms have considerable advantages over transform methods for computed tomography, but they each have their own drawbacks. In particular, the maximum-likelihood expectation-maximization (MLEM) algorithm reconstructs high-quality images even with noisy projection data, but it is slow. On the other hand, the simultaneous multiplicative algebraic reconstruction technique (SMART) converges faster at early iterations but is susceptible to noise. Here, we construct a novel algorithm that has the advantages of these different iterative schemes by combining ordered-subsets EM (OS-EM) and MART (OS-MART) with weighted geometric or hybrid means. It is theoretically shown that the objective function decreases with every iteration and the amount of decrease is greater than the mean between the decreases for OS-EM and OS-MART. We conducted image reconstruction experiments on simulated phantoms and deduced that our algorithm outperforms OS-EM and OS-MART alone. Our algorithm would be effective in practice since it incorporates OS-EM, which is currently the most popular technique of iterative image reconstruction from noisy measured projections.

Application and algorithm research of TDLAS

Tunable diode laser absorption spectroscopy (TDLAS) is extensively utilized in monitoring of trace gases in the environment. With the relative entropy tomographic reconstruction, simultaneous multiplicative algebraic reconstruction technique algorithm and optimization of existing functions and models, TDLAS has been applied to reconstruction of temperature and humidity field, combustion diagnosis, mass flow monitoring and other domains, this paper will analyze the existing TDLAS application and algorithm research.

A study on two-dimensional temperature and concentration distribution of Propane-Air premixed flame using CT-TDLAS

To use supplying gases and energy resources efficiently, accurate measurement of irregular gas is necessary. The TDLAS (Tunable laser absorption spectroscopy) technique can be used to control and monitor the supplying gas conditions and combustion of industrial processes. Recently, CT-TDLAS (Computed tomography-tunable diode laser absorption spectroscopy) has been developed to measure the temperature and concentration field of gases. In this study, the 2-dimensional temperature distribution of the Propane-Air premixed flame in several mixing conditions of fuel has been measured by the constructed CT-TDLAS system. 2-Dimensional temperature distributions are measured by 16 path cells. Further, the third-order polynomial regression analysis was applied to resolve the absorption spectra from the incident and transmitted light for a particular gas. The SMART (simultaneous multiplicative algebraic reconstruction technique) algorithm has been adopted for reconstructing the absorption coefficients on the detecting area. As a result of comparing the temperature for the 2-dimensional detecting area using the thermocouple and CT-TDLAS technique, it has been verified that the relative error for the temperatures measured by the thermocouples and calculated by the CT-TDLAS was up to 8%.

Measurement Enhancement on Two-Dimensional Temperature Distribution of Methane-Air Premixed Flame Using SMART Algorithm in CT-TDLAS

In this study, the temperature distribution of the Methane-Air premixed flame was measured. In order to enhance the measurement accuracy of the CT-TDLAS (Computed tomography-tunable diode laser absorption spectroscopy), the SMART (simultaneous multiplicative algebraic reconstruction technique) algorithm has been adopted. Further, the SLOS (summation of line of sight) and the CSLOS (corrective summation of line of sight) methods have been adopted to increase measurement accuracies. It has been verified that the relative error for the temperatures measured by the thermocouples and calculated by the CT-TDLAS was about 10%.

Evaluation of 3D measurement using CT-TDLAS

In order to satisfy the requirements of high quality and optimal material manufacturing process, it is important to control the environment of the manufacturing process. Depending on these processes, it is possible to improve the quality of the product by adjusting various gases. With the advent of the tunable laser absorption spectroscopy (TDLAS) technique, the temperature and concentration of the gases can be measured simultaneously. Among them, computed tomography-tunable diode laser absorption spectroscopy (CT-TDLAS) is the most important technique for measuring the distributions of temperature and concentration across the two-dimensional planes. This study suggests a three-dimensional measurement to consider the irregular flow of supplying gases. The simultaneous multiplicative algebraic reconstruction technique (SMART) algorithm was used among the CT algorithms. Phantom datasets have been generated by using Gaussian distribution method. It can show expected temperature and concentration distributions. The (HITRAN) database in which the thermo-dynamical properties and the light spectra of H2O are listed were used for the numerical test. The relative average temperature error ratio in the results obtained by the SMART algorithm was about 3.2% for temperature. The maximum error was 86.8 K.

Tomographic imaging of OH laser-induced fluorescence in laminar and turbulent jet flames

In this paper a new approach for 3D flame structure diagnostics using tomographic laser-induced fluorescence (Tomo-LIF) of the OH radical was evaluated. The approach combined volumetric illumination with a multi-camera detection system of eight views. Single-shot measurements were performed in a methane/air premixed laminar flame and in a non-premixed turbulent methane jet flame. 3D OH fluorescence distributions in the flames were reconstructed using the simultaneous multiplicative algebraic reconstruction technique. The tomographic measurements were compared and validated against results of OH-PLIF in the laminar flame. The effects of the experimental setup of the detection system and the size of the volumetric illumination on the quality of the tomographic reconstructions were evaluated. Results revealed that the Tomo-LIF is suitable for volumetric reconstruction of flame structures with acceptable spatial resolution and uncertainty. It was found that the number of views and their angular orientation have a strong influence on the quality and accuracy of the tomographic reconstruction while the illumination volume thickness influences mainly the spatial resolution.

Performances of new reconstruction algorithms for CT-TDLAS (computer tomography-tunable diode laser absorption spectroscopy)

Recent advent of the tunable lasers made to measure simultaneous temperature and concentration fields of the gases. CT-TDLAS (computed tomography-tunable diode laser absorption spectroscopy) is one the leading techniques for the measurements of temperature and concentration fields of the gases. In CT-TDLAS, the accuracies of the measurement results are strongly dependent upon the reconstruction algorithms. In this study, four different reconstruction algorithms have been tested numerically using experimental data sets measured by thermocouples for combustion fields. Three reconstruction algorithms, MART (multiplicative algebraic reconstruction technique) algorithm, SART (simultaneous algebraic reconstruction technique) algorithm and SMART (simultaneous multiplicative algebraic reconstruction technique) algorithm, are newly proposed for CT-TDLAS in this study. The calculation results obtained by the three algorithms have been compared with previous algorithm, ART (algebraic reconstruction technique) algorithm. Phantom data sets have been generated by the use of thermocouples data obtained in an actual experiment. The data of the Harvard HITRAN table in which the thermo-dynamical properties and the light spectrum of the H2O are listed were used for the numerical test. The reconstructed temperature and concentration fields were compared with the original HITRAN data, through which the constructed methods are validated. The performances of the four reconstruction algorithms were demonstrated. This method is expected to enhance the practicality of CT-TDLAS.

20-kHz-rate three-dimensional tomographic imaging of the concentration field in a turbulent jet

Three-dimensional imaging of the tracer concentration field is demonstrated at a rate of 20kHz in a turbulent gaseous free jet. The acetone tracer species that is seeded into the jet is excited by the fourth-harmonic output of a Nd:YAG burst-mode laser. The laser beam is expanded and re-collimated to a 35-mm-diameter beam and passed through a diffuser to reduce spatial variations within the beam profile. Seven high-speed cameras coupled to high-speed intensifiers with vertical stereoscopes collect fourteen simultaneous views of the fluorescence emission. The images are processed and a linear relationship between signal intensity and acetone concentration was verified. Eight of the fourteen processed views are then reconstructed into volumes using a simultaneous multiplicative algebraic-reconstruction technique, limited by the software. The mixing behavior is characterized and compared with turbulent-jet scaling laws and data from the literature at similar conditions. The accuracy, precision, and limitations of the technique are discussed, and potential strategies for implementation in reacting flows are considered.

Development of a three-dimensional correction method for optical distortion of flow field inside a liquid droplet.

In this Letter, a three-dimensional (3D) optical correction method, which was verified by simulation, was developed to reconstruct droplet-based flow fields. In the simulation, a synthetic phantom was reconstructed using a simultaneous multiplicative algebraic reconstruction technique with three detectors positioned at the synthetic object (represented by the phantom), with offset angles of 30° relative to each other. Additionally, a projection matrix was developed using the ray tracing method. If the phantom is in liquid, the image of the phantom can be distorted since the light passes through a convex liquid-vapor interface. Because of the optical distortion effect, the projection matrix used to reconstruct a 3D field should be supplemented by the revision ray, instead of the original projection ray. The revision ray can be obtained from the refraction ray occurring on the surface of the liquid. As a result, the error on the reconstruction field of the phantom could be reduced using the developed optical correction method. In addition, the developed optical method was applied to a Taylor cone which was caused by the high voltage between the droplet and the substrate.

Multifunctional, three-dimensional tomography for analysis of eletrectrohydrodynamic jetting

A three-dimensional optical tomography technique was developed to reconstruct three-dimensional objects using a set of two-dimensional shadowgraphic images and normal gray images. From three high-speed cameras, which were positioned at an offset angle of 45° between each other, number, size, and location of electrohydrodynamic jets with respect to the nozzle position were analyzed using shadowgraphic tomography employing multiplicative algebraic reconstruction technique (MART). Additionally, a flow field inside a cone-shaped liquid (Taylor cone) induced under an electric field was observed using a simultaneous multiplicative algebraic reconstruction technique (SMART), a tomographic method for reconstructing light intensities of particles, combined with three-dimensional cross-correlation. Various velocity fields of circulating flows inside the cone-shaped liquid caused by various physico-chemical properties of liquid were also investigated.

Tomographic PIV: particles versus blobs

We present an alternative approach to tomographic particle image velocimetry (tomo-PIV) that seeks to recover nearly single voxel particles rather than blobs of extended size. The baseline of our approach is a particle-based representation of image data. An appropriate discretization of this representation yields an original linear forward model with a weight matrix built with specific samples of the system’s point spread function (PSF). Such an approach requires only a few voxels to explain the image appearance, therefore it favors much more sparsely reconstructed volumes than classic tomo-PIV. The proposed forward model is general and flexible and can be embedded in a classical multiplicative algebraic reconstruction technique (MART) or a simultaneous multiplicative algebraic reconstruction technique (SMART) inversion procedure. We show, using synthetic PIV images and by way of a large exploration of the generating conditions and a variety of performance metrics, that the model leads to better results than the classical tomo-PIV approach, in particular in the case of seeding densities greater than 0.06 particles per pixel and of PSFs characterized by a standard deviation larger than 0.8 pixels.

Optimization of the volume reconstruction for classical Tomo-PIV algorithms (MART, BIMART and SMART): synthetic and experimental studies

Optimization of multiplicative algebraic reconstruction technique (MART), simultaneous MART and block iterative MART reconstruction techniques was carried out on synthetic and experimental data. Different criteria were defined to improve the preprocessing of the initial images. Knowledge of how each reconstruction parameter influences the quality of particle volume reconstruction and computing time is the key in Tomo-PIV. These criteria were applied to a real case, a jet in cross flow, and were validated.

Alternating Minimization as Sequential Unconstrained Minimization: A Survey

Sequential unconstrained minimization is a general iterative method for minimizing a function over a given set. At each step of the iteration we minimize the sum of the objective function and an auxiliary function. The aim is to select the auxiliary functions so that, at least, we get convergence in function value to the constrained minimum. The SUMMA is a broad class of these methods for which such convergence holds. Included in the SUMMA class are the barrier-function methods, entropic and other proximal minimization algorithms, the simultaneous multiplicative algebraic reconstruction technique, and, after some reformulation, penalty-function methods. The alternating minimization method of Csiszar and Tusnady also falls within the SUMMA class, whenever their five-point property holds. Therefore, the expectation maximization maximum likelihood algorithm for the Poisson case is also in the SUMMA class.

Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions

Tomographic shadowgraphy is an image-based optical technique capable of reconstructing the three dimensional instantaneous spray distributions within a given volume. The method is based on a multiple view imaging setup with inline illumination provided by current-pulsed LEDs, which results in droplet shadows being projected onto multiple sensor planes. Each camera records image pairs with short inter-framing times that allow the trajectories of the individual droplets to be estimated using conventional three-dimensional particle tracking approaches. The observed volume is calibrated with a traversed micro-target. A comparison is made between several photogrammetric and polynomial least-square camera calibration techniques regarding their accuracy in deep volume calibration at magnifications close to unity. A calibration method based on volume calibration from multiple planar homographies at equally spaced z-planes was found to produce the most reliable calibration. The combination of back-projected images at each voxel plane efficiently reproduces the droplet positions in three-dimensional space by line-of-sight (LOS) intensity reconstruction. Further improvement of the reconstruction can be achieved by iterative tomographic reconstruction, namely simultaneous multiplicative algebraic reconstruction technique (SMART). The quality of spray reconstruction is investigated using experimental data from multiple view shadowgraphs of hollow cone and flat fan water sprays. The investigations are further substantiated with simulations using synthetic data.

Suitability of an MRMCE (multi-resolution minimum cross entropy) algorithm for online monitoring of a two-phase flow

The flow regimes are important characteristics to describe two-phase flows, and measurement of two-phase flow parameters is becoming increasingly important in many industrial processes. Computerized tomography (CT) has been applied to two-phase/multi-phase flow measurement in recent years. Image reconstruction of CT often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive, especially for the case of online flow regime identification. In this paper, minimum cross entropy reconstruction based on multi-resolution processing (MRMCE) is presented for oil–gas two-phase flow regime identification. A regularized MCE solution is obtained using the simultaneous multiplicative algebraic reconstruction technique (SMART) at a coarse resolution level, where important information on the reconstructed image is contained. Then, the solution in the finest resolution is obtained by inverse fast wavelet transformation. Both computer simulation and static/dynamic experiments were carried out for typical flow regimes. Results obtained indicate that the proposed method can dramatically reduce the computational time and improve the quality of the reconstructed image with suitable decomposition levels compared with the single-resolution maximum likelihood expectation maximization (MLEM), alternating minimization (AM), Landweber, iterative least square technique (ILST) and minimum cross entropy (MCE) methods. Therefore, the MRMCE method is suitable for identification of dynamic two-phase flow regimes.

Fast reconstruction of computerized tomography images based on the cross-entropy method

Computerized tomography (CT) has been applied to multi-phase flow measurement in recent years. Image reconstruction of CT often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive, especially for the case of on-line flow regime identification. In this paper, a minimum cross-entropy (MCE) reconstruction based on wavelet multi-resolution processing, i.e., an MRMCE method, is proposed for fast reconstruction of CT images. Each row of the system’s matrix is transformed by 1-D wavelet decomposition. A regularized MCE solution is obtained using the simultaneous multiplicative algebraic reconstruction technique (SMART) at a coarse resolution level, where important information of the reconstructed image is contained. Then the solution in the finest resolution is obtained by inverse fast wavelet transformation (IFWT). Both computer simulation and experimental work were carried out for oil–gas two-phase flow regimes. Results obtained indicate that the MRMCE method improves the resolution of the reconstructed images and dramatically reduces the computation time compared with the traditional linear back-projection (LBP), MCE and algebraic reconstruction technique (ART) methods. Furthermore, the new method can also be used to accurately estimate the local time-averaged void fraction of dynamic two-phase flow. It is suitable for on-line multi-phase flow measurement.

Tomographic particle image velocimetry investigation of the flow in a modeled human carotid artery bifurcation

Hemodynamic forces within the human carotid artery are well known to play a key role in the initiation and progression of vascular diseases such as atherosclerosis. The degree and extent of the disease largely depends on the prevailing three-dimensional flow structure and wall shear stress (WSS) distribution. This work presents tomographic PIV (Tomo-PIV) measurements of the flow structure and WSS in a physiologically accurate model of the human carotid artery bifurcation. The vascular geometry is reconstructed from patient-specific data and reproduced in a transparent flow phantom to demonstrate the feasibility of Tomo-PIV in a complex three-dimensional geometry. Tomographic reconstruction is performed with the multiplicative line-of-sight (MLOS) estimation and simultaneous multiplicative algebraic reconstruction (SMART) technique. The implemented methodology is validated by comparing the results with Stereo-PIV measurements in the same facility. Using a steady flow assumption, the measurement error and RMS uncertainty are directly inferred from the measured velocity field. It is shown that the measurement uncertainty increases for increasing light sheet thickness and increasing velocity gradients, which are largest near the vessel walls. For a typical volume depth of 6 mm (or 256 pixel), the analysis indicates that the velocity derived from 3D cross-correlation can be measured within ±2% of the maximum velocity (or ±0.2 pixel) near the center of the vessel and within ±5% (±0.6 pixel) near the vessel wall. The technique is then applied to acquire 3D-3C velocity field data at multiple axial locations within the carotid artery model, which are combined to yield the flow field and WSS in a volume of approximately 26 mm × 27 mm × 60 mm. Shear stress is computed from the velocity gradient tensor and a method for inferring the WSS distribution on the vessel wall is presented. The results indicate the presence of a complex and three-dimensional flow structure, with regions of flow separation and strong velocity gradients. The WSS distribution is markedly asymmetric confirming a complex swirling flow structure within the vessel. A comparison of the measured WSS with Stereo-PIV data returns an acceptable agreement with some differences in stress magnitude.

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.

Sequential unconstrained minimization algorithms for constrained optimization

The problem of minimizing a function f(x):RJ → R, subject to constraints on the vector variable x, occurs frequently in inverse problems. Even without constraints, finding a minimizer of f(x) may require iterative methods. We consider here a general class of iterative algorithms that find a solution to the constrained minimization problem as the limit of a sequence of vectors, each solving an unconstrained minimization problem. Our sequential unconstrained minimization algorithm (SUMMA) is an iterative procedure for constrained minimization. At the kth step we minimize the function to obtain xk. The auxiliary functions gk(x):D ⊆ RJ → R+ are nonnegative on the set D, each xk is assumed to lie within D, and the objective is to minimize the continuous function f:RJ → R over x in the set , the closure of D. We assume that such minimizers exist, and denote one such by . We assume that the functions gk(x) satisfy the inequalities for k = 2, 3, …. Using this assumption, we show that the sequence {f(xk)} is decreasing and converges to . If the restriction of f(x) to D has bounded level sets, which happens if is unique and f(x) is closed, proper and convex, then the sequence {xk} is bounded, and , for any cluster point x*. Therefore, if is unique, and . When is not unique, convergence can still be obtained, in particular cases. The SUMMA includes, as particular cases, the well-known barrier- and penalty-function methods, the simultaneous multiplicative algebraic reconstruction technique (SMART), the proximal minimization algorithm of Censor and Zenios, the entropic proximal methods of Teboulle, as well as certain cases of gradient descent and the Newton–Raphson method. The proof techniques used for SUMMA can be extended to obtain related results for the induced proximal distance method of Auslander and Teboulle.