Iterative Linear Back Projection Research Articles

Image Reconstruction Method Based on Iterative Linear Back Projection and Logistic Forward Solver for Electrical Capacitance Tomography Measurement System

Image Reconstruction Method Based on Iterative Linear Back Projection and Logistic Forward Solver for Electrical Capacitance Tomography Measurement System

Simulasi Rekonstruksi Citra Pada Sensor Brain ECVT (Electrical Capacitance Volume Tomography) dengan Metode ILBP (Iterative Linear Back Projection)

<p>The purpose of this study is to simulate the sensor 32-channel Brain ECVT image reconstruction using ILBP (Iterative Linear Back Projection) methods. ECVT is a dynamic volume imaging technique that utilizes non-linear difference of electric field distribution to determine the distribution of permittivity in the sensing area. ECVT has measured the capacitance of data as a result of changes in the permittivity distribution between the electrode pairs. ECVT device consists of three main parts: helmet-shaped sensors, DAS (Data Acquisition System), PC for display and image reconstruction process. Simulation of sensor design using COMSOL Multiphysics 3.5 software, while the process of image reconstruction and analysis of the results using Matlab software 2009a. The principle of ECVT includes two stages of data collection capacitance of electrodes (forward problem) and image reconstruction from the measured capacitance (inverse problem). In the study, the simulation of image reconstruction was done by varying the object position, the number of objects and charge density of the object. From the simulation results showed that the reconstructed image with ILBP method is influenced by several parameters: the object's position in the sensor,charge density value of the object, an alpha value and the number of iterations was selected.</p>

A review of image reconstruction methods in electrical capacitance tomography

In this paper, we review image reconstruction methods and their suitability in electrical capacitance tomography measurement system. These methods can be grouped into direct and iterative methods. Direct methods include Linear back projection, Singular value decomposition, and Tikhonov regularization. Iterative methods are further divided into algebraic and optimization methods. Algebraic reconstruction methods include iterative linear back projection, iterative Tikhonov, Landweber iteration, simultaneously algebraic reconstruction, and model$ - $based reconstruction. Optimization methods include fuzzy mathematical modeling, genetic algorithms, artificial neural networks, generalized vector sampled pattern matching, total variation regularization, regularized total least squares, extended Tikhonov regularization, simulated annealing, compressed sensing principle, population entropy, adaptive differential evolution, least$ - $squares support vector machine, and self-adaptive particle swarm optimization. Some of these methods have been examined through experiments and their comparative analysis have been given. Results show that iterative methods generate high quality images compared with non-iterative ones when evaluated over full component fraction range. However, iterative methods are computationally expensive, and hence used for research and off-line investigations rather than for on-line process monitoring.

Flame Imaging Using 3D Electrical Capacitance Tomography

Electrical Capacitance Tomography for visualization of combustion process is based on measurement of variation of electrical properties of flame, such as electrical permittivity and conductivity of the reaction the zone. The signal level depends on the concentration of various charged particles in the combustion zone. Possible carriers are electrons and positive and negative ions. These charged particles may be formed as a result of chemical reactions, which are called chemi-ionization and thermal ionization. These properties in a combustion chamber are measured with specially designed electrodes. Distribution of charged particles in the combustion zone is reconstructed from measurements of electrical signal from the electrodes using linear back projection or iterative linear back projection algorithm.

Charge distribution around a rising bubble in a two-dimensional fluidized bed by signal reconstruction

A signal reconstruction technique was developed recently to measure the electrostatic charge density distribution surrounding a bubble rising in a two-dimensional gas–solid fluidized bed using four induction probes flush with the outside wall of a two-dimensional fluidized bed and connected to charge amplifiers for recording induced charge signals as bubbles pass by the probes. The model was implemented in Visual FORTRAN using the LSGRR Subroutine to invert the matrix for the signal reconstruction. However, if the matrix was mathematically singular or ill-conditioned, a least-squares routine or the singular value decomposition routine provided had to be used to give approximate results. If the dimension of the matrix exceeds the permissible limit, or the number of pixels is much larger than the number of measurements, the matrix cannot be inverted using the LSGRR subroutine. This paper shows that an iterative linear back projection algorithm (LBP), often used in linear tomography, can be applied to improve the reconstruction resolution of the charge distribution around rising single bubbles in a gas–solid fluidized bed. The experimentally measured induced charges from four induction probes were then applied to reconstruct the real charge distribution around a single rising gas bubble injected in a two-dimensional column as it passed the probes. The results reconstructed using the LBP method are found to be smoother and more accurate than those obtained from the LSGRR subroutine.

Effects of probe numbers and arrangement on the measurement of charge distributions around a rising bubble in a two-dimensional fluidized bed

The charge density distribution around a rising bubble in a two-dimensional fluidized bed was measured using eight induction probes flush with the outside wall of the column and connected to charge amplifiers for recording induced charge signals as bubbles passed by. The charge distribution surrounding the bubble was reconstructed using an iterative linear back projection (LBP) algorithm by assuming that the bubble is symmetrical and the charge around the bubble remains constant as the bubble rises. The results showed that the emulsion phase far from the bubble in a two-dimensional fluidized bed of glass beads was charged negatively, and the charge density decreased gradually toward the bubble-dense phase interface, with a nearly zero charge density inside the bubble. The effects of the number of probes are also investigated. The reconstructed results using both simulated charge distribution and experimental data for different numbers of probes of the same probe diameter of 3 mm showed that increasing the number of probes can improve the reconstruction resolution. The addition of one or two more probes outside the bubble path also increased the reconstruction resolution in the region outside the bubble.

Nonlinear forward problem solution for electrical capacitance tomography using feed-forward neural network

A new technique for solving the forward problem in electrical capacitance tomography sensor systems is introduced. The new technique is based on training a feed-forward neural network (NN) to predict capacitance data from permittivity distributions. The capacitance data used in training and testing the NN is obtained from preprocessed and filtered experimental measurements. The new technique has shown better results when compared to the commonly used linear forward projection (LFP) while maintaining fast prediction speed. The new technique has also been integrated into a modified iterative linear back projection (Landweber) reconstruction algorithm. Reconstruction results are found to be in favor of the NN forward solver when compared to the widely used Landweber reconstruction technique with LFP forward solver.

The dynamic calibration of an electrical capacitance tomography sensor applied to the fluidized bed drying of pharmaceutical granule

Electrical capacitance tomographic data collected in a lab-scale fluidized bed used for the drying of pharmaceutical granule have been corrected for the influence of moisture on the permittivity of the drying material. The correction is based on a linear least-squares fit to measurements of capacitance in a packed bed of granule at various moisture contents. X-ray tomography has been used to independently verify this correction procedure. The influence of permittivity models and number of iterations used for the reconstruction of tomograms have also been examined. It has been determined that the Böttcher permittivity model performs best at bed moistures above approximately 5 wt% while the parallel model is superior at bed moisture below this value. The reconstruction technique based on iterative linear back-projection utilized for the reconstruction of ECT data required approximately 50 iterations to successfully reproduce the density behaviour seen in the x-ray tomographs. Instability in the reconstruction technique at higher numbers of iterations indicates that a linear least-squares fit does not completely capture the response of the sensor to moisture changes. For future applications, changes in bed voidage associated with the drying of pharmaceuticals must be addressed and included in this calibration procedure in order to implement this calibration technique throughout the drying process. Nevertheless, the viability of this technique for on-line calibration of an ECT sensor applied to the drying process has been demonstrated.

Neural network based multi-criterion optimization image reconstructiontechnique for imaging two- and three-phase flow systems usingelectrical capacitance tomography

In this work a new image reconstruction technique for imaging two-and three-phase flows using electrical capacitance tomography (ECT) has beendeveloped. A brief review on reconstruction techniques developed recently forECT is also given. The reconstruction technique proposed here is based onmulti-criterion optimization using an analogue neural network, hereafterreferred to as neural network multi-criteria optimization image reconstruction(NN-MOIRT). The reconstruction technique is a combination between amulti-criterion optimization image reconstruction technique for lineartomography, and the so-called linear back projection (LBP) technique commonlyused for capacitance tomography. The multi-criterion optimization imagereconstruction problem is solved using Hopfield model dynamic neural networkcomputing. For three-component imaging, the single-step sigmoid function inthe Hopfield networks is replaced by a double-step sigmoid function, allowingthe neural computation to converge to three distinct stable regions in theoutput space corresponding to the three components, enabling differentiationamong the single phases. The technique has been tested on a capacitance dataset obtained from simulated measurement as well as experiment using a12-electrode sensor. The performance of the technique has been compared withother commonly used iterative techniques, i.e. iterative linear backprojection technique (ILBP) and the simultaneous image reconstructiontechnique (SIRT) for two-phase system imaging, and has shown greatimprovements in the accuracy and the consistency as compared with thosetechniques. The technique has also shown the capability of three-phase imagereconstruction with high accuracy.