Linear Back Projection Algorithm Research Articles

DEVELOPMENT OF IMAGE RECONSTRUCTION FOR DETECTING STATIC OIL-GAS REGIMES USING INVASIVE ELECTRICAL CAPACITANCE TOMOGRAPHY IN STEEL PIPE APPLICATION – AN INITIAL STUDY An Initial Study

Electrical Capacitance Tomography (ECT) is a well-known technique for identifying two-phase regimes when a non-conducting medium is the main medium inside a pipe. However, the common non-invasive techniques of ECT are not suitable for monitoring non-conducting systems that use steel pipes. This is because the placement of the common ECT sensor is outside of the pipe and thus cannot penetrate the conducting pipe. Therefore, this paper presents the development of image reconstruction techniques for invasive Electrical Capacitance Tomography (ECT) in steel pipe applications. The study uses eight electrodes for invasive ECT that are independently designed for easy replacement. The shield guard of each electrode is individually designed, unlike the common sensor of ECT. Moreover, it produces a sensitivity map in the forward problem by modeling the geometry to mimic the real hardware of invasive ECT in Comsol Multiphysics livelink with MATLAB. The data from real hardware is exported offline and a linear back projection algorithm is used as the inverse problem. The phantom of gas-oil with different sizes, positions, and multiple phantoms from the range of 20mm, 25 mm and 33mm are tested. The tomograms of the region of interest can be obtained as a result. The paper concludes that the developed image reconstruction techniques for invasive ECT in steel pipe applications can provide acceptable and reliable results. This study can be useful for researchers and practitioners in the field of ECT and steel pipe applications.

Defect imaging and identification in asphalt materials using coplanar capacitance sensors with single-pair electrodes

Coplanar capacitance imaging technology (CCIT) is a non-destructive method with intuitive and accurate identification. This paper aims to realize defect identification in asphalt materials based on the CCIT using coplanar single-pair electrode capacitance sensor (CSCS). Firstly, the Linear Back Projection (LBP) algorithm, the Landweber algorithm, and the Kalman-Filter (KF) algorithm, are compared and evaluated. Then, the principal component analysis (PCA) method is utilized to fuse the reconstructed images. In addition, the OTSU method, the iterative threshold (IT) method, and the genetic algorithm (OA) method, is compared and utilized to quantify the defective region. Finally, this investigation analyzes the reconstructed and segmented images of defects in asphalt materials. It is concluded that the KL algorithm is the most suitable algorithm to reconstruct the defective images. The PCA method improve the quality of the reconstructed defective images. The defective region is determined by the OTSU method, which is the most approximate imaging segment method. It is found that the CCIT can detect the invisible defect depth in asphalt materials. The different defect mediums in various asphalt materials can be identified by the CCIT. The segmented defective region error in asphalt materials is less than 13%, demonstrating that the CCIT is effective for the identification of defect shape details in asphalt materials. The segmented imaging precision of square defects in asphalt materials is the highest; circular defects are the next lowest; and triangular defects are the lowest. The outcomes of this research can assist engineers in realizing intuitive and high-accuracy identification of various invisible defects in shallow asphalt layers in bridge deck asphalt pavement utilizing the CCIT.

Real Time Measurement of Multiphase Flow Velocity using Electrical Capacitance Tomography

Accurate and real-time measurement of fluid flow velocity is crucial in various industrial processes, especially when dealing with multiple phase fluids. Traditional flow measurement methods often struggle to accurately quantify the velocity of complex multiphase flows within pipes. This challenge necessitates the exploration of innovative techniques capable of providing reliable measurements. This paper proposes the utilization of Electrical Capacitance Tomography (ECT) as a promising approach for measuring the velocity of multiple phase fluids in pipes. The ECT technique involves the non-intrusive imaging of the electrical capacitance distribution within the pipe. By utilizing an array of electrodes placed around the pipe circumference, the capacitance distribution can be reconstructed, offering insight into the fluid flow patterns. By analyzing the temporal changes in the capacitance distribution, the velocity of different phases within the pipe can be estimated. To achieve accurate velocity measurements, an ECT system needs to account for the complexities introduced by multiphase flows. Various image reconstruction algorithms, such as linear back-projection and iterative algorithms like Gauss-Newton and Levenberg-Marquardt, are employed to reconstruct the capacitance distribution. Additionally, advanced signal processing techniques, such as cross-correlation analysis and time-difference methods, are used to extract velocity information from the reconstructed images. This paper presents an experimental investigation of measuring the velocity of multiple-phase fluids in pipes using the ECT technique. The study aims to address the challenges associated with different flow regimes, fluid properties, and pipe geometries by exploring advancements in electrode design, system calibration, and data processing techniques to enhance the accuracy and robustness of ECT-based velocity measurements.

Void fraction measurement of gas–liquid two-phase flow based on compressed sensing theory and capacitively coupled electrical resistance tomography system

Capacitively coupled electrical resistance tomography (CCERT) is an innovative technique for electrical resistance tomography based on capacitively coupled contactless conductivity detection (C4D). Despite its potential, there are only a few studies on image reconstruction algorithms for CCERT. To address this, a CCERT measurement system is developed, and the compressed sensing (CS) theory is applied to the inverse problem imaging of CCERT to improve the image reconstruction quality and speed. Firstly, a mathematical CCERT image reconstruction model is constructed under CS theory and three algorithms under CS theory are employed to solve the convex optimization problem of the reconstruction model. Then a thresholding operation is applied to obtain the post-processed image and compared it with the classical linear back projection and Landweber algorithms. The simulation results demonstrate that the Barzilai–Borwein gradient projection for sparse reconstruction (GPSR-BB) algorithm yields more satisfactory imaging results than the other four algorithms. Additionally, three sensitivity matrix optimization methods for GPSR-BB algorithm are compared and find that the new method of screening the rows of the sensitivity matrix to zero is more effective than the other two common optimization methods in terms of reconstructed image quality. Finally, the static experiments of void fraction measurement are conducted using the developed CCERT system. The results indicated that the absolute error of void fraction measurement by GPSR-BB algorithm was less than 6.59% in the range of void fraction from 0.90% to 66.29%.

An Investigation of Microwave Tomography Technique to Image Brain Tumour Through Cross-Section Imaging with Different Number of Electrode

Brain tumours resulted from the irregular growth and cell division within the skull, indicating a highrisk for malignancies to develop and can lead to brain injury or even death. The brain tumour can affectnervoussystem’s function based on the tumour’s growth rate and location. Early detection of brain tumour is essential to improve patients’ survival rates through appropriate medical care. As the current clinical imaging has a few impediments e.g. radiation-based and expensive, tomography technique is seen possible to provide safe and inexpensive technology. The aim of this research is to investigate the feasibility of brain tumour detection using microwave tomography technique with different numbers of electrodes. The 2D finite element modelling approach is applied, and the images are reconstructed using a linear back projection (LBP) algorithm in MATLAB. A different number of rectangular sensing electrodes are arranged around the head phantom in an elliptical array, working in pairs as transmitters and receivers. The simulation shows that the system is able to detect the permittivity difference, thus detecting the existence of the tumour in the head phantom.Theimage reconstruction presented promising tumour images with an 8-antenna microwave tomography system at all locations, i.e. left, right, top, centre, and bottom, in comparison to 4-antenna and 12-antenna systems.

A Positive Data Extraction Method for Electrical Impedance Tomography (EIT) Based on the Novel MSA-Net

The nonlinear and ill-posed Electrical Impedance Tomography (EIT) inverse problem leads to reconstructed images with distortion and low resolution. A positive data extraction method based on the deep learning is proposed in this study. This method realizes the accurate classification of the positive data and the general data in voltage measurements through a deep learning network called Multi Scale Attention Network (MSA-Net). The positive data is used for image reconstruction to improve the imaging quality. Multi scale feature extraction, residual learning and attention mechanism are introduced in the MSA-Net to improve classification accuracy. The Linear Back Projection (LBP) algorithm and the Tikhonov Regularization (TR) algorithm are used to verify the effectiveness of the proposed method. Both simulation and experiment are conducted around imaging of bubble flow. The simulation results indicate that there are fewer artifacts in the reconstructed images using the positive data of MSA-Net, and the shape and position of the bubbles can be better described. Moreover, the imaging quality of experimental samples can also be effectively improved. The existing test results preliminarily confirm that the distribution of the positive data and the general data in voltage measurements is related to the position of bubbles in the measurement domain.

Electrode configuration study for three-dimensional imaging of on-chip ECT

Conventional electrical capacitance tomography (ECT) is widely used for monitoring the fluids flow in a pipeline. As the emergence of microfluidics, the tomography system has been miniaturized and integrated into the microfludic platform for imaging purposes. The on-chip ECT is designed to monitor the permittivity distribution of the micro-platform by integrating the planar electrodes with the sensing region. However, limited research has been reported on the electrode design of on-chip ECT, especially for three-dimensional imaging. Thus, this study investigated the electrode design of an on-chip ECT that is capable for image reconstruction in three-dimensions. Four different electrode configurations with different numbers of electrode and arrangements are investigated by simulation to determine the appropriate configuration for three-dimensional imaging. The electrode dimension is optimized based on the sensitivity distribution using the sensitivity variation parameter (SVP). The simulation results shows that the electrode configuration with dual sensing planes enable three-dimensional imaging. The central electrode of each sensing plane is crucial for restoring a floating object. In experiment, the imaging object that was positioned at different vertical and horizontal locations was reconstructed successfully with an average correlation coefficient of 0.4370 using linear back projection (LBP) algorithm. This work has disclosed the appropriate electrode configuration for the three-dimensional imaging of an on-chip ECT system.

Evaluation of Image Enhancement Techniques for Electrical Capacitance Tomography Applications

The fast generation of images in Electrical Capacitance Tomography (ECT) systems is a desirable feature for many industrial applications. Non-iterative reconstruction algorithms which qualify for this requirement generate poor-quality images. The Linear Back Projection (LBP) is the fastest non-iterative reconstruction algorithm. The challenge is to find a technique to improve the quality of images from LBP at a low computational cost. Image enhancement techniques have been investigated for improving the quality of images reconstructed from the LBP algorithm. Simulated and measured static and dynamic flow data were used in the evaluation. The performance results were benchmarked with results from the Projected Land Weber (PLW) one of the accurate iterative reconstruction algorithms. The Gompertz enhancement algorithm was found to have 3.5 times more computation cost than the LBP reconstruction algorithm and the accuracy of the iterative PLW reconstruction algorithm. This is noteworthy since the algorithm does achieve a good balance between accuracy and speed. The fact that the accuracy gained satisfies the reservoir management standards in the multiphase hydrocarbon production sector is significant in this regard.
 Keywords: Electrical Capacitance tomography, Multiphase flow imaging, Maximum entropy thresholding, Gompertz distribution, Image enhancement

Planar array capacitive imaging method based on data optimization

This paper studies the problem of unstable capacitance data collected by the planar array capacitance imaging system, and proposes a method of capacitance data optimization based on improved fuzzy c-means clustering (FCM) algorithm. For the sensor with 3 × 4 array electrodes, considering that the coplanar arrangement of electrodes produces a weak fringe electric field, the measured capacitance data will be unstable. This method first uses the optimal solution of the particle swarm optimization algorithm as the initial clustering center of the FCM algorithm. Then the improved FCM algorithm is used to optimize the unstable capacitance data. This improved method can avoid falling into local optimization and makes the capacitance data closer to the real values. The optimized capacitance data are used to reconstruction image by Linear Back Projection (LBP) algorithm and Landweber algorithm, respectively. The experimental results show that the stability of the processed capacitance data is enhanced, the relative image error I e is reduced, and the image correlation coefficient I c is improved. It can be seen that the effectiveness of the proposed method for defects detection has been validated. • In this paper, the quality of imaging is improved by reducing the noise of capacitance data measured by planar array capacitance imaging system. • In this paper, the FCM algorithm optimized by PSO algorithm is applied to planar array capacitance imaging for the first time.

Wavelet-fused richer convolution feature for multiphase flow visual monitoring of oil and gas production processes

Multiphase flow monitoring of the oil and gas production process is of great significance to the safety of oil and gas exploitation and production. Electrical capacitance tomography (ECT) is one of the most attractive technologies in the field of multiphase flow measurement due to the advantages of its non-radioactive and non-contact properties, good visualization, and low cost. We propose a reconstruction algorithm based on wavelet and richer convolution feature (W-RCF) for solving the problem of artifacts and edge blurring in ECT imaging. In the algorithm, the two-channel source images of Tikhonov regularization and Landweber are simultaneously decomposed by a three-level wavelet. On this basis, an image fusion rule combining Bayesian decision and maximum entropy threshold is established to optimize the wavelet coefficients at each scale. The rule can reduce image artifacts and compensate for the defects in the source images. Afterward, the fused images are input to the RCF network for training and testing, and ECT reconstructed images with higher quality are obtained. Based on the simulation and experimental results, it can be seen that the image reconstruction quality of W-RCF is significantly better than that of the linear back projection, Tikhonov regularization, Landweber, and convolutional neural network algorithms. Therefore, the W-RCF algorithm has higher accuracy and stronger adaptability for multiphase flow under different flow patterns, which provides an effective method of ECT image reconstruction and is more suitable for visual monitoring of multiphase flow in the oil and gas production process.

Forward-looking ground penetrating radar image reconstruction using fully connected neural network

One way to identify targets buried in the ground is to use forward-looking ground penetration radars. The two components of speed and accuracy are very important in reconstructing the images obtained from this method. Distinguishing the target from the Earth clutter is one of the main challenges of this type of imaging. This article proposes a novel fast algorithm that reconstructs scattered images created by forward-looking ground-penetrating radar. The linear back-projection algorithm is used for fast image reconstruction. Because our problem is nonlinear ill-posed inverse, errors and distortions are compensated by a deep fully connected neural network. The difference between received and reconstructed signal is the input of the neural network, and output is the error between reconstructed and actual coefficients of the Interested region. Our assumption is the region of interest has a few electromagnetic scatterers. Because of types of soils and non-stationary situations, it is difficult to estimate the probability density function of noise plus clutter. Therefore, we modified order statistic constant false alarm rate to detect shallowly buried scatterers. The simulation results show that the algorithm improves signal-to-noise and clutter ratio in output and detects objects with a constant probability of false alarm in a fast way.

Multi-frequency ultrasound tomography based on modified matrix regularization method and wavelet fusion

Ultrasound tomography (UT) is a promising sensing technique for industrial processes owing to its advantages non-invasive, low cost, implement flexibility. Traditional UT may lack the distinguishability to resolve the flow with the complicated distribution. We propose a method that exploits the multi-frequency information to improve spatial resolution and resolve different inclusions. Firstly, multi-frequency ultrasound attenuation measurement information was collected and demodulated for tomographic reconstruction. Secondly, a hybrid reconstruction algorithm is proposed consisting of the modified matrix regularization and wavelet fusion methods. The proposed method can effectively reduce the artefact for the inclusion and sharpen the boundary, and detailed information can be reserved from the wavelet fusion. Thirdly, a multi-frequency experimental UT system is established to accomplish the 32 channels ultrasound signal excitation and reception. The performance of the proposed method is validated through numerical simulation and experimental study. The results show that the reconstruction metrics have been improved compared with the linear back projection and Tikhonov algorithms. We believe the proposed method can be used in the flow process prediction and diagnosis for industrial applications.

Image reconstruction method for electrical capacitance tomography using adaptive simulated annealing algorithm.

Image reconstruction of electrical capacitance tomography (ECT) is an ill-posed inverse problem. The simulated annealing (SA) algorithm is suitable for the solution of the ECT inverse problem. However, selection of related parameters of the SA algorithm will influence the reconstruction performance of ECT. We present an ECT image reconstruction method based on the adaptive simulated annealing (ASA) algorithm. We adopt the bat algorithm in the new solution generation strategy of the ASA algorithm. Moreover, the definition of the energy function introduces the sparsity of the reconstructed image. As a result, an adaptive annealing strategy is proposed to select the appropriate annealing rate. We made reconstructed image comparisons among linear back-projection, Landweber iteration, SA, and ASA algorithms via simulation and static experiment. Results show that improved reconstructed images can be obtained using the ASA algorithm.

Image reconstruction of electrical capacitance tomography based on optimal simulated annealing algorithm using orthogonal test method

Electrical capacitance tomography (ECT) is a visualization measurement method for two-phase flow. Imaging permittivity distributions using electrical capacitance tomography has always been one of the most significant issues studied by scholars, and the algorithm will have a great impact on the accuracy of image reconstruction result. This paper applies simulated annealing (SA) algorithm to image reconstruction in ECT. However, some parameters of SA algorithm need to be optimized in order to obtain better reconstructed images in ECT. The influence of different parameter values in SA algorithm for image reconstruction in ECT is studied, and a set of optimal parameters of the SA algorithm is obtained based on the orthogonal experimental design method in this paper. At the same time, simulation and static experiments are conducted. Reconstructed images by SA algorithm with optimized parameter are compared with the linear back projection (LBP) and Landweber iterative algorithms. The results show that better images can be obtained for typical oil-gas two-phase flow using SA algorithm. The quality and shape fidelity of reconstructed image for the central object are obviously improved.

An Investigation of Microwave Tomography Technique to Detect Brain Tumour Through Cross-Section Imaging at Frequency 0.5 GHz to 1.5 GHz

The growing significance of cancerous tissue including brain tumour requires a fast and efficient technology detection. The most current technologies being applied for brain imaging system are Computed Tomography (CT) scan and Magnetic Resonance Imaging (MRI). Whilst these two detection applications are very well established, both systems are expensive, time and space consuming, and raise safety issues to patients due to the radiation and strong magnetic effects. This research aims to assess the feasibility and potential performance of microwave tomography (MWT) for brain imaging with a particular focus on brain tumour detection. The study was conducted using Finite Element Model software, COMSOL Multiphysics to develop a 2D modelling of an antenna array and measure the scattered electric field by solving forward problem. MATLAB software will be used as an inverse problem solver to reconstruct 2D images of the tumour by using Linear Back Projection (LBP) algorithm.

Development of Electrical Resistance Tomography Applying Vertical Metallic Column

Majority of industrial pipelines and process vessels are constructed from conducting composites. This paper focusing on the hardware and software development of laboratory test Electrical Resistance Tomography (ERT) measurement methods to obtain the cross-sectional image of the conductivity distribution of gas bubble phantom in a static vertical metallic column filled with water. The system with sixteen sensors implementation was investigated on a stainless steel vertical column of 100 mm inner diameter. The conducting boundary strategy was applied as the measurement strategy. Software for the current study was developed using Graphical User Interface (GUI) application program in MATLAB. The software contains many functions to ease user to get necessary information from the research done. The cross section image of the bubble phantom was reconstructed using Linear Back Projection (LBP) algorithm after the data collection process was completed. The system has been tested and can successfully generate the phantom under test.

An Image Reconstruction Method of Capacitively Coupled Electrical Impedance Tomography (CCEIT) Based on DBSCAN and Image Fusion

Based on linear back projection (LBP) algorithm, density-based spatial clustering of applications with noise (DBSCAN) algorithm and image fusion technique, a new image reconstruction method of capacitively coupled electrical impedance tomography (CCEIT) is proposed in this work. LBP is used to obtain the original image of the real part and the original image of the imaginary part. The gray level thresholds of the two original images are determined by DBSCAN clustering algorithm and the initial image of the real part and the initial image of the imaginary part are obtained by gray level threshold filtering, respectively. Finally, the two initial images are fused and the final image is obtained. Image reconstruction experiments are carried out with a 12-electrode CCEIT system prototype. The experimental results verify the effectiveness of the proposed image reconstruction method. Experimental results show that the quality of the final image is satisfactory. Compared with the conventional electrical tomography (ET) image reconstruction methods, the new proposed image reconstruction method needs less prior knowledge or manual intervention and realizes more effective usage of the impedance information. The research results also indicate that the DBSCAN clustering algorithm is an effective way to determine the gray level thresholds of the original images and the mean square error (MSE) is a reasonable criterion for image fusion. Meanwhile, LBP + DBSCAN is an effective algorithm for image reconstruction and image fusion technique is an effective way to utilize the whole impedance information of the conductive gas–liquid two-phase flow.

A study on early detection of sewer pipeline blockage using CCD tomography approach

In a sewage system, congealed mass is created by mixing non-biodegradable solid matter with fat, oil and grease. Congealed mass might cause a sewer blockage and overflow. This issue may impose a risk to public health and environment. It also leads to increased operational and maintenance costs of sewer system. A robust and durable sensor system are required to monitor the sewer network blockage which could cause a fluctuation in the data. CCD tomography approach will be used to detect the congealed mass forming in sewer network at early stage. The main concept of CCD tomography approach is to analyze the structure and composition of congealed mass by examining the light intensity after penetrated. Therefore, the location and size of the sewer blockage can be predicted. Light reflection from the congealed mass will strikes onto CCD surfaces. This light source will be converted into an electrical signal which is in voltage output value. Filtered images of Linear Back Projection (LBP) algorithm will be applied to reconstruct the image and identify the characteristic of congealed mass either fat, oil or grease. The location and the size of the congealed mass forming also can be identified using this CCD tomography approach.

New image reconstruction algorithm for CCERT: LBP + Gaussian mixture model (GMM) clustering

This work focuses on the study of the image reconstruction algorithm of capacitively coupled electrical resistance tomography (CCERT). With the combination of a linear back projection (LBP) algorithm and an unsupervised Gaussian mixture model (GMM) algorithm, a new image reconstruction algorithm for CCERT is proposed. The LBP algorithm is used to implement the initial image reconstruction. The GMM algorithm is adopted to acquire the gray level threshold which will be used for the establishment of the gray level threshold filter. The final reconstructed image can be obtained with the thresholding operation. With a developed 12-electrode CCERT prototype system, the new image reconstruction algorithm is tested in image reconstruction experiments. The experimental results show that the proposed new image reconstruction algorithm is effective. The image reconstruction results are satisfactory. Compared with the conventional image reconstruction algorithms, the new image reconstruction algorithm (LBP + GMM) can obtain better reconstructed images with smaller relative image errors. It can obtain the reconstructed images with fewer empirical preset parameters and less manual intervention. In addition, with the introduction of the GMM algorithm, a relatively more suitable and reasonable gray level threshold can be obtained because the GMM algorithm implements the clustering process by utilizing both mean and variance information on the gray level distribution. Thus, better image reconstruction results can be obtained.

Localización de emuladores de carcinomas en modelos experimentales de mama mediante tomografía de impedancia eléctrica basada en linear back projection

Introducción: La medición y caracterización de la impedancia eléctrica de los tejidos biológicos permite distinguir entre tejidos sanos y patológicos. El uso de técnicas como la tomografía de impedancia eléctrica es muy utilizada en pruebas clínicas a través de diversas aplicaciones. En este trabajo se emplea el método Linear Back Proyection (LBP) para reconstruir imágenes a partir de la medición de impedancia eléctrica con el objetivo de localizar emuladores de carcinoma insertados en modelos de agar-agar con forma de mama femenina.Método: Un arreglo anillar de ocho electrodos fue empleado para realizar mediciones de impedancia en siete modelos de agar-agar con forma de mama femenina. Se diseñó y simuló en el software COMSOL un corte transversal de una mama femenina sana (sin emuladores) que representa el plano de medición del arreglo anillar de electrodos. Se calcularon los mapas de sensibilidad de cada par de electrodos a lo largo de la medición de impedancia utilizando los datos de la distribución de conductividad del modelo simulado. Finalmente, la reconstrucción de la imagen de tomografía eléctrica para cada modelo se obtuvo aplicando el algoritmo LBP a los valores de impedancia eléctrica medidos en el arreglo anillar de electrodos.Resultados: Se calcularon los mapas de sensibilidad a partir de las mediciones de impedancia obtenidas de cada modelo experimental considerado. Como resultado se generó una matriz de sensibilidad que caracteriza la distribución de los potenciales eléctricos dentro del plano de medición simulado en COMSOL. La zona de localización obtenida fue correcta para todos los modelos experimentales con emuladores de carcinomas insertados fuera del centro del arreglo anillar de electrodos.Discusión o Conclusión: De acuerdo con los resultados obtenidos del proyecto descrito, la metodología propuesta permite la generación de imágenes para localizar emuladores de carcinoma con diámetros aproximados de 1 cm, ello a través de un enfoque no iterativo. Por lo anterior, la localización no requiere una alta complejidad computacional. La localización de un emulador de carcinoma insertado en la zona central del modelo de mama femenina no se obtuvo correctamente debido a la baja sensibilidad de la configuración anillar de los electrodos en dicha zona.