Linear Back Projection Research Articles

A modified capacitance tomography image reconstruction approach based on iterative shrinkage-thresholding algorithm combined with deep networks

Abstract Due to the ‘soft-field’ effect and the challenges posed by ill-posed and ill-conditioned inverse problems, it is difficult to obtain high quality images from an electrical capacitance tomography (ECT) system. To achieve both high-quality images and fast imaging speed with limited measurement data, an image reconstruction algorithm, which was initially proposed for compressive sensing, is adapted for ECT image reconstruction to optimize the ill-posed nature of its inverse problem. The proposed algorithm leverages deep learning networks inspired by the iterative shrinkage-thresholding algorithm (ISTA), thereby creating a model that is both mathematically interpretable and endowed with trainable parameters. Building upon this foundation, the conventional Landweber iteration is integrated with the ISTA-Net to refine the optimization process for ECT image reconstruction. In order to propose an effective model adapting to the actual multiphase flow characteristics and complex flow pattern changes, the training and test process is driven by a comprehensive dataset generated from dynamic simulations, rather than artificial samples of multiphase distributions. This numerical methodology simulates the dynamic measurement process of a virtual ECT sensor by coupling the gas–liquid two-phase flow field and the ECT electrostatic field. The results of the testing phase indicate that the proposed algorithm outperforms traditional ECT image reconstruction methods. Compared with the linear back projection algorithm, the average image error and gas fraction error have been reduced by 20.44% and 16.74%, respectively, while maintaining a computational speed comparable to that of the Landweber iteration. The accuracy of the new algorithm in reconstructing the two-phase interface and estimating the gas fraction has been validated by static experimental tests, showing its potential for practical application in online gas–liquid two-phase flow measurement scenarios.

Optimised electrical resistance tomography performance for coarse-particle suspensions with a settled bed

Electrical Resistance Tomography (ERT) offers a non-intrusive method to visualise the dynamic distribution of internal solids in suspension flows. While ERT can produce good qualitative images, quantitative analysis faces challenges due to low spatial resolution, sensitivity to electric noise, and the ill-posed nature of the inverse problem. This study aims to enhance ERT's performance for coarse-particle suspensions by considering system configuration, injection current, background conductivity and reconstruction techniques. Validation is performed on both static and dynamic suspensions with physically sensible flow scenarios. To ensure high-quality ERT data acquisition, the background conductivity must allow a range of injection current while maintaining a favourable signal-to-noise ratio. A more conductive carrier is needed for effective current injection in densely packed beds or larger-scale pipes. Reconstruction based on current and voltage measurements following Ohm's law is essential. The commonly adopted Linear Back Projection (LBP) algorithm in a commercial ERT system exhibits limited information in the bed-occupied area, leading to underestimations of integrated concentration. ERT predictions of chord-averaged concentration profiles in a dynamic suspension display similar trends as those from the one-dimensional Eskin model. When compared to experimental measurements, ERT results generally underestimate the integrated concentration by approximately 15 % v/v in a dynamic suspension.

The Inclusion and Initial Damage Inspection of Intelligent Cementitious Materials Containing Graphene Using Electrical Resistivity Tomography (ERT)

This paper examines the theoretical foundations of electrical resistivity tomography (ERT) technology, followed by the finite element analysis method, for the positive problem and the linear back-projection (LBP) procedure for the inverse problem. The conductivity distribution image of the modeled concrete is then reconstructed, which includes one circular aggregate and the surrounding mortar. It is discovered that the conductivity obtained can be used to find the inclusive aggregate, mortar, and interfacial transition zone (ITZ). Natural aggregate and mortar have conductivities of 0.046 ms/cm and 0.115 ms/cm, respectively. Additionally, the conductivity of the ITZ, which is always regarded as the initial damage, is about 0.081 ms/cm. ERT is a cost-effective and readily available technique for determining the initial distribution of the aggregate and related ITZ. Therefore, ERT is a promising tool for determining inclusions and initial damage in concrete.

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

IMAGING OF BUBBLY FLOW USING ULTRASOUND

Flow measurement is a vital ‎issue in instrumentation and has been applied in the various industries. The characteristics of a single phase regime has been extensively researched. On the other hand obtaining the characteristics of a multi-component flow is more complex and traditional equipment do not provide ‎reliable results. As such, tomography utilizing non-invasive ‎transducers is getting attention in the industries because it does not invade the flow. Ultrasonic tomography is among the methods which is suitable for flow containing bubbles. In this project, 16 ultrasonic transducers are placed around a flow pipe. Five different phantoms representing solid flow are placed in the pipe. The flow is imaged using the linear back projection algorithm. The results show that the system was able to image the phantoms which are placed at different locations.

MEASUREMENT OF RICE MOISTURE CONTENT BASED ON QUANTITATIVE ANALYSIS FROM RADIO TOMOGRAPHY IMAGES

Inefficient storage of paddy and rice grains can lead to grain deterioration, resulting in post-harvest losses ranging from 10% to 30%. The quality of grains cannot be improved throughout the storage period. Therefore, following the mechanisation of agricultural industries, air dryers have been developed to control the crops’ moisture level by blowing ambient or heated air into the silo to improve the aeration and allow the grains to be preserved with minimal loss of quality until the appropriate time for managing and marketing processes. However, the conventional sampling method used to measure the moisture level is inefficient because it is very localised and only represents part of the moisture distribution inside the bulk grains. Additionally, incorporating advanced technologies can be a significant cost limitation for small-scale industries. Thus, to address the issue, this research study developed a radio tomographic imaging (RTI) system in a silo-scale prototype using 20 sensor nodes operating at 2.4 GHz to localise and monitor the moisture level constructively. The RTI system reconstructs the cross-sectional images across the rice silo by measuring radio frequency attenuation, in terms of received signal strength (RSS) quality, caused by the rice moisture phantoms within the wireless sensor network (WSN) area. A total of five phantoms’ profiles having a percentage of moisture content (MC) of 15%, 20% and 25% were reconstructed using four image reconstruction algorithms, Linear Back Projection (LBP), Filtered Back Projection (FBP), Newton’s One-step Error Reconstruction (NOSER) and Tikhonov Regularisation.

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.

Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax.

Electrical impedance tomography (EIT) is a non-invasive technique for visualizing the internal structure of a human body. Capacitively coupled electrical impedance tomography (CCEIT) is a new contactless EIT technique that can potentially be used as a wearable device. Recent studies have shown that a machine learning-based approach is very promising for EIT image reconstruction. Most of the studies concern models containing up to 22 electrodes and focus on using different artificial neural network models, from simple shallow networks to complex convolutional networks. However, the use of convolutional networks in image reconstruction with a higher number of electrodes requires further investigation. In this work, two different architectures of artificial networks were used for CCEIT image reconstruction: a fully connected deep neural network and a conditional generative adversarial network (cGAN). The training dataset was generated by the numerical simulation of a thorax phantom with healthy and illness-affected lungs. Three kinds of illnesses, pneumothorax, pleural effusion, and hydropneumothorax, were modeled using the electrical properties of the tissues. The thorax phantom included the heart, aorta, spine, and lungs. The sensor with 32 area electrodes was used in the numerical model. The ECTsim custom-designed toolbox for Matlab was used to solve the forward problem and measurement simulation. Two artificial neural networks were trained with supervision for image reconstruction. Reconstruction quality was compared between those networks and one-step algebraic reconstruction methods such as linear back projection and pseudoinverse with Tikhonov regularization. This evaluation was based on pixel-to-pixel metrics such as root-mean-square error, structural similarity index, 2D correlation coefficient, and peak signal-to-noise ratio. Additionally, the diagnostic value measured by the ROC AUC metric was used to assess the image quality. The results showed that obtaining information about regional lung function (regions affected by pneumothorax or pleural effusion) is possible using image reconstruction based on supervised learning and deep neural networks in EIT. The results obtained using cGAN are strongly better than those obtained using a fully connected network, especially in the case of noisy measurement data. However, diagnostic value estimation showed that even algebraic methods allow us to obtain satisfactory results.

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.

Robot sensing based on electrical capacitance tomography sensor with rotation

The existing sensing technology for industrial robot hands cannot sense inside of an object. To recognise the material and internal distribution of an object when it is grasped, electrical capacitance tomography (ECT) may be used if the object is non-conductive, as ECT can measure the permittivity distribution inside an object from external capacitance measurements. An ECT sensor normally has 8 or 12 electrodes equally distributed around an object. This paper introduces the first attempt to make use of ECT with robot hands. Because the number of electrodes is limited, it is necessary to rotate the object to be imaged mechanically, so that sufficient measurements can be taken. Four aspects of the ECT sensor are discussed based on simulation: (1) the structure of electrodes; (2) the number of rotation times; (3) the starting position of rotation; and (4) the diameter of rotation. Two image reconstruction algorithms are used: the linear-back projection and Landweber iteration with three typical distributions. The results show that the rotational three-electrode ECT structure has good ability to produce useful images, showing the internal distribution of unknown objects.

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

A New Image Reconstruction Algorithm for CCERT Based on Improved DPC and K-Means

Based on density peaks clustering (DPC) and K-means, this work aims to propose a new image reconstruction algorithm for capacitively coupled electrical resistance tomography (CCERT). To better apply DPC and K-means to CCERT, DPC is improved by automatically selecting the cluster centers and K-means is improved by introducing a post-processing in consider of the non-uniform sensitivity characteristic in the sensing area. With the proposed algorithm, linear back projection (LBP) is adopted to obtain the initial image. With the initial image, the improved DPC is adopted to identify the number of targets and get the region of each target. The improved K-means is adopted to determine the gray level threshold in the region of each target according to the distance between the centroid of the target and the center of the pipe. The final image is obtained by gray level threshold filtering. Image reconstruction experiments are carried out by a 12-electrode CCERT system. The experimental results verify the effectiveness of the proposed image reconstruction algorithm. Results also indicate that the improvements of DPC and K-means are successful. Compared with conventional image reconstruction algorithms, the proposed image reconstruction algorithm could get better image reconstruction results with less manual intervention.

Magneto-thermal-acoustic imaging of magnetic nanoparticles with tissue structure imaging function

Magneto-thermal-acoustic imaging with magnetic nanoparticles (MNPs) is a novel medical imaging modality based on the thermoacoustic (TA) effect of MNPs. We proposed a new dual-modality imaging strategy that combines the TA and echo signals. Based on the synthetic aperture method, we used TA signals to image cancer tissues labeled with MNPs and applied echo signals to achieve tissue structure imaging. In the simulation, we constructed a breast cancer model and assumed that cancer tissue was labeled with MNPs. Under a limited field of view, the TA and echo signals were collected using a multi-element transducer array. By fusing the imaging results of the TA and echo signals, we obtained a boundary distribution map of the breast cancer model, and accurately located the tumor tissue. In this experiment, we built a multi-channel acquisition system. Pork tissue labeled with MNPs was used as the breast cancer phantom. We collected a total of 120 TA and echo signals at 1 mm intervals using a multi-element transducer array and faithfully imaged the boundary distribution map of the phantom. Compared with the traditional linear back projection method based on focused transducers, we demonstrated that the proposed method not only improves the lateral resolution of the image, but also makes accurate cancer identification easier. This provides a promising medical imaging technology for clinical applications.

On the Image Reconstruction of Capacitively Coupled Electrical Resistance Tomography (CCERT) with Entropy Priors.

Regularization with priors is an effective approach to solve the ill-posed inverse problem of electrical tomography. Entropy priors have been proven to be promising in radiation tomography but have received less attention in the literature of electrical tomography. This work aims to investigate the image reconstruction of capacitively coupled electrical resistance tomography (CCERT) with entropy priors. Four types of entropy priors are introduced, including the image entropy, the projection entropy, the image-projection joint entropy, and the cross-entropy between the measurement projection and the forward projection. Correspondingly, objective functions with the four entropy priors are developed, where the first three are implemented under the maximum entropy strategy and the last one is implemented under the minimum cross-entropy strategy. Linear back-projection is adopted to obtain the initial image. The steepest descent method is utilized to optimize the objective function and obtain the final image. Experimental results show that the four entropy priors are effective in regularization of the ill-posed inverse problem of CCERT to obtain a reasonable solution. Compared with the initial image obtained by linear back projection, all the four entropy priors make sense in improving the image quality. Results also indicate that cross-entropy has the best performance among the four entropy priors in the image reconstruction of CCERT.

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.