Linear Back Projection Research Articles

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.

Two-dimensional and pseudo three-dimensional visualisation of foreign objects in milk carton using ultrasonic tomography

This paper presents the development of two-dimensional and pseudo three-dimensional visualisation of foreign object in milk carton using ultrasonic tomography system. Mathematical modelling based on ultrasonic amplitude wave and correlation between ultrasonic projection distance and voltage sensor are elaborated in this paper. Physical hazard contaminants such as metal, plastic, wood and glass materials were placed in the milk. The forward problem and the inverse problem of image reconstruction technique have been discussed briefly. 2D images of the contaminants are reconstructed using Linear Back-Projection (LBP) and Convolution Back-Projection (CBP) with Hanning, Hamming and Ram-Lak filter. A median filter technique has been combined to the algorithms for filtering noise of reconstructed images. The results show that image reconstruction using CBP-Ram-Lak has significantly yield the best image reconstruction for most tested phantoms. The application of median filter with 20 × 20 matrix have obtained a better image quality as they achieved the best values of PSNR and SSIM compared to non-median filter with 13.2765 and 0.7318, respectively for pairs of metal A - glass B (phantom Y-2). Pseudo three-dimensional (3D) image reconstruction for the foreign object has been carried out to provide more sufficient monitoring process in milk cartons. The 3D images were constructed based on stacking the 2D slice images in z-axis. Thus, the exact location of the object in the milk carton can be exposed clearly from various viewing angles. The results indicate that the ultrasonic tomography imaging system promises to be a non-invasive tool in quality monitoring especially for the detection of foreign objects in milk carton.

Electrical Capacitance Tomography Sensor With House Structure for Assisting Recognition of Objects

As a fast and non-invasive visualization technology, electrical capacitance tomography(ECT) avoids the problem that camera imaging technology is interfered by light and can’t identify material properties. However, the traditional ECT sensor research mainly focused on the image reconstruction of multiphase flow between electrodes, without considering the object recognition performance through the dielectric distribution of the objects. Therefore, we propose a new ECT sensor (called House Sensor) with house-like structure, which is suitable for multi features detection of household objects. We analyze the sensitivity distribution of House Sensor, and use linear back projection (LBP) and Tikhonov regularization for high-speed image reconstruction. 20 objects with different sizes and dielectric constants are visually clustered by t-distributed stochastic neighbor embedding (t-SNE) to verify the feasibility of classification, and the accuracy of Random Forest (RF) is up to 95.3% within 3.5ms. This implies that House Sensor provide a new feasible scheme to assist object recognition under non-vision conditions.

Visualization Detection of Solid–Liquid Two-Phase Flow in Filling Pipeline by Electrical Capacitance Tomography Technology

During mine filling, the caking in the pipeline and the waste rock in the filling slurry may cause serious safety accidents such as pipe blocking or explosion. Therefore, the visualization of the inner mine filling of the solid–liquid two-phase flow in the pipeline is important. This paper proposes a method based on capacitance tomography for the visualization of the solid–liquid distribution on the section of a filling pipe. A feedback network is used for electrical capacitance tomography reconstruction. This reconstruction method uses radial basis function neural network fitting to determine the relationship between the capacitance vector and medium distribution error. In the reconstruction process, the error in the linear back projection is removed; thus, the reconstruction problem becomes an accurate linear problem. The simulation results show that the reconstruction accuracy of this algorithm is better than that of many traditional algorithms; furthermore, the reconstructed image artifacts are fewer, and the phase distribution boundary is clearer. This method can help determine the location and size of the caking and waste rock in the cross section of the pipeline more accurately and has great application prospects in the visualization of filling pipelines in mines.

Optimization of large scale concentric-annulus electrical capacitance tomography sensor with internal electrodes

To improve the spatial resolution of electrical capacitance tomography (ECT) images for visualizing large-scale concentric-annulus measuring area, ECT sensors with 12 external electrodes (EE) and different number of internal electrodes, 4, 6 and 8 are designed. The outer radius of the sensors is 500 mm and inter radius is 100, 150, 200, 250 mm respectively. Two excitation strategies are used, which are external-opposite-internal (EOI) and external-opposite (EO). The obtained capacitance data are used to reconstruct images using linear back projection (LBP) and Landweber iteration. Based on numerical simulation and experimental measurement, it is found that increasing the number of internal electrodes does not improve the quality of images. When LBP is used with normalized sensitivity matrix, the 12–4 internal-external-electrode (IEE) sensor with EOI excitation strategy has advantages over the EE sensor and other IEE sensors in terms of image quality and contrast. When Landweber iteration is used, the IEE sensors with EO excitation strategy can effectively eliminate the influence of abnormal capacitances. Landweber iteration can reconstruct high quality images when the sensitivity matrix is normalized according to discrete elements of measurement area, while the reconstructed images are more sensitive to the noise level.

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.

Analysis and Performance Evaluation of Entropic Thresholding Image Processing Techniques for Electrical Capacitance Tomography Measurement System

To improve image quality generated from the electrical capacitance tomography measurement system, the use of entropic thresholding techniques is investigated in this article. Based on the analysis of the principle of Electrical Capacitance Tomography (ECT) image reconstruction and entropic thresholding, various algorithms have been proposed for easy extraction of quantitative information from tomograms generated from the ECT system. Experiments indicate that proposed algorithms can provide high-quality images at no or minimum computational cost. It is easier to implement and integrate with classical algorithms such as Linear Back Projection, Singular value decomposition, Tikhonov regularization, and Landweber. Entropic thresholding techniques present a feasible and effective way toward the industrial utilization of ECT measurement systems.
 Keywords: Electrical Capacitance Tomography; Inverse Problem; Image Reconstruction; Entropic Thresholding

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.

Model-Based Hardware-Software Codesign of ECT Digital Processing Unit

Image reconstruction algorithm and its controller constitute the main modules of the electrical capacitance tomography (ECT) system; in order to achieve the trade-off between the attainable performance and the flexibility of the image reconstruction and control design of the ECT system, hardware-software codesign of a digital processing unit (DPU) targeting FPGA system-on-chip (SoC) is presented. Design and implementation of software and hardware components of the ECT-DPU and their integration and verification based on the model-based design (MBD) paradigm are proposed. The inner-product of large vectors constitutes the core of the majority of these ECT image reconstruction algorithms. Full parallel implementation of large vector multiplication on FPGA consumes a huge number of resources and incurs long combinational path delay. The proposed MBD of the ECT-DPU tackles this problem by crafting a parametric segmented parallel inner-product architecture so as to work as the shared hardware core unit for the parallel matrix multiplication in the image reconstruction and control of the ECT system. This allowed the parameterized core unit to be configured at system-level to tackle large matrices with the segment length working as a design degree of freedom. It allows the trade-off between performance and resource usage and determines the level of computation parallelism. Using MBD with the proposed segmented architecture, the system design can be flexibly tailored to the designer specifications to fulfill the required performance while meeting the resources constraint. In the linear-back projection image reconstruction algorithm, the segmentation scheme has exhibited high resource saving of 43% and 71% for a small degradation in a frame rate of 3% and 14%, respectively.

Quantitative Evaluations with 2d Electrical Resistance Tomography in the Low-Conductivity Solutions Using 3d-Printed Phantoms and Sucrose Crystal Agglomerate Assessments.

Crystallization is a significant procedure in the manufacturing of many pharmaceutical and solid food products. In-situ electrical resistance tomography (ERT) is a novel process analytical tool (PAT) to provide a cheap and quick way to test, visualize, and evaluate the progress of crystallization processes. In this work, the spatial accuracy of the nonconductive phantoms in low-conductivity solutions was evaluated. Gauss–Newton, linear back projection, and iterative total variation reconstruction algorithms were used to compare the phantom reconstructions for tap water, industrial-grade saturated sucrose solution, and demineralized water. A cylindrical phantom measuring 10 mm in diameter and a cross-section area of 1.5% of the total beaker area was detected at the center of the beaker. Two phantoms with a 10-mm diameter were visualized separately in noncentral locations. The quantitative evaluations were done for the phantoms with radii ranging from 10 mm to 50 mm in demineralized water. Multiple factors, such as ERT device and sensor development, Finite Element Model (FEM) mesh density and simulations, image reconstruction algorithms, number of iterations, segmentation methods, and morphological image processing methods, were discussed and analyzed to achieve spatial accuracy. The development of ERT imaging modality for the purpose of monitoring crystallization in low-conductivity solutions was performed satisfactorily.

A least squares support vector regression coupled linear reconstruction algorithm for ECT

Linearization error of the simplified linear electrical capacitance tomography (ECT) model is one of the leading causes of ECT reconstruction errors. In this paper, the least squares support vector regression (LSSVR) is used to fit the correlation between the capacitance vector and the linearization error. And it is trained by the training samples of typical phase distributions. When removing the linearization error from equations derived by the linear model, the reconstruction problem becomes an exact linear inverse problem because the nonlinearity of ECT is completely included in the linearization error. Then a reconstruction algorithm combining the LSSVR and the Landweber iteration is proposed. Numerical results show that the proposed algorithm achieves significantly better reconstruction accuracies than the linear back projection and the Landweber algorithm for both the noise-free and noisy cases. Compared with the Landweber algorithm, The image errors of the reconstructions are reduced by about 23%–68%, and the correlation coefficient increased by about 0.04–0.14. And the calculation time of the proposed algorithm for all the tested cases is about 0.4–0.6s, which makes it have the potential for real-time imaging. Static experimental results show that the reconstructions of the proposed algorithm have more accurate phase boundary shapes and fewer artifacts.

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.

Revised Calderon Method of Annular ECT for Imaging Flashback Flame of a Bluff-Body Burner

In this article, an annular electrical capacitance tomography (ECT) sensor was designed, and a revised Calderon image reconstruction method was proposed for monitoring the flashback flame of a bluff-body burner. The central support of the bluff-body was used as the internal electrode of the sensor, and the external electrode array was fixed on the outer surface of the burner. The capacitance values of all pairs of electrodes, including the internal and external, composed a boundary capacitance matrix of the annular sensing field. The revised Calderon method was compared with the commonly used sensitivity matrix-based methods including the linear back projection (LBP) and Landweber methods for imaging the cross-sectional distribution of permittivity which is continuous in value. Simulation results show that the revised Calderon method is of higher image reconstruction quality than the LBP and Landweber methods. In the experiment, the designed annular ECT sensor and revised Calderon method were used to monitor the flame flashback phenomenon of the bluff-body burner. The experiment results not only monitored the occurrence of flame flashback, revealed the variations of flame flashback intensity and time with the fuel:air equivalent ratio, but also determined the boundary condition of flame flashback of the bluff-body burner. The proposed method provides a new approach for experimental study on the influencing factors of flame flashback, and thus can be applied to research on combustion stability and high-performance burner design.

Real-Time 3-D Imaging and Velocity Measurement of Two-Phase Flow Using a Twin-Plane ECT Sensor

This article presents a method for real-time 3-D imaging and velocity measurement of two-phase flows using a twin-plane electrical capacitance tomography (ECT) sensor with 24 electrodes. A dedicated digital ECT system with a data acquisition rate of 241 frames/s is used for capacitance measurement. In this article, the sensitivity distribution of the ECT sensor is analyzed, and the two most commonly used algorithms, linear back projection (LBP) and Tikhonov, are used to achieve high-speed 3-D image reconstruction. The cross correlation technique is used to calculate the velocity of a two-phase flow. Experiments were carried out to evaluate the performance of the proposed method. Several typical distributions were constructed and used to analyze the axial imaging resolution. A free-falling sphere was used to test the ability of the system in velocity measurement. Experimental results show that the proposed method can provide high axial resolution in the central zone of the 3-D sensor and high temporal resolution in velocity measurement.

Planar array capacitance imaging based on adaptive Kalman filter

Planar array capacitance imaging system has the characteristics of uneven distribution of sensitive field, serious ill posed problem and measurement data vulnerable to external interference, and these characteristics will make the image artifacts particularly serious, affect the quality of the reconstructed image, and even determine the number of defects with difficulty. In order to solve the problem that the edge electric field and ill conditioned characteristics of planar array electrode seriously affect the quality of capacitance image reconstruction, an improved image reconstruction algorithm based on adaptive Kalman filter is proposed to reduce the noise of capacitance data and dielectric constant matrix. On the basis of constructing the state model of planar array capacitance imaging with noise, the maximum likelihood criterion is used to estimate and modify the noise variance matrix of dielectric constant matrix on-line, and the noise variance matrix of dielectric constant matrix is modified in real time. In order to restrain the filtering divergence and accelerate the convergence speed, different weighting coefficients are provided for the error covariance matrix with time going by. Through designing four kinds of samples from simple to complex structure, the defect detection experiment of composite structure is carried out. The experimental results show that compared with linear back projection (LBP), Tikhonov regularization (TR) algorithm and Kalman filtering algorithm, the image error of adaptive Kalman filtering algorithm can be reduced by about 20%, the image correlation coefficient is as high as 0.79 and the convergence speed can be improved by about 15%, the image artifacts of the four samples are greatly reduced. The experimental data show that the proposed adaptive Kalman filter image reconstruction algorithm can effectively reduce the noise of capacitance and permittivity matrix, enhance the stability of planar array capacitance imaging, and reduce the image error, so that the quality of the image can be significantly improved. This study provides a strong technical basis for improving the quantization accuracy of planar array capacitance imaging detection. In the future, we will further consider the image reconstruction under the condition of complex object field.