Search Results (12)

Variable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irregular sampling and variable apertures, use iterative techniques to reconstruct measurements of the Earth’s surface. However, many of these iterative techniques tend to over-amplify noise features outside the reconstructable bandwidth. Because the reconstruction of discrete samples is inherently bandlimited, solving a bandlimited inverse can focus on recovering signal features and prevent the over-amplification of noise outside the signal bandwidth. To approximate a bandlimited inverse, we apply bandlimited constraints to several well-known iterative reconstruction techniques: Landweber iteration, additive reconstruction technique (ART), Richardson–Lucy iteration, and conjugate gradient descent. In the context of these iterative techniques, we derive an iterative method for inverting variable aperture samples, taking advantage of the regular and irregular content of variable apertures. We find that this iterative method for variable aperture reconstruction is equivalent to solving a bandlimited conjugate gradient descent algorithm. Full article

This study investigated the potential of the generative adversarial neural network (cGAN) image reconstruction in industrial electrical capacitance tomography. The image reconstruction quality was examined using image patterns typical for a two-phase flow. The training dataset was prepared by generating images of random test objects and simulating the corresponding capacitance measurements. Numerical simulations were performed using the ECTsim toolkit for MATLAB. A cylindrical sixteen-electrode ECT sensor was used in the experiments. Real measurements were obtained using the EVT4 data acquisition system. The reconstructed images were evaluated using selected image quality metrics. The results obtained using cGAN are better than those obtained using the Landweber iteration and simplified Levenberg–Marquardt algorithm. The suggested method offers a promising solution for a fast reconstruction algorithm suitable for real-time monitoring and the control of a two-phase flow using ECT. Full article

In this paper, the Cauchy problem for the Helmholtz equation, also known as the continuation problem, is considered. The continuation problem is reduced to a boundary inverse problem for a well-posed direct problem. A generalized solution to the direct problem is obtained and an estimate of its stability is given. The inverse problem is reduced to an optimization problem solved using the gradient method. The convergence of the Landweber method with respect to the functionals is compared with the convergence of the Nesterov method. The calculation of the gradient in discrete form, which is often used in the numerical solutions of the inverse problem, is described. The formulation of the conjugate problem in discrete form is presented. After calculating the gradient, an algorithm for solving the inverse problem using the Nesterov method is constructed. A computational experiment for the boundary inverse problem is carried out, and the results of the comparative analysis of the Landweber and Nesterov methods in a graphical form are presented. Full article

The electric capacitance tomography (ECT) technique has been widely used in phase distribution reconstruction, while the practical application raised nonideal noise and other errors for cryogenic conditions, requiring a more accurate algorithm. This paper develops a new image reconstruction algorithm for ECT by coupling the traditional Landweber algorithm with the least square support vector regression (LSSVR) for cryogenic fluids. The performance of the algorithm is quantitatively evaluated by comparing the inversion images with the experimental results for both the room temperature working medium with the dielectric constant ratio close to cryogenic fluid and the cryogenic fluid of liquid nitrogen/nitrogen vapor (LN₂-VN₂). The inversion images based on the conventional LBP and Landweber algorithms are also presented for comparison. The benefits and drawbacks of the developed algorithms are revealed and discussed, according to the results. It is demonstrated that the correlated coefficients of the images based on the developed algorithm reach more than 0.88 and a maximum of 0.975. In addition, the minimum void fraction error of the algorithm is reduced to 0.534%, which indicates the significant optimization of the LSSVR coupled method over the Landweber algorithm. Full article

Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton-Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments. Full article

The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the main methods and algorithms to achieve the best results. We considered in this work the linear operator equation and the use of a new version of the Landweber iterative method as an iterative solver. The main goal of updating the Landweber iteration method is to make the iteration process fast and more accurate. We used a polar decomposition to achieve a symmetric positive definite operator instead of an identity operator in the classical Landweber method. We carried out the convergence and other necessary analyses to prove the usability of the new iteration method. The residual method was used as an analysis method to rate the convergence of the iteration. The modified iterative method was compared to the classical Landweber method. A numerical experiment illustrates the effectiveness of this method by applying it to solve the inverse boundary value problem of the heat equation (IBVP). Full article

Electrical impedance tomography (EIT) is a non-invasive, radiation-free imaging technique with a lot of promise in clinical monitoring. However, since EIT image reconstruction is a non-linear, pathological, and ill-posed issue, the quality of the reconstructed images needs constant improvement. To increase image reconstruction accuracy, a grey wolf optimized radial basis function neural network (GWO-RBFNN) is proposed in this paper. The grey wolf algorithm is used to optimize the weights in the radial base neural network, determine the mapping between the weights and the initial position of the grey wolf, and calculate the optimal position of the grey wolf to find the optimal solution for the weights, thus improving the image resolution of EIT imaging. COMSOL and MATLAB were used to numerically simulate the EIT system with 16 electrodes, producing 1700 simulation samples. The standard Landweber, RBFNN, and GWO-RBFNN approaches were used to train the sets separately. The obtained image correlation coefficient (ICC) of the test set after training with GWO-RBFNN is 0.9551. After adding 30, 40, and 50 dB of Gaussian white noise to the test set, the attained ICCs with GWO-RBFNN are 0.8966, 0.9197, and 0.9319, respectively. The findings reveal that the proposed GWO-RBFNN approach outperforms the existing methods when it comes to image reconstruction. Full article

The transmission of high-volume multimedia content (e.g., images) is challenging for a resource-constrained wireless multimedia sensor network (WMSN) due to energy consumption requirements. Redundant image information can be compressed using traditional compression techniques at the cost of considerable energy consumption. Fortunately, compressed sensing (CS) has been introduced as a low-complexity coding scheme for WMSNs. However, the storage and processing of CS-generated images and measurement matrices require substantial memory. Block compressed sensing (BCS) can mitigate this problem. Nevertheless, allocating a fixed sampling to all blocks is impractical since each block holds different information. Although solutions such as adaptive block compressed sensing (ABCS) exist, they lack robustness across various types of images. As a solution, we propose a holistic WMSN architecture for image transmission that performs well on diverse images by leveraging saliency and standard deviation features. A fuzzy logic system (FLS) is then used to determine the appropriate features when allocating the sampling, and each corresponding block is resized using CS. The combined FLS and BCS algorithms are implemented with smoothed projected Landweber (SPL) reconstruction to determine the convergence speed. The experiments confirm the promising performance of the proposed algorithm compared with that of conventional and state-of-the-art algorithms. Full article

In this paper, Landweber iteration with a relaxation factor is proposed to solve nonlinear ill-posed integral equations. A compression multiscale Galerkin method that retains the properties of the Landweber iteration is used to discretize the Landweber iteration. This method leads to the optimal convergence rates under certain conditions. As a consequence, we propose a multiscale compression algorithm to solve nonlinear ill-posed integral equations. Finally, the theoretical analysis is verified by numerical results. Full article

Electrical capacitance tomography (ECT) is one of non-invasive visualization techniques which can be used for industrial process monitoring. However, acquiring images trough 3D ECT often requires performing time consuming complex computations on large size matrices. Therefore, a new parallel approach for 3D ECT image reconstruction is proposed, which is based on application of multi-GPU, multi-node algorithms in heterogeneous distributed system. This solution allows to speed up the required data processing. Distributed measurement system with a new framework for parallel computing and a special plugin dedicated to ECT are presented in the paper. Computing system architecture and its main features are described. Both data distribution as well as transmission between the computing nodes are discussed. System performance was measured using LBP and the Landweber’s reconstruction algorithms which were implemented as a part of the ECT plugin. Application of the framework with a new network communication layer reduced data transfer times significantly and improved the overall system efficiency. Full article

Photo-Acoustic Tomography (PAT) is an emerging non-invasive hybrid modality driven by a constant yearning for superior imaging performance. The image quality, however, hinges on the acoustic reflection, which may compromise the diagnostic performance. To address this challenge, we propose to incorporate a deep neural network into conventional iterative algorithms to accelerate and improve the correction of reflection artifacts. Based on the simulated PAT dataset from computed tomography (CT) scans, this network-accelerated reconstruction approach is shown to outperform two state-of-the-art iterative algorithms in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) in the presence of noise. The proposed network also demonstrates considerably higher computational efficiency than conventional iterative algorithms, which are time-consuming and cumbersome. Full article

The paper proposes a capacitance-sensor-array-based imaging system to detect water leakage inside insulating slabs with porous cells, such as anechoic acoustic rubber tiles. The modeling is conducted by using the finite element method to obtain the electrical potential distribution and sensitivity map with the proposed capacitance sensor array. An experimental test setup, which is composed of an eight-electrode capacitance sensor array and a commercialized capacitance bridge instrument for measurement, is developed. Experiments regarding different leakage scenarios are carried out by using the test setup. Preliminary results standing for different water leakage cases, which are based on the experimental data obtained from the test setup, are presented and depicted as images reconstructed by using different algorithms including the linear back projection (LBP), the projected Landweber iteration, and the total variation regularization. These results demonstrate that the proposed capacitance sensor array is feasible and has a great potential for imaging of water leakage inside insulating slabs with porous cells. A cost-effective capacitance measurement circuit for practical applications is also proposed and simulated. Full article