Proposed Reconstruction Algorithm Research Articles

Graph signal reconstruction based on spatio-temporal features learning

This paper presents a new algorithm for reconstructing time-varying graph signals using spatiotemporal feature learning. We introduce a time series analysis method to capture the temporal stationarity of graph signals and propose a reconstruction model based on spatiotemporal coupling features. However, prior knowledge of the temporal stationarity of graph signals is required for this task. To address the issue, we analyze the spatio-temporal coupling feature in a graph-spectral view and design a learning framework to capture only the temporal feature based on the sampled signals. We reconstruct the graph signals using the proposed reconstruction model and feature-learning framework by solving an unconstrained optimization problem consisting of data fidelity and two regularization terms. Numerical results using both synthetic and real-world datasets demonstrate the superiority of the proposed reconstruction algorithm over existing methods.

Vehicle trajectory reconstruction for freeway traffic considering lane changing behaviors

Vehicle trajectory data provides critical information for many transportation applications. Due to limitations in the data collection techniques, usually, only partial trajectories can be obtained. As a result, trajectory reconstruction where the missing trajectories are inferenced by the observed data is an essential step for many downstream applications. Existing studies usually consider a connected vehicle (CV) environment for trajectory data collection and ignore the lane-changing (LC) behaviors in the reconstruction process. The deployment of connected and autonomous vehicles (CAVs) makes it possible to collect trajectory data more efficiently with much lower penetrations. This study proposes a vehicle trajectory reconstruction algorithm considering LC maneuvers in the CAV environment. The Pettit test and a rule-based optimization algorithm are designed to predict the possible LC time points. Then two car-following models are applied to reconstruct trajectories. The NGSIM US101 dataset is applied to evaluate the proposed reconstruction algorithm under varying CAV penetration rates (PRs) (e.g., 2%, 3%, 5%). The prediction of LC time points achieves high accuracy with average prediction errors less than 1 s under CAV PRs greater than 2%. Compared to the ground truth trajectories, the reconstructed trajectories have the mean absolute error (MAE) less than one vehicle length under 3% and higher CAV PRs.

Limited-angle artifacts removal and jitter correction in soft x-ray tomography via physical model-driven deep learning

Soft x-ray nanoscale tomography provides high-resolution three-dimensional visualization of the imaged objects and promotes the development of multiple research fields. However, the current challenges lie in the presence of limited-angle artifacts and projection jitter, which degrade the imaging resolution and quality. To address these issues, we propose a physical model-driven deep learning including forward and backward CT models. Combing with the iterative algorithm, the proposed method simultaneously suppresses the limited-angle and jitter artifacts. Furthermore, the physical model generates plenty of data to overcome the requirement of abundant experimental datasets. Both simulation and experiment demonstrate the feasibility and validity of the proposed reconstruction algorithm.

Ground Radioactivity Distribution Reconstruction and Dose Rate Estimation Based on Spectrum Deconvolution

Estimating the gamma dose rate at one meter above ground level and determining the distribution of radioactive pollution from aerial radiation monitoring data are the core technical issues of unmanned aerial vehicle nuclear radiation monitoring. In this paper, a reconstruction algorithm of the ground radioactivity distribution based on spectral deconvolution was proposed for the problem of regional surface source radioactivity distribution reconstruction and dose rate estimation. The algorithm estimates unknown radioactive nuclide types and their distributions using spectrum deconvolution and introduces energy windows to improve the accuracy of the deconvolution results, achieving accurate reconstruction of multiple continuous distribution radioactive nuclides and their distributions, as well as dose rate estimation of one meter above ground level. The feasibility and effectiveness of the method were verified through cases of single-nuclide (137Cs) and multi-nuclide (137Cs and 60Co) surface sources by modeling and solving them. The results showed that the cosine similarities between the estimated ground radioactivity distribution and dose rate distribution with the true value were 0.9950 and 0.9965, respectively, which could prove that the proposed reconstruction algorithm would effectively distinguish multiple radioactive nuclides and accurately restore their radioactivity distribution. Finally, the influences of statistical fluctuation levels and the number of energy windows on the deconvolution results were analyzed, showing that the lower the statistical fluctuation level and the more energy window divisions, the better the deconvolution results.

3D directional gradient L0 norm minimization guided limited-view reconstruction in a dual-panel positron emission mammography

BackgroundDual-panel PET is often used for local organ imaging, especially breast imaging, due to its simple structure, high sensitivity, good in-plane resolution, and straightforward fusion with other imaging modalities. Nevertheless, because of data loss caused by the dual-panel structure, using conventional image reconstruction methods results in limited-view artifacts and low image quality in dual-panel positron emission mammography (PEM), which may seriously affect the diagnosis. To mitigate the limited-view artifacts in the dual-panel PEM, we propose a 3D directional gradient L0 norm minimization (3D-DL0) guided reconstruction method. MethodsThe detailed derivation and reasonable simplification of the 3D-DL0 algorithm are given first. Using this algorithm, we then obtain a prior image with edge recovery but contrast loss. To limit the solution space, the 3D-DL0 prior is introduced into the Maximum a Posteriori reconstruction. Meanwhile, a space-invariant point spread function is also implemented to restore image contrast and boundaries. Finally, the reconstructed images with limited-view artifact suppression are obtained. The proposed method was evaluated using the data acquired from physical phantoms and patients with breast tumors on a commercial dual-panel PET system. ResultsThe qualitative and quantitative studies for phantom data and the blind reader study for clinical data show that the proposed method is more effective in reaching a balance between artifact elimination and image contrast improvement compared with various limited-view reconstruction methods. In addition, the iteration process of the method is proved convergent numerically. ConclusionsThe image quality improvement confirms the potential value of the proposed reconstruction algorithm to address the limited-view problem, and thus improve diagnostic accuracy in dual-panel PEM imaging.

Signal restoration algorithm for photoacoustic imaging systems.

In a photoacoustic (PA) imaging system, the detectors are bandwidth-limited. Therefore, they capture PA signals with some unwanted ripples. This limitation degrades the resolution/contrast and induces sidelobes and artifacts in the reconstructed images along the axial direction. To compensate for the limited bandwidth effect, we present a PA signal restoration algorithm, where a mask is designed to extract the signals at the absorber positions and remove the unwanted ripples. This restoration improves the axial resolution and contrast in the reconstructed image. The restored PA signals can be considered as the input of the conventional reconstruction algorithms (e.g., Delay-and-sum (DAS) and Delay-multiply-and-sum (DMAS)). To compare the performance of the proposed method, DAS and DMAS reconstruction algorithms were performed with both the initial and restored PA signals on numerical and experimental studies (numerical targets, tungsten wires, and human forearm). The results show that, compared with the initial PA signals, the restored PA signals can improve the axial resolution and contrast by 45% and 16.1 dB, respectively, and suppress background artifacts by 80%.

A Refinement Boosted and Attention Guided Deep FISTA Reconstruction Framework for Compressive Spectral Imaging

Hyperspectral images (HSIs) contain rich spatial and spectral information. A double dispersers coded aperture snapshot spectral imaging (DD-CASSI) system takes advantage of compressive sensing (CS) theory to map 3D HSI data into a single 2D measurement. One of key components of DD-CASSI is to reconstruct high quality hyperspectral image from measurement. Traditional model-based methods use mathematical optimization to reconstruct hyperspectral images according to prior knowledge. Current deep learning based methods achieve pleasant results. But fully learned deep learning methods lack interpretability, and model-based deep learning methods cannot achieve pleasant performance. In this paper, we propose a novel HSI reconstruction framework named Refinement Boosted and Attention Guided Tensor FISTA(Fast Iterative Shrinkage-Thresholding Algorithm)-Net (ReAttFISTA-Net), which combines model-based deep learning and fully learned deep learning reconstruction strategies. In this framework, we introduces Attention Guided Fusion Mechanism which enhances spatial-spectral information, refinement sub-network and auxiliary loss terms to improve the reconstruction performance. Extensive experimental results show that the proposed reconstruction algorithm outperforms the state-of-the-art algorithms on both simulation and real-world datasets.

Distributed reconstruction of time-varying graph signals via a modified Newton’s method

This paper develops a distributed reconstruction algorithm, that can be implemented efficiently, for time-varying graph signals. The reconstruction problem is formulated as an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and the regularization term. The regularizer used is the nonsmoothness measure of the temporal difference signal. The classical Newton’s method can be used to solve the optimization problem. However, computation of the Hessian matrix inverse is required, and this does not scale well with the graph size. Furthermore, a distributed implementation is not possible. An approximation to the inverse Hessian, that exploits the graph topology, is developed here. The resulting iterative algorithm can be implemented in a distributed manner, and scales well with the graph size. Convergence analysis of the algorithm is presented, which shows convergence to the global optimum. Numerical results, using both synthetic and real world datasets, will demonstrate the superiority of the proposed reconstruction algorithm over existing methods.

Real-time single-pixel imaging using a system on a chip field-programmable gate array

Unlike conventional imaging, the single-pixel imaging technique uses a single-element detector, which enables high sensitivity, broad wavelength, and noise robustness imaging. However, it has several challenges, particularly requiring extensive computations for image reconstruction with high image quality. Therefore, high-performance computers are required for real-time reconstruction with higher image quality. In this study, we developed a compact dedicated computer for single-pixel imaging using a system on a chip field-programmable gate array (FPGA), which enables real-time reconstruction at 40 frames per second with an image size of 128 × 128 pixels. An FPGA circuit was implemented with the proposed reconstruction algorithm to obtain higher image quality by introducing encoding mask pattern optimization. The dedicated computer can accelerate the reconstruction 10 times faster than a recent CPU. Because it is very compact compared with typical computers, it can expand the application of single-pixel imaging to the Internet of Things and outdoor applications.

Tilted Fiber Bragg Grating Measurements During Laser Ablation of Hepatic Tissues: Quasi-Distributed Temperature Reconstruction and Cladding Mode Resonances Analysis

In this work, we investigate the application of tilted fiber Bragg grating (TFBG) sensors during <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex vivo</i> laser ablation of porcine hepatic tissues. Initially, TFBG’s ability to measure the surrounding refractive index (RI) for different sucrose concentrations and the possibility to measure the RI of the targeted tissue during laser ablation (LA) is analyzed. After, the temperature sensing modality of TFBG is investigated in detail. We have implemented an algorithm for quasi-distributed spatial temperature profile reconstruction along TFBG. The algorithm models the TFBG core mode spectrum as a chain of Bragg gratings (each Bragg grating is modeled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">via</i> coupled mode theory), where each grating is sensitive to local temperature changes. After, the Gaussian-shape temperature profile along the TFBG is reconstructed using the iterative optimization technique. Temperature measurements have been compared with highly-dense FBG array measurements and with conventional TFBG point temperature measurements based on the core mode tracking techniques (maximum tracking, X-dB Bandwidth, centroid methods). Overall, the proposed reconstruction algorithm is able to provide a quasi-distributed temperature profile along TFBG, which is not possible to obtain using conventional point temperature measurements based on the TFBG’s core mode tracking. The resulted root-mean-square error in comparison to FBG array reference measurements is 7.8±1.7 °C. In general, the results show that the main reliable sensing modality of TFBG during LA is temperature monitoring, which can be significantly improved by the proposed algorithm.

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Measurement Estimation of Virtual Electrodes

For biomedical imaging in mini-scale, the inverse problem of electrical impedance tomography (EIT) is severely ill-conditioned due to the number of electrodes is very limited. In this paper, a novel difference imaging algorithm for 2D-EIT using measurement estimation of virtual electrodes is proposed. The proposed reconstruction algorithm breaks though the limitation of micro EIT sensor’s structure and tackles the problem of low spatial resolution in mini-scale by introducing virtual electrodes. The inverse problem of EIT is decomposed into two separately tasks: estimation potentials of virtual electrodes with proper priors, determination of the conductivity distribution using both virtual and real electrodes. It is formulated as a possibility model using virtual electrodes’ potentials as latent variables. Real electrodes’ potentials are regarded as the observable variables. Conductivity distribution is predicted by a maximum likelihood of the possibility model by using EM algorithm. The proposed algorithm is verified by both simulation and experiment. In experiment, medaka fish embryo which is about 1mm in diameter is reconstructed. Comparing with Tikhonov and NOSER regularization method, average ICC is improved 11.54% from 0.7620 to 0.8499 in simulation and improved 5.79% from 0.6978 to 0.7382 in experiment. The algorithm not only performs well in conductivity reconstruction, but also in shape reconstruction. Average position error is decreased 47.57%, average shape error is decreased 24.44% in experiment. It is very suitable for image reconstruction in mini-scale.

Transmission reconstruction algorithm by combining maximum-likelihood expectation maximization and a convolutional neural network for radioactive drum characterization

One of the most critical factors that affect reconstructions of the activity of a radioactive drum is the accuracy of tomographic gamma scanning transmission reconstruction. The traditional algorithms applied for reconstructing the density map, such as maximum-likelihood expectation maximization (MLEM), algebraic reconstruction technique, or filtered back-projection, produce a grid distribution with severe grid artifacts and a high level of noise, which significantly degrade the detail of the transmission image, thereby increasing the reconstruction error for both the density map and the activity. Thus, we propose a novel algorithm for transmission reconstruction by combining MLEM and a deep convolutional neural network (CNN). The CNN is trained using a supervised learning approach with image pairs obtained from the drum's ground truth (target) and the result constructed using MLEM (input). Our experimental results indicate that the proposed reconstruction algorithm can significantly improve the spatial resolution while also removing grid artifacts. In addition, the algorithm is sufficiently robust when dealing with a noisy input image. When the input image contained 20% noise, the mean squared error of the output image decreased by 78.51% compared with the conventional reconstruction method, and the peak signal-to-noise ratio and structural similarity index measure for the output image improved by 81.19% and 71.74%, respectively. The new algorithm improves the accuracy of the radioactive drum density map reconstruction as well as decreasing the measurement time required. We consider that the proposed algorithm is an effective new method for use in the field of radioactive waste drum transmission image reconstruction.

Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry

&lt;p style='text-indent:20px;'&gt;In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.&lt;/p&gt;

Forecasting carbon futures price: a hybrid method incorporating fuzzy entropy and extreme learning machine

In this paper, we propose a novel hybrid model that extends prior work involving ensemble empirical mode decomposition (EEMD) by using fuzzy entropy and extreme learning machine (ELM) methods. We demonstrate this 3-stage model by applying it to forecast carbon futures prices which are characterized by chaos and complexity. First, we employ the EEMD method to decompose carbon futures prices into a couple of intrinsic mode functions (IMFs) and one residue. Second, the fuzzy entropy and K-means clustering methods are used to reconstruct the IMFs and the residue to obtain three reconstructed components, specifically a high frequency series, a low frequency series, and a trend series. Third, the ARMA model is implemented for the stationary high and low frequency series, while the extreme learning machine (ELM) model is utilized for the non-stationary trend series. Finally, all the component forecasts are aggregated to form final forecasts of the carbon price for each model. The empirical results show that the proposed reconstruction algorithm can bring more than 40% improvement in prediction accuracy compared to the traditional fine-to-coarse reconstruction algorithm under the same forecasting framework. The hybrid forecasting model proposed in this paper also well captures the direction of the price changes, with strong and robust forecasting ability, which is significantly better than the single forecasting models and the other hybrid forecasting models.

UAV-Assisted Three-Dimensional Spectrum Mapping Driven by Spectrum Data and Channel Model

As the number of civil aerial vehicles increase explosively, spectrum scarcity and security become an increasingly challenge in both the airspace and terrestrial space. To address this difficulty, this paper presents an unmanned aerial vehicle-assisted (UAV-assisted) spectrum mapping system and a spectrum data reconstruction algorithm driven by spectrum data and channel model are proposed. The reconstruction algorithm, which includes a model-driven spectrum data inference method and a spectrum data completion method with uniformity decision mechanism, can reconstruct limited and incomplete spectrum data to a three-dimensional (3D) spectrum map. As a result, spectrum scarcity and security can be achieved. Spectrum mapping is a symmetry-based digital twin technology. By employing an uniformity decision mechanism, the proposed completion method can effectively interpolate spatial data even when the collected data are unevenly distributed. The effectiveness of the proposed mapping scheme is evaluated by comparing its results with the ray-tracing simulated data of the campus scenario. Simulation results show that the proposed reconstruction algorithm outperforms the classical inverse distance weighted (IDW) interpolation method and the tensor completion method by about 12.5% and 92.3%, respectively, in terms of reconstruction accuracy when the collected spectrum data are regularly missing, unevenly distributed and limited.

Dynamic Data Driven Multistatic Radio Frequency Imaging

Multistatic radio frequency (RF) imaging systems utilize distributed RF sensors which transmit waveforms to illuminate a target scene and estimate the dielectric properties of the region of interest from the received echoes. This article applies the principles of dynamic data driven systems to improve the performance of multistatic RF imaging system in terms of power efficiency and image reconstruction accuracy. Target location information derived from initial image reconstruction is applied to dynamically reconfigure the imaging system. Based on the geolocation of targets relative to the distributed RF sensors, Fisher information matrices associated with the targets and multistatic sensor pairs are calculated and applied to derive optimum power allocation strategies under different constraints. Image reconstruction of multistatic RF imaging often suffers from artifacts and ghost targets caused by multipath propagation and multiorder reflections.A grouped-coordinate descent type reconstruction algorithm is developed to exploit target location information. The iterative optimization alternates between the groups of target space parameters and nontarget space parameters. The dictionary of reconstruction is dynamically updated to include the secondary reflections from target locations. The improved model fidelity leads to more accurate reconstructions without a significant increase in computational complexity. Numerical simulations demonstrate that the proposed power allocation strategies are effective in energy saving. The proposed reconstruction algorithm converges faster than sequential parameter update algorithms, and the reconstruction accuracy is superior to that using a fixed dictionary containing the first order reflections only.

A three-dimensional reconstruction method for the inner surface of a deep hole using a rotating mechanism

An inner surface 3D reconstruction device structure is proposed in this paper to reconstruct the complex curved inner surface of a deep hole. First, the optical paths of the camera and the structured light transmitter are converged on the deep hole inner surface through plane mirrors to form a multi-line structured light projection system (MSLPS). The parameters of the MSLPS are then calibrated before the measurement. Second, the MSLPS rotates during the measurement process to obtain the point cloud collections of the inner surface and the rotation angles at different measurement positions are recorded. The point clouds contain the 3D surface information of the measured areas. Finally, the entire surface shape is reconstructed by the proposed reconstruction algorithm, and the feature parameters of the deep hole inner surface can be calculated by the reconstructed point cloud. The development process of the system was demonstrated in the experiment. The proposed system is validated through the reconstruction experiment of different areas in a deep hole.

Dynamic PET reconstruction using the kernel method with non-local means denoising

Non-local means with a spatiotemporal search window (NLM-ST) has been developed to denoise dynamic positron emission tomography (PET) images. The improved image quality, however, may not be good enough to generate reliable parametric images. In this work, we propose an iterative reconstruction algorithm which aims to improve the quality of dynamic PET images by incorporating NLM-ST denoising directly within the kernelized expectation-maximization (KEM) reconstruction algorithm. Since the NLM-ST denoising was employed after each KEM update, the proposed algorithm was called NLM-ST-AU-KEM. Computer simulations were conducted to evaluate the performance of the proposed reconstruction algorithm, and the results were compared to KEM with a post-reconstruction NLM-ST denoising filter (KEM + NLM-ST). The root mean squared errors (RMSE) of the dynamic PET images reconstructed using the KEM algorithm were increased after 40 iterations. Both the NLM-ST-AU-KEM and the KEM + NLM-ST methods could achieve stable RMSE values after 50 iterations, but the former had lower RMSE values. Compared to the proposed NLM-ST-AU-KEM method, the KEM + NLM-ST method tended to over-smooth dynamic PET images and parametric images. For K1 and Ki, the proposed NLM-ST-AU-KEM method had lower bias but higher variance than the KEM + NLM-ST method. For k2 and k3, the proposed NLM-ST-AU-KEM method had higher variance than the KEM + NLM-ST method, but the higher variance could be reduced by applying a kernel-based post-filtering method to the NLM-ST-AU-KEM-generated parametric images. NLM-ST denoising during image reconstruction seems to be a better strategy than that after image reconstruction.

Numerical method for solving inverse source problem for Poisson equation

We consider an inverse problem for the Poisson equation [Formula: see text] in the square [Formula: see text] which consists of determining the source [Formula: see text] from boundary measurements. Such problem is ill-posed. We restrict ourselves to a class of functions [Formula: see text]. To illustrate our method, we first assume that [Formula: see text] and [Formula: see text] are known functions with partial data at the boundary. For the reconstruction, we consider approximations by the Fourier series, therefore we obtain an ill-posed linear system which requires a regularization strategy. In the general case, we propose an iterative algorithm based on the full data at the boundary. Finally, some numerical results are presented to show the effectiveness of the proposed reconstruction algorithms.

A Modified Omega-K Algorithm for Near-Field Single-Frequency MIMO-Arc-Array-Based Azimuth Imaging

Inspired by the circular-aperture synthetic aperture radar (Circular-SAR) imaging regime that can provide higher azimuth image resolution, the imaging regime employing the multiple-input-multiple-output (MIMO) arc array is proposed. Moreover, no efficient imaging algorithm is now available for these MIMO arc array setups. This article proposes a modified Omega-K algorithm for near-field azimuth image reconstruction based on the geometry transformation from the single-frequency MIMO arc array to the equivalent MIMO linear array. Note that this geometry transformation relies on the calculation of the phase difference and the definition of the corresponding compensation function. Compared with the single-input-single-output (SISO) arc scan requiring more elements, simulations with good agreement were performed to validate the azimuth image reconstructions of single/multiple targets. Although the computing efficiency of the proposed algorithm for MIMO arc array is lower than that of the traditional Omega-K algorithm for the SISO arc scan, it still has an obvious advantage relative to the traditional backprojection (BP) algorithm that is always taken as the gold standard. Furthermore, three realistic imaging geometries, including the metal strips at different radii, the tilted metal plate, and the human body torso cross section, were simulated to test the fidelity of the proposed reconstruction algorithm. Proof-of-principle experiments were also carried out based on an MIMO arc array with the help of one arc scanner. Finally, both simulation and experimental results validate the effectiveness of the proposed algorithm on azimuth image reconstruction quality.