An Extended Simultaneous Algebraic Reconstruction Technique for Imaging the Ionosphere Using GNSS Data and Its Preliminary Results

Ray tracing analysis and a first‐order treatment of the wave frequency and electron energy dependence of gyroresonant pitch angle scattering reveals the L shell dependence of the time‐integrated energetic electron (>150 keV) precipitation flux in the drift loss cone due to a single cloud‐to‐ground lightning stroke. Primary features of the L dependence are determined by the ray paths of magnetospherically reflecting nonducted whistler waves, as well as the refraction of the wave normal vectors due to ionospheric horizontal electron density gradients at low latitudes. Calculations for lightning source latitudes of 25°, 35°, and 45°, with an assumed “average” ionospheric electron density profile, as well as an International Reference Ionosphere model profile, indicate that horizontal ionospheric electron density gradients can cause the whistler wave energy to focus near the geomagnetic equator on the first magnetospheric traverse, resulting in a spatially narrow precipitation signature at low L shells (1.4 < L < 1.65). The magnitude of this low‐L peak is found to be sensitively dependent on the local ionospheric density gradients. Subsequent magnetospheric reflections result in a broad precipitation peak at higher L shells (1.8 < L < 4.2), which is robustly present, with magnitude being relatively insensitive to lightning source‐latitude and ionospheric horizontal gradients. The calculated L dependences were found to be in excellent agreement with drift‐loss cone fluxes measured aboard the SAMPEX satellite.

An improved algebraic reconstruction technique (IART) is presented for the tomographic reconstruction of ionospheric electron density (IED). This method applies the total electron content (TEC) measurements to invert the spatial distribution of the IED from a set of apriori IED distributions. In this new method, a data-driven adjustment of the relaxation parameter is performed to improve the computation efficiency and image quality of the classical algebraic reconstruction technique (ART). In addition, the new algorithm is also combined with ionospheric space discretization technique to simplify the inversion of IED, and it applies CHAMP occultation data to improve the vertical resolution. A numerical simulation experiment is carried out to validate the reliability of the new method. It is then applied to the inversion of IED from real GPS data. Inverted results show that the IART algorithm has better accuracy and efficiency than the conventional ART algorithm. The reliability of the IART algorithm is also validated by ionosonde data recorded at Wuhan station.

<p>Ionosphere is one of the main errors in the signal propagation of global navigation system satellite (GNSS), and it is also the key issue of space weather. The International Reference Ionosphere (IRI) is the most important empirical model described the ionospheric characteristics, and it provides the monthly averages of electron densities and vertical total electron content (VTEC) in the altitude range of 50km-2000km. The IRI-2016 model is the latest version. But some studies showed that the accuracy of the IRI model is not high enough in China due to the use of fewer data sources. This paper will assess the performance of IRI-2016 model in China, and a modified IRI 2016 model by adjusting the driving parameters IG and RZ index of IRI2016 model with GNSS TEC data are also investigated. In this contribution, GNSS data from the Crustal Movement Observation Network of China (CMONC) are used to estimate TEC values, and the ionosonde data from three stations are used as references for the ionospheric electron densities. Three ionosonde stations are located at Beijing (BP440, 40.3°N/116.2°E), Wuhan (WU430, 30.5°N/114.4°E) and Sanya (SA418, 18.3°N/ 109.6°E). The above data respectively cover a period of 6 days in the high year (2015) and low year (2019) of solar activity.</p><p>The study shows that the biggest reason for the difference (DTEC) between GPS-TEC and IRI2016-TEC in China is that the poor estimation of NmF2 and hmF2 by IRI model, and the driving parameters IG and RZ index of IRI2016 can be updated by constraining DTEC. Finally, the performance of the modified IRI-2016 model is improved by the updated IG and RZ indexes as the short-term driving values of ionospheric parameters. The analysis show that the modified IRI-2016 model is more accurate at estimating both the TEC and the electron density profile than the original model.</p>

Predicting the behaviour of the Earth’s ionosphere is crucial for the ground-based and spaceborne technologies that rely on it. This paper presents a novel way of inferring ionospheric electron density profiles and electron temperature profiles using machine learning. The analysis is based on the Nearest Neighbour (NNB) and Radial Basis Function (RBF) regression models. Synthetic data sets used to train and validate these two inference models are constructed using the International Reference Ionosphere (IRI 2020) model with randomly chosen years (1987–2022), months (1–12), days (1–31), latitudes (−60 to 60°), longitudes (0, 360°), and times (0–23 h), at altitudes ranging from 95 to 600 km. The NNB and RBF models use the constructed ionosonde-like profiles to infer complete ISR-like profiles. The results show that the inference of ionospheric electron density profiles is better with the NNB model than with the RBF model, while the RBF model is better at inferring the electron temperature profiles. A major and unexpected finding of this research is the ability of the two models to infer full electron temperature profiles that are not provided by ionosondes using the same truncated electron density data set used to infer electron density profiles. NNB and RBF models generally over- or underestimate the inferred electron density and electron temperature values, especially at higher altitudes, but they tend to produce good matches at lower altitudes. Additionally, maximum absolute relative errors for electron density and temperature inferences are found at higher altitudes for both NNB and RBF models.

New parallel iteration algorithms that provide real-time reconstruction of the 3D breast images restored from an incomplete set of noisy mammograms are studied. The simultaneous algebraic reconstruction technique (SART) and Bayesian inference reconstruction (BIR) are considered as advantageous iteration methods that are most suitable for improving the quality of the reconstructed 3D images. The graphics processing unit (GPU) is used to accelerate the reconstruction. The minimization of total variation (TV) is used as a priori support for the regularization of the iteration process and decrease of the noise level in the reconstructed images. Preliminary results for medical physical phantoms show that all the methods are sufficient for the layer-by-layer reconstruction of medical model objects and separation of layers whose images are overlapped on a mammogram that corresponds to vertical transmission (direction along the OZ axis). The traditional shift-and-add (SAA) tomosynthesis is established to be less efficient than SART and BIR in terms of the anatomical-noise reduction and blurring of reconstructed 3D images between conjugate layers. Despite the fact that the estimated contrast-noise ratio, given internal structures with low contrast, is higher for SAA as compared to SART and BIR, its efficiency is very low given the highly structured background. In our opinion, optimal results can be achieved using BIR.

Computed tomography (CT) has been extensively studied for years and widely used in the modern society. Although the filtered back-projection algorithm is the method of choice by manufacturers, efforts are being made to revisit iterative methods due to their unique advantages, such as superior performance with incomplete noisy data. In 1984, the simultaneous algebraic reconstruction technique (SART) was developed as a major refinement of the algebraic reconstruction technique (ART). However, the convergence of the SART has never been established since then. In this paper, the convergence is proved under the condition that coefficients of the linear imaging system are nonnegative. It is shown that from any initial guess the sequence generated by the SART converges to a weighted least square solution.

The experiment of ionospheric tomographic reconstruction using satellite beacon TEC data from two or more adjacent GRBR observation stations following equatorial latitude and longitude have been conducted on campaign-based observation in Sumedang, Pameungpeuk and Indramayu West Java on 2016 and 2017. The reconstruction technique utilized is a simple algebraic reconstruction technique (ART). The result obtained is the ionosphere electron density distribution along the longitude of 108 degrees East over the area of West Java and Indonesia. The ionosphere electron density parameters obtained from the IRI-2012 Model were used as the initiation to construct ionospheric tomographic reconstruction. The validation performed by correlating foF2 from the ionospheric tomographic reconstruction with foF2 obtained from ionosonde observation at Sumedang station, one of the GRBR observation sites shows that corresponded to the correlation coefficient value of 0.8665, with a bias frequency of 1.386 MHz, whereas the correlation with the maximum electron density value obtained from the IRI-2016 model gives a correlation coefficient value of 0.8958. a bias frequency of 1.386 MHz, whereas the correlation with the maximum electron density value obtained from the IRI-2016 model gives a correlation coefficient value of 0.8958.

<span lang="EN-US">Electrical impedance tomography (EIT), as a non-ionizing tomography method, has been widely used in various fields of application, such as engineering and medical fields. This study applies an iterative process to reconstruct EIT images using the simultaneous algebraic reconstruction technique (SART) algorithm combined with K-means clustering. The reconstruction started with defining the finite element method (FEM) model and filtering the measurement data with a Butterworth low-pass filter. The next step is solving the inverse problem in the EIT case with the SART algorithm. The results of the SART algorithm approach were classified using the K-means clustering and thresholding. The reconstruction results were evaluated with the peak signal noise ratio (PSNR), structural similarity indices (SSIM), and normalized root mean square error (NRMSE). They were compared with the one-step gauss-newton (GN) and total variation regularization based on iteratively reweighted least-squares (TV-IRLS) methods. The evaluation shows that the average PSNR and SSIM of the proposed reconstruction method are the highest of the other methods, each being 24.24 and 0.94; meanwhile, the average NRMSE value is the lowest, which is 0.04. The performance evaluation also shows that the proposed method is faster than the other methods.</span>

When solar flares occur, as results of increases in X-rays and extreme ultraviolet (EUV) radiations the electron density in the ionosphere increases. The increase in the electron density can cause problems with satellite attitude control, satellite communication and GPS positioning accuracy. To validate the impacts of solar flares on satellites, it is necessary to quantify the increase in ionospheric plasma density caused by solar flares, although this process has not yet been precisely clarified. It is widely known that soft X-rays (0.1-0.8nm) generated during solar flares ionize the D-region ionosphere (60–90 km) and affect the propagation path of VLF (very low frequency, 3–30 kHz)/LF (low frequency, 30–300 kHz) radio waves (especially the reflection height). Lyman-alpha radiation (121.6 nm) is the major component of ultraviolet radiation, and is known to affect the D-region. However, the response of the D-region ionosphere to Lyman-alpha during solar flares remains unclear. In this study, we used the LF transmitter signals to investigate D-region ionospheric variations for the X5.89class solar flare that occurred at 01:10 UT on May 11, 2024. This was the largest solar flare among the consecutive solar flares that occurred in May 2024. The LF transmitter signals used in this study were OCTAVE/AVON data operated by our research group around the world. The LF waves were transmitted from JJY60 (60.0 kHz) in Japan and BPC (68.5 kHz) in China, and received at Pontianak (PTK), Indonesia and Rikubetsu (RKB), Japan. When a solar flare occurs the LF phase normally exhibits time variations similar to those of X-ray flux. However, during the X5.89-class solar flare, unusual oscillations in phase and amplitude were observed. Based on wavelet analysis of these oscillations, the periods were 549 s for the phase of the JJY60-PTK path and 388 s for the phase of the BPC-PTK path. To investigate the cause of the LF oscillations, we compared between the LF waves and EUV data observed by GOES-16 and SDO satellites. A part of LF oscillations shows similar time variations with that of the summation of EUV in the 20–140 nm range. A few peaks of the LF oscillation coincided with peaks in the composited EUV emissions. Coherence analysis was conducted to examine the relationship with EUV emissions at wavelengths of 117.5 nm, 133.5 nm, and 140.5 nm. The analysis revealed statistically significant coherence between the LF phase and EUV emissions within the 300–1000 s period range across all wavelengths, with particularly prominent peaks observed around 400–800 s. These results strongly suggest that the periodic variations in EUV emissions associated with the solar flare affected the electron density in the D-region ionosphere.

Longitudinal behaviors of the IRI-B parameters of the equatorial electron density profiles retrieved from FORMOSAT-3/COSMIC radio occultation measurements

The projection access order in which the projections are used in the Simultaneous Algebraic Reconstruction Technique (SART) has great influence on the convergence rate and the quality of the reconstructed image. It is a well known fact that the correlation between the used projections should be as small as possible. Common methods achieve a small correlation based on the projection angles by applying special angle schemes. In this paper, we present a novel Greedy Projection Access Order (GPAO). GPAO is an angle-independent method, which is based on the structural information of the object itself. We create a projection-based information vector for each angle. By using the pairwise correlation of these vectors, a Greedy algorithm finds a short path through all projections. In this order the SART uses the projections to reconstruct the image. As the simulation results show, the performance of GPAO is similar to the performance of a random order. Advantageously, GPAO is robust and adapted to the object. Potentially, more complex path finding algorithms will show better results than the Greedy solution.

This study investigates the impacts of geomagnetic storms on the performance of the International Reference Ionosphere 2016 (IRI-2016) foF2 predictions at different latitudes during geomagnetically disturbed periods in different seasons of the year 1989 which is around maximum solar activity. For this purpose, hourly foF2 data measured from the ionosonde stations Manila (14.7° N, 121.1° E), Rome (41.8° N, 12.5° E), Argentia NF (47.3° N, 54.0° W) and Uppsala (59.8° N, 17.6° E) that are located at low, middle and high latitudes, and hourly foF2 data calculated from the IRI-2016 for the same locations are used. In our study, a comparison between observational results and that of the IRI-2016 foF2 predictions is made. Planetary geomagnetic activity “3h-Kp” and “3h-ap” indices are used as geomagnetic activity indicators. In order to test the performance of the IRI-2016 for disturbed geomagnetic conditions, the percentile deviations and root mean square errors (RMSE) are calculated using the foF2 data from the IRI-2016 and the ionosonde stations. These analyzes are done for four seasons based on geomagnetic stormy days around equinoxes (March 21, September 23) and solstices (June 21, December 21). Therefore, it is found that during geomagnetically disturbed periods, the IRI-2016 foF2 predictions deviate considerably from the foF2 data taken from the ionosonde stations and this deviation differs according to the seasons and latitudes. The results show that the last version of the IRI model that includes the foF2 storm model is not sufficient to properly represent the real conditions of a disturbed ionosphere and there is still space for improving the IRI model for geomagnetically disturbed conditions.

• Lightning waveforms reliably yield estimates for D-region electron density profiles when analysed. Lightning waveforms in the low frequency (LF; 30–300 kHz) and the very low frequency (VLF; 3–30 kHz) bands can be exploited to produce data-driven ionospheric D-region electron density profile (EDP) estimates with significantly higher spatial and temporal coverage than previously available. The lightning waveforms used in this paper are signals detected in the LF/VLF of negative cloud-to-ground lightning by the Earth Networks Total Lightning Detection Network. Each waveform contains a ground wave and a time-delayed ionospheric reflection. The time delay between the ground wave and ionospheric reflection has previously been used to estimate a single specular reflection altitude, where LF/VLF emissions are reflected by the ionosphere. Here, we expand upon previous methods to include filtering and spectral analysis, and account for oblique propagation to produce higher-order estimates for reflection altitudes and corresponding electron densities. Once estimated, reflection altitudes and corresponding electron densities can be used to derive parameters β and h ′, which define an EDP for the D-region. In this study, the lightning waveform (LW) analysis is demonstrated using a single representative 24-h dataset over the Southeast United States, and then extended to a total of 10 separate datasets with varying locations and ionospheric conditions. The LW-derived D-region EDPs are in agreement with predictions made by the Faraday International Reference Ionosphere model, and the LW EDPs β and h ′ values are consistent with previous LF/VLF-derived estimates.

Computed tomography (CT) is an ill-posed problem. Reconstruction on unstructured grid reduces the computational cost and alleviates the ill-posedness by decreasing the dimension of the solution space. However, there was no systematic study on edge-preserving regularization methods for CT reconstruction on unstructured grid. In this work, we propose a novel regularization method for CT reconstruction on unstructured grid, such as triangular or tetrahedral meshes generated from the initial images reconstructed via analysis reconstruction method (e.g., filtered back-projection). The proposed regularization method is modeled as a three-term optimization problem, containing a weighted least square fidelity term motivated by the simultaneous algebraic reconstruction technique (SART). The related cost function contains two non-differentiable terms, which bring difficulty to the development of the fast solver. A fixed-point proximity algorithm with SART is developed for solving the related optimization problem, and accelerating the convergence. Finally, we compare the regularized CT reconstruction method to SART with different regularization methods. Numerical experiments demonstrated that the proposed regularization method on unstructured grid is effective to suppress noise and preserve edge features.

We developed a novel dual-energy (DE) virtual monochromatic (VM) very-deep super-resolution (VDSR) method with an unsharp masking reconstruction algorithm (DE-VM-VDSR) that uses projection data to improve the nodule contrast and reduce ripple artifacts during chest digital tomosynthesis (DT). For estimating the residual errors from high-resolution and multiscale VM images from the projection space, the DE-VM-VDSR algorithm employs a training network (mini-batch stochastic gradient-descent algorithm with momentum) and a hybrid super-resolution (SR) image [simultaneous algebraic reconstruction technique (SART) total-variation (TV) first-iterative shrinkage-thresholding algorithm (FISTA); SART-TV-FISTA] that involves subjective reconstruction with bilateral filtering (BF) [DE-VM-VDSR with BF]. DE-DT imaging was accomplished by pulsed X-ray exposures rapidly switched between low (60 kV, 37 projection) and high (120 kV, 37 projection) tube-potential kVp by employing a 40° swing angle. This was followed by comparison of images obtained employing the conventional polychromatic filtered backprojection (FBP), SART, SART-TV-FISTA, and DE-VM-SART-TV-FISTA algorithms. The improvements in contrast, ripple artifacts, and resolution were compared using the signal-difference-to-noise ratio (SDNR), Gumbel distribution of the largest variations, radial modulation transfer function (radial MTF) for a chest phantom with simulated ground-glass opacity (GGO) nodules, and noise power spectrum (NPS) for uniform water phantom. The novel DE-VM-VDSR with BF improved the overall performance in terms of SDNR (DE-VM-VDSR with BF: 0.1603, without BF: 0.1517; FBP: 0.0521; SART: 0.0645; SART-TV-FISTA: 0.0984; and DE-VM-SART-TV-FISTA: 0.1004), obtained a Gumbel distribution that yielded good images showing the type of simulated GGO nodules used in the chest phantom, and reduced the ripple artifacts. The NPS of DE-VM-VDSR with BF showed the lowest noise characteristics in the high-frequency region (~0.8 cycles/mm). The DE-VM-VDSR without BF yielded an improved resolution relative to that of the conventional reconstruction algorithms for radial MTF analysis (0.2-0.3 cycles/mm). Finally, based on the overall image quality, DE-VM-VDSR with BF improved the contrast and reduced the high-frequency ripple artifacts and noise.