A block iterative algorithm for tomographic reconstruction of ionospheric electron density

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.

Rapid system and hardware development of X-ray computed tomography (CT) technologies has been accompanied by equally exciting advances in image reconstruction algorithms. Of the two reconstruction algorithms, analytical and iterative, iterative reconstruction (IR) algorithms have become a clinically viable option in CT imaging. The first CT scanners in the early 1970s used IR algorithms, but lack of computation power prevented their clinical use. In 2009, the first IR algorithms became commercially available and replaced conventionally established analytical algorithms as filtered back projection. Since then, IR has played a vital role in the field of radiology. Although all available IR algorithms share the common mechanism of artifact reduction and/or potential for radiation dose reduction, the magnitude of these effects depends upon specific IR algorithms. IR reconstructs images by iteratively optimizing an objective function. The objective function typically consists of a data integrity term and a regularization term. Therefore, different regularization priors are used in IR algorithms. This paper will briefly look at the overall evolution of CT image reconstruction and the regularization priors used in IR algorithms. Finally, a discussion is presented based on the reality of various reconstruction methodologies at a glance to find the preferred one. Consequently, we will present anticipation towards future advancements in this domain.

Electrical capacitance tomography (ECT) is used to obtain information about the distribution of a mixture of dielectric materials inside a vessel or pipe. ECT has several advantages over other reconstruction algorithms and has found many applications in the industrial fields. However, there are some difficulties with image reconstruction in ECT: The relationship between the permittivity distribution and measured capacitance is nonlinear. And inverse problem is ill-posed so that the inverse solution is sensitive to measurement error. To cope with these difficulties iterative image reconstruction algorithms have been developed. In general, the iterative reconstruction algorithms in ECT have comparatively good-quality in reconstructed images but result in intensive computational burden. This paper presents the iterative image reconstruction algorithm for ECT that can enhance the speed of image reconstruction without degradation in the quality of reconstructed image. The main contribution of the proposed algorithm is new weighting matrices, which are obtained by the interpolation of the grouped electrical field centre lines (EFCLs). Extensive simulation results have demonstrated that proposed algorithm provides improved reconstruction performance in terms of computational time and image quality.

For tomography reconstruction, the iteration methods based on spare regularization have recently emerged and are proven effective especially in the situation that projection data is insufficient or noisy in low radiation dose. Because iterative tomography reconstruction algorithms have heavy computational demanding especially for clinical data sets and is far from being close to real-time reconstruction. So there is incentive to develop fast algorithms of the optimization problem. We present new accelerating iterative shrinkage algorithms for sparse-based tomography reconstruction, which base on the existing shrinkage algorithms and combine with traditional algebra methods, linear search method and preconditioning techniques to solve large dense linear systems. We give two different weighted matrixes as the preconditioner and get the different convergence speeds. From the experimental results it can be seen that using the sparsity in the transform domain as the regularization term can greatly improve the visual effect of the reconstructed images compared with corresponding algebraic algorithms, and the linear search method can obviously accelerates the converge rate.

The possibility of reconstructing two‐dimensional electron‐density profiles in the ionosphere with ionospheric tomography is significant. However, due to the nature of the imaging system, there are several resolution degradation parameters. In order to compensate for these degradation parameters, a priori information must be used. This article introduces the orthogonal decomposition algorithm for image reconstruction, which uses the a priori information to generate a set of orthogonal basis functions for the source domain. This algorithm consists of two simple steps: orthogonal decomposition and recombination. In the development of the algorithm, it is shown that the degradation parameters of the imaging system result in correlations among projections of orthogonal functions. Gram–Schmidt orthogonalization is used to compensate for these correlations, producing a matrix that measures the degradation of the system. Any set of basis functions can be used, and depending upon this choice, the nature of the algorithm varies greatly. Choosing the basis functions of the source domain to be the Fourier kernels produces an algorithm capable of isolating individual frequency components of individual projections. This particular choice of basis functions also results in an algorithm that strongly resembles the direct Fourier method, but without requiring the use of inverse Fourier transforms.

To investigate feasibility of applying deep learning image reconstruction (DLIR) algorithm in a low-kilovolt enhanced scan of the upper abdomen. A total of 64 patients (BMI<28) are selected for the enhanced upper abdomen scan and divided evenly into two groups. The tube voltages in Group A are 100kV in arterial phase and 80kV in venous phase, while tube voltages are 120kV during two phases in Group B. Image reconstruction algorithms used in Group A include the filtered back projection (FBP) algorithm, the adaptive statistical iterative reconstruction-Veo (ASIR-V 40% and 80%) algorithm, and the DLIR algorithm (DL-L, DL-M, DL-H). Image reconstruction algorithm used in Group B is ASIR-V40%. The different reconstruction algorithm images are used to measure the common hepatic artery, liver, renal cortex, erector spinae, and subcutaneous adipose in the arterial phase and the average CT value and standard deviation of the portal vein, liver, spleen, erector spinae, and subcutaneous adipose in the portal phase. The signal-to-noise ratio (SNR) is calculated, and the images are also scored subjectively. In Group A, noise in the aorta, liver, portal vein (the portal phase), spleen (the portal phase), renal cortex, retroperitoneal adipose, and muscle is significantly lower in both the DL-H and ASIR-V80% images, and the SNR is significantly higher than those in the remaining groups (P<0.05). The SNR of each tissue and organ in Group B is not significantly different from that in DL-M, DL-L, and ASIR-V40% in Group A (P>0.05). The subjective image quality scores in the DL-H and B groups are higher than those in the other groups, and the FBP group has significantly lower image quality than the remaining groups (P<0.05). For upper abdominal low-kilovolt enhanced scan data, the DLIR-H gear yields a more satisfactory image quality than the FBP and ASIR-V.

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at https://zenodo.org/record/7273314.

Low-dose computed tomography (CT) has attracted much attention in clinical applications since X-ray radiations can cause serious health risks to patients. Sparse-view CT imaging is one of the major ways to reduce radiation dose. However, if reconstructing the sparse-view CT images with conventional filtered backprojection (FBP) algorithm, image quality may be significantly degraded due to the severe streaking artifacts. Therefore, iterative sparse-view CT image reconstruction (IR) algorithms have been developed and utilized to improve image quality. One drawback of using the IR algorithms is they usually spend long computation time. Additionally, adjusting and optimizing the hyper-parameters that are needed during iteration procedures is also time-consuming, some- times may even depend on individual experience. These potential drawbacks strongly limit the wide applications of IR algorithms. Aiming at partially overcome such difficulties, in the present work, we propose a deep iterative reconstruction (DIR) framework to generalize the conventional IR algorithms by mapping them into the deep neural network (DNN) technique. With this proposed DIR algorithms, the prior term, the data fidelity term, and the hyper-parameters can all be represented and learned by network. By doing so, some generalized iterative models can be used to perform high quality sparse-view CT image reconstructions. Numerical experiments based on clinical patient data demonstrated that the proposed DIR algorithms can mitigate the streaking artifacts more effectively while well preserving the subtle structures.

To generate high-quality reconstructions of ionospheric electron density (IED), we propose an extended simultaneous algebraic reconstruction technique (ESART). The ESART method distributes the discrepancy between the actual GNSS TEC and the calculated TEC among the ray–voxels based on the contribution of voxels to GNSS TEC, rather than the ratio of the length of ray–voxel intersection to the sum of the lengths of all ray–voxel intersections, as is adopted by conventional methods. The feasibility of the ESART method for reconstructing the IED under different levels of geomagnetic activities is addressed. Additionally, a preliminary experiment is performed using the reconstructed IED profiles and comparing them with ionosonde measurements, which provide direct observations of electron density. The root mean square errors (RMSE) and absolute errors of the ESART method, the simultaneous algebraic reconstruction technique (SART) method, and the International Reference Ionosphere (IRI) 2016 model are calculated to evaluate the effectiveness of the proposed method. Compared to the conventional SART method of ionospheric tomography and the IRI-2016 model, the reconstructed IED profiles obtained using the ESART method are in better agreement with the electron density obtained from the ionosondes, especially for the peak electron densities (NmF2). In addition, a case study of an intense geomagnetic storm on 17–19 March 2015 shows that the spatial and temporal features of storm-related ionospheric disturbances can be more clearly depicted using the ESART method than with the SART method.

To characterize the noise and spatial resolution properties of a commercially available deep learning-based computed tomography (CT) reconstruction algorithm. Two phantom experiments were performed. The first used a multisized image quality phantom (Mercury v3.0, Duke University) imaged at five radiation dose levels (CTDIvol : 0.9, 1.2, 3.6, 7.0, and 22.3mGy) with a fixed tube current technique on a commercial CT scanner (GE Revolution CT). Images were reconstructed with conventional (FBP), iterative (GE ASiR-V), and deep learning-based (GE True Fidelity) reconstruction algorithms. Noise power spectrum (NPS), high-contrast (air-polyethylene interface), and intermediate-contrast (water-polyethylene interface) task transfer functions (TTF) were measured for each dose level and phantom size and summarized in terms of average noise frequency (fav ) and frequency at which the TTF was reduced to 50% (f50% ), respectively. The second experiment used a custom phantom with low-contrast rods and lung texture sections for the assessment of low-contrast TTF and noise spatial distribution. The phantom was imaged at five dose levels (CTDIvol : 1.0, 2.1, 3.0, 6.0, and 10.0mGy) with 20 repeated scans at each dose, and images reconstructed with the same reconstruction algorithms. The local noise stationarity was assessed by generating spatial noise maps from the ensemble of repeated images and computing a noise inhomogeneity index, , following AAPM TG233 methods. All measurements were compared among the algorithms. Compared to FBP, noise magnitude was reduced on average (± one standard deviation) by 74±6% and 68±4% for ASiR-V (at "100%" setting) and True Fidelity (at "High" setting), respectively. The noise texture from ASiR-V had substantially lower noise frequency content with 55±4% lower NPS fav compared to FBP while True Fidelity had only marginally different noise frequency content with 9±5% lower NPS fav compared to FBP. Both ASiR-V and True Fidelity demonstrated locally nonstationary noise in a lung texture background at all radiation dose levels, with higher noise near high-contrast edges of vessels and lower noise in uniform regions. At the 1.0mGy dose level values were 314% and 271% higher in ASiR-V and True Fidelity compared to FBP, respectively. High-contrast spatial resolution was similar between all algorithms for all dose levels and phantom sizes (<3% difference in TTF f50% ). Compared to FBP, low-contrast spatial resolution was lower for ASiR-V and True Fidelity with a reduction of TTF f50% of up to 42% and 36%, respectively. The deep learning-based CT reconstruction demonstrated a strong noise magnitude reduction compared to FBP while maintaining similar noise texture and high-contrast spatial resolution. However, the algorithm resulted in images with a locally nonstationary noise in lung textured backgrounds and had somewhat degraded low-contrast spatial resolution similar to what has been observed in currently available iterative reconstruction techniques.

To explore the application value of the reconstruction algorithm based on an iterative algorithm in the analysis of CT image and analyze the therapeutic effect of honey-fried Herba Ephedrae combined with Western medicine on acute exacerbation chronic obstructive pulmonary disease (AECOPD), a total of 96 AECOPD patients admitted to our hospital from January 2018 to December 2019 were selected as research subjects. According to a different treatment method, the subjects were divided into a control group (Ctrl group, conventional therapy) and an observation group (OG, conventional therapy + honey-fried Herba Ephedrae), with 48 in each group. The CT image algorithm was established based on the iterative algorithm, and the CT dose indexes of the reconstruction algorithm and the Filtered Back Projection (FBP) algorithm under the same conditions were compared ( P &lt; 0.05 ). After using CT to confirm the diagnosis of the subjects, the difference in indicators of forced expiratory volume in one second (FEV1), forced expiratory volume in one second to forced vital capacity ratio (FEV1%), and forced vital capacity (FVC), inflammatory factors of serum interleukin-8 (IL-8), serum interleukin-10 (IL-10), and tumor necrosis factor (TNF-α), the bronchial wall area, and the total treatment efficiency before and after different treatment was analyzed. The results suggested that the Computed Tomography Dose Index (CTDI) of iterative reconstruction (IR) algorithm when scanning different parts was higher than that of the FBP algorithm. The pulmonary function indexes and the expression of IL-8 and TNF-α in the OG were higher than those in the Ctrl group ( P &lt; 0.05 ); the bronchial wall area, bronchial wall area percentage, and IL-10 expression in the OG were all lower than those in the Ctrl group ( P &lt; 0.05 ). The effectiveness and improvement rates of the Ctrl group were 47.92% and 25%, respectively, significantly lower than those in the OG group, 56.25% and 31.25% ( P &lt; 0.05 ), and the total efficiency of the observation group was 87.5%, which was significantly higher than that in the Ctrl group (72.92%) ( P &lt; 0.05 ). In conclusion, based on the iterative algorithm, a CT reconstruction algorithm with better noise reduction performance was established, and the use of honey-fried Herba Ephedrae combined with Western medicine can improve the effective rate of treatment.

To obtain three-dimensional refractive index or density spatial distribution inside optically transparent living cells, it is necessary to combine computed tomography and interference microscopy. These methods use the oblique illumination and the sample viewing angles scanning for recording a number of the projections. A new application Linnik microscope reflected type for obtaining a high quality phase projections with spatially incoherent laser illumination is described. Phase-shifting technique for automated interferogram analysis is used. Interferometric computed- tomography Linnik laser microscope are fully automated integrated systems that incorporate CCD camera, frame grabber, computed operated PZT mirror as well as intelligible software for interferogram processing, projections preprocessing and tomographic reconstruction. Microscope measurement system and performance characterization are presented. There are some features in angle scanning, projections proceeding, and reconstruction for tomographic investigation of the phase samples that are placed near the mirror surface. For plane mirror the projections viewing angle range may be limited to 90-degree and the investigation object may be represented as a sum of the original object and its mirror reflection. The iterative algorithms for limited-angle tomographic reconstruction were used. Three-dimensional images of living blood cells (lymphocytes) were obtained.

The parallel chaotic iterative algorithms for image reconstruction by method of asynchronous chaotic relaxation with delay using the Monte-Carlo method are proposed. These algorithms are some generalization of parallel chaotic iteration methods considered by Bru, Elsner and Neumann. The accuracy and the rate of convergence of these algorithms are evaluated through their computer simulation with application to physical researches by tomographic reconstruction from incomplete data. Numerical calculations for solving this problem for some modeling objects, comparing evaluations of errors and the rate of convergence of these algorithms are presented.

To evaluate the image quality produced by six different iterative reconstruction (IR) algorithms in four CT systems in the setting of brain CT, using different radiation dose levels and iterative image optimisation levels. An image quality phantom, supplied with a bone mimicking annulus, was examined using four CT systems from different vendors and four radiation dose levels. Acquisitions were reconstructed using conventional filtered back-projection (FBP), three levels of statistical IR and, when available, a model-based IR algorithm. The evaluated image quality parameters were CT numbers, uniformity, noise, noise-power spectra, low-contrast resolution and spatial resolution. Compared with FBP, noise reduction was achieved by all six IR algorithms at all radiation dose levels, with further improvement seen at higher IR levels. Noise-power spectra revealed changes in noise distribution relative to the FBP for most statistical IR algorithms, especially the two model-based IR algorithms. Compared with FBP, variable degrees of improvements were seen in both objective and subjective low-contrast resolutions for all IR algorithms. Spatial resolution was improved with both model-based IR algorithms and one of the statistical IR algorithms. The four statistical IR algorithms evaluated in the study all improved the general image quality compared with FBP, with improvement seen for most or all evaluated quality criteria. Further improvement was achieved with one of the model-based IR algorithms. The six evaluated IR algorithms all improve the image quality in brain CT but show different strengths and weaknesses.

Application of hybrid regularization method for tomographic reconstruction of midlatitude ionospheric electron density