Статті в журналах: "Reconstruction à angles limités"

1

Schüle, T., C. Schnörr, J. Hornegger, and S. Weber. "A Linear Programming Approach to Limited Angle 3D Reconstruction from DSA Projections." Methods of Information in Medicine 43, no. 04 (2004): 320–26. http://dx.doi.org/10.1055/s-0038-1633875.

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Summary Objectives: We investigate the feasibility of binary-valued 3D tomographic reconstruction using only a small number of projections acquired over a limited range of angles. Methods: Regularization of this strongly ill-posed problem is achieved by (i) confining the reconstruction to binary vessel/non-vessel decisions, and (ii) by minimizing a global functional involving a smoothness prior. Results: Our approach successfully reconstructs volumetric vessel structures from three projections taken within 90°. The percentage of reconstructed voxels differing from ground truth is below 1%. Conclusion: We demonstrate that for particular applications – like Digital Subtraction Angiography – 3D reconstructions are possible where conventional methods must fail, due to a severely limited imaging geometry. This could play an important role for dose reduction and 3D reconstruction using non-conventional technical setups.

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2

Shen, Enxiang, Yuxin Wang, Jie Yuan, and Paul L. Carson. "Limited-Angle Computer Tomography with Truncated Projection Artifacts Removal." Applied Sciences 12, no. 22 (November 16, 2022): 11627. http://dx.doi.org/10.3390/app122211627.

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Breast cancer is the most common cancer in women and the second most common cancer in the world. Digital breast tomosynthesis (DBT) is an effective medical imaging method. It can reduce the overlap of breast tissue in reconstructed images, which is beneficial to the early detection of breast cancer. DBT uses projection data from a limited range of angles and the simultaneous algebraic reconstruction technique (SART) based reconstruction method. Since the detector’s field of view (FOV) is limited, the updates of the large projection angles in SART cannot include all the voxels of the imaging target, which causes truncated projection artifacts (TPA) at the edges of the image. In this work, we use the images reconstructed by SART to perform re-projection on the virtually expanded detector panel and use a gradient calculation method to compensate for missing projection data to ensure that each update can include all the voxels. Experiments on simulation and human breast demonstrated that TPA can be effectively reduced while retaining the detailed tissue structure, thus improving the image quality at the border and recovering the obscured structural information. It might provide a better imaging result for the consequential clinical diagnosis.

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3

Krimmel, S., J. Baumann, Z. Kiss, A. Kuba, A. Nagy, and J. Stephan. "Discrete tomography for reconstruction from limited view angles in non-destructive testing." Electronic Notes in Discrete Mathematics 20 (July 2005): 455–74. http://dx.doi.org/10.1016/j.endm.2005.05.078.

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4

Huang, Yixing, Shengxiang Wang, Yong Guan, and Andreas Maier. "Limited angle tomography for transmission X-ray microscopy using deep learning." Journal of Synchrotron Radiation 27, no. 2 (February 13, 2020): 477–85. http://dx.doi.org/10.1107/s160057752000017x.

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In transmission X-ray microscopy (TXM) systems, the rotation of a scanned sample might be restricted to a limited angular range to avoid collision with other system parts or high attenuation at certain tilting angles. Image reconstruction from such limited angle data suffers from artifacts because of missing data. In this work, deep learning is applied to limited angle reconstruction in TXMs for the first time. With the challenge to obtain sufficient real data for training, training a deep neural network from synthetic data is investigated. In particular, U-Net, the state-of-the-art neural network in biomedical imaging, is trained from synthetic ellipsoid data and multi-category data to reduce artifacts in filtered back-projection (FBP) reconstruction images. The proposed method is evaluated on synthetic data and real scanned chlorella data in 100° limited angle tomography. For synthetic test data, U-Net significantly reduces the root-mean-square error (RMSE) from 2.55 × 10−3 µm−1 in the FBP reconstruction to 1.21 × 10−3 µm−1 in the U-Net reconstruction and also improves the structural similarity (SSIM) index from 0.625 to 0.920. With penalized weighted least-square denoising of measured projections, the RMSE and SSIM are further improved to 1.16 × 10−3 µm−1 and 0.932, respectively. For real test data, the proposed method remarkably improves the 3D visualization of the subcellular structures in the chlorella cell, which indicates its important value for nanoscale imaging in biology, nanoscience and materials science.

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5

Gong, Changcheng, Li Zeng, Yumeng Guo, Chengxiang Wang, and Shengmiao Wang. "Multiple limited-angles computed tomography reconstruction based on multi-direction total variation minimization." Review of Scientific Instruments 89, no. 12 (December 2018): 125121. http://dx.doi.org/10.1063/1.5030673.

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6

Goy, Alexandre, Girish Rughoobur, Shuai Li, Kwabena Arthur, Akintunde I. Akinwande, and George Barbastathis. "High-resolution limited-angle phase tomography of dense layered objects using deep neural networks." Proceedings of the National Academy of Sciences 116, no. 40 (September 16, 2019): 19848–56. http://dx.doi.org/10.1073/pnas.1821378116.

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We present a machine learning-based method for tomographic reconstruction of dense layered objects, with range of projection angles limited to ±10○. Whereas previous approaches to phase tomography generally require 2 steps, first to retrieve phase projections from intensity projections and then to perform tomographic reconstruction on the retrieved phase projections, in our work a physics-informed preprocessor followed by a deep neural network (DNN) conduct the 3-dimensional reconstruction directly from the intensity projections. We demonstrate this single-step method experimentally in the visible optical domain on a scaled-up integrated circuit phantom. We show that even under conditions of highly attenuated photon fluxes a DNN trained only on synthetic data can be used to successfully reconstruct physical samples disjoint from the synthetic training set. Thus, the need for producing a large number of physical examples for training is ameliorated. The method is generally applicable to tomography with electromagnetic or other types of radiation at all bands.

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7

Dang Nguyen, Ngoc An, Hoang Nhut Huynh, Trung Nghia Tran, and Koichi Shimizu. "Reconstructing 3D De-Blurred Structures from Limited Angles of View through Turbid Media Using Deep Learning." Applied Sciences 14, no. 5 (February 20, 2024): 1689. http://dx.doi.org/10.3390/app14051689.

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Recent studies in transillumination imaging for developing an optical computed tomography device for small animal and human body parts have used deep learning networks to suppress the scattering effect, estimate depth information of light-absorbing structures, and reconstruct three-dimensional images of de-blurred structures. However, they still have limitations, such as knowing the information of the structure in advance, only processing simple structures, limited effectiveness for structures with a depth of about 15 mm, and the need to use separated deep learning networks for de-blurring and estimating information. Furthermore, the current technique cannot handle multiple structures distributed at different depths next to each other in the same image. To overcome the mentioned limitations in transillumination imaging, this study proposed a pixel-by-pixel scanning technique in combination with deep learning networks (Attention Res-UNet for scattering suppression and DenseNet-169 for depth estimation) to estimate the existence of each pixel and the relative structural depth information. The efficacy of the proposed method was evaluated through experiments that involved a complex model within a tissue-equivalent phantom and a mouse, achieving a reconstruction error of 2.18% compared to the dimensions of the ground truth when using the fully convolutional network. Furthermore, we could use the depth matrix obtained from the convolutional neural network (DenseNet-169) to reconstruct the absorbing structures using a binary thresholding method, which produced a reconstruction error of 6.82%. Therefore, only one convolutional neural network (DenseNet-169) must be used for depth estimation and explicit image reconstruction. Therefore, it reduces time and computational resources. With depth information at each pixel, reconstruction of 3D image of the de-blurred structures could be performed even from a single blurred image. These results confirm the feasibility and robustness of the proposed pixel-by-pixel scanning technique to restore the internal structure of the body, including intricate networks such as blood vessels or abnormal tissues.

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8

Ohler, M., M. Sanchez del Rio, A. Tuffanelli, M. Gambaccini, A. Taibi, A. Fantini, and G. Pareschi. "X-ray topographic determination of the granular structure in a graphite mosaic crystal: a three-dimensional reconstruction." Journal of Applied Crystallography 33, no. 4 (August 1, 2000): 1023–30. http://dx.doi.org/10.1107/s0021889800005975.

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Section topographs recorded at different spatial locations and at different rocking angles of a highly oriented pyrolytic graphite (HOPG) crystal allow three-dimensional maps of the local angular-dependent scattering power to be obtained. This is performed with a direct reconstruction from the intensity distribution on such topographs. The maps allow the extraction of information on local structural parameters such as size, form and internal mosaic spread of crystalline domains. This data analysis leads to a new method for the characterization of mosaic crystals. Perspectives and limits of applicability of this method are discussed.

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9

Van Veen, Dave, Jesús G. Galaz-Montoya, Liyue Shen, Philip Baldwin, Akshay S. Chaudhari, Dmitry Lyumkis, Michael F. Schmid, Wah Chiu, and John Pauly. "Missing Wedge Completion via Unsupervised Learning with Coordinate Networks." International Journal of Molecular Sciences 25, no. 10 (May 17, 2024): 5473. http://dx.doi.org/10.3390/ijms25105473.

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Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3–20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.

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10

Hui, CheukKai, Daniel Robertson, and Sam Beddar. "3D reconstruction of scintillation light emission from proton pencil beams using limited viewing angles—a simulation study." Physics in Medicine and Biology 59, no. 16 (July 23, 2014): 4477–92. http://dx.doi.org/10.1088/0031-9155/59/16/4477.

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11

Columbano, Laura, Lennart H. Stieglitz, Karsten H. Wrede, Amir Samii, Madjid Samii, and Wolf O. Luedemann. "Anatomic Study of the Quadrigeminal Cistern in Patients With 3-Dimensional Magnetic Resonance Cisternography." Neurosurgery 66, no. 5 (May 1, 2010): 991–98. http://dx.doi.org/10.1227/01.neu.0000368384.06288.4c.

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Abstract OBJECT The aim of this study was to demonstrate the anatomy of the quadrigeminal cistern, define the anatomic landmarks, and measure the extension of the cistern in the living by using magnetic resonance (MR) cisternography with 3-dimensional reconstruction. METHODS The quadrigeminal cistern was examined in 38 patients. We focused on measurements of the superior, posterior, and lateral limits; the anterior and posterior maximal rostrocaudal diameter; the distance between the right and left superior colliculus and the right and left inferior colliculus; and the angle between the quadrigeminal plate and pineal gland. RESULTS The highest variability was observed for the posterior rostrocaudal diameter with a standard deviation of 3.1 and a range from 8 to 21.1 mm followed by the anterior-posterior diameter with a standard deviation of 2.8 and a range from 6.4 to 16.5 mm. In all cases the distance between the right and left superior colliculus (13.3 ± 1.8 mm; mean ± SD) was longer than the distance between the right and left inferior colliculus (11.4 ± 1.3 mm; mean ± SD). We classified 2 types of cisterns: closed cisterns with angles between the quadrigeminal plate and the pineal gland ranging from 39° to 63° and open cisterns with angles ranging from 63° to 76°. The analysis of variability by age and sex showed no significant differences. CONCLUSIONS The MR cisternography with 3-dimensional reconstruction was a simple and noninvasive tool providing detailed anatomic information in the living. It allowed measurement of the high variability of morphology of the quadrigeminal cistern. We defined the lateral landmarks and identified the lateral limit of the cistern. We classified the different shapes of the quadrigeminal cistern as open or closed cisterns. This can be helpful in the choice of the surgical approach to the lesions arising in this area.

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12

Skoulakis, Alexandros, Evaggelos Kaselouris, Antonis Kavroulakis, Christos Karvounis, Ioannis Fitilis, John Chatzakis, Vasilis Dimitriou, Nektarios A. Papadogiannis, and Michael Tatarakis. "Characterization of an X-ray Source Generated by a Portable Low-Current X-Pinch." Applied Sciences 11, no. 23 (November 25, 2021): 11173. http://dx.doi.org/10.3390/app112311173.

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An X-pinch scheme of a low-current generator (45 kA, 50 ns rise time) is characterized as a potential efficient source of soft X-rays. The X-pinch target consists of wires of 5 μm in diameter—made from either tungsten (W) or gold (Au)-plated W—loaded at two angles of 55° and 98° between the crossed wires. Time-resolved soft X-ray emission measurements are performed to provide a secure correlation with the optical probing results. A reconstruction of the actual photodiode current profile procedure was adopted, capable of overcoming the limits of the slow rising and falling times due to the “slow” response of the diodes and the noise. The pure and Au-plated W deliver an average X-ray yield, which depends only on the angle of the crossed wires, and is measured to be ~50 mJ and ~70 mJ for the 98° and 55° crossed wire angles, respectively. An additional experimental setup was developed to characterize the X-pinch as a source of X-rays with energy higher than ~6 keV, via time-integrated measurements. The X-ray emission spectrum was found to have an upper limit at 13 keV for the Au-plated W configuration at 55°. The portable tabletop X-pinch proved to be ideal for use in X-ray radiography applications, such as the detection of interior defects in biological samples.

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13

Kulikajevas, Audrius, Rytis Maskeliūnas, Robertas Damaševičius, and Marta Wlodarczyk-Sielicka. "Auto-Refining Reconstruction Algorithm for Recreation of Limited Angle Humanoid Depth Data." Sensors 21, no. 11 (May 26, 2021): 3702. http://dx.doi.org/10.3390/s21113702.

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With the majority of research, in relation to 3D object reconstruction, focusing on single static synthetic object reconstruction, there is a need for a method capable of reconstructing morphing objects in dynamic scenes without external influence. However, such research requires a time-consuming creation of real world object ground truths. To solve this, we propose a novel three-staged deep adversarial neural network architecture capable of denoising and refining real-world depth sensor input for full human body posture reconstruction. The proposed network has achieved Earth Mover and Chamfer distances of 0.059 and 0.079 on synthetic datasets, respectively, which indicates on-par experimental results with other approaches, in addition to the ability of reconstructing from maskless real world depth frames. Additional visual inspection to the reconstructed pointclouds has shown that the suggested approach manages to deal with the majority of the real world depth sensor noise, with the exception of large deformities to the depth field.

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14

Sobau, Christian, Alexander Zimmerer, Max Fallscheer, and Andree Ellermann. "Radiographic analysis of Re-Ruptures of reconstructed ACLs - Evaluation of tunnel position as a possible cause of Failure." Orthopaedic Journal of Sports Medicine 5, no. 4_suppl4 (April 1, 2017): 2325967117S0014. http://dx.doi.org/10.1177/2325967117s00140.

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Objectives: Previous studies detected femoral and / or tibial tunnel malpositioning as possible causes for the failure of an anterior cruciate ligament reconstruction. We investigated various radiological angles and criterias for ACL revision surgery to find possible causes for the failure of the primary reconstructed ACLs based on digital X-ray images. Materials and Methods: 529 ACL revisions after previous reconstruction were carried out between 1993 and 2013, of which we were able to include 100 patients with digital radiographs in our study. We investigated the angles of the femoral and tibial tunnel position in the coronal and sagittal plane. Furthermore we analyzed the entry point on the femur in accordance with the quadrant method described by Bernard and Hertel. We divided into: A) adequate trauma (n = 87) and non-trauma group (n = 13); B) Hamstring (n = 76) and Patella-BTB group (n = 24); C) transtibial (n = 83) and anteromedial group (n = 17). In addition we built subgroups B1/C1 adequate re-trauma or B2/C2 no adequate trauma to analyze whether there were differences in these groups. Results: The trauma group differed significantly from the non-trauma group in the measured angle of the tibial tunnel in the ap radiograph (trauma group 28.4°, non-trauma group 22.67°; p = 0.013). The Hamstring group differed significantly from the BTB group in the measured inclination angle of the femoral tunnel in the ap radiograph (HS group 54.86°, BTB group 62.78°; p = 0.015). There was also a significant difference concerning the tibial tunnel in the ap radiograph (HS group 29.56°, BTB group 21.63°; p = 0.0001). Comparing the two groups for the femoral tunnel placement-techniques we could find significant differences in the femoral ap-radiographs (inclination angle: TT = 59.04°, AM = 45.64°; p = 0.0001). The analysis of the 4 subgroups revealed differences in the tibial ap images: The BTB trauma group had an average of 23.56° relative to the BTB non-trauma group of 16.91° (p=0.013). The HS groups among themselves did not differ significantly, but the HS non-trauma group had a significantly higher angle with 29.38° to 16.91° in the BTB non-trauma group (p = 0.0003). In addition there was a significant difference when comparing the transtibial trauma group with the transtibial non trauma group (TT trauma = 27.66°, TT non trauma = 21.15°; p = 0.017) Conclusion: Overall we could only find a few significant differences in the measured angles and only a few deviations from the values described within the literature. Therefore a real trauma was necessary to rupture the reconstructed ACL in 87%. In 13% we could find a possible cause within the tibial tunnel: the steeper the tibial tunnel was, less trauma was necessary for failure, especially when using the transtibial drilling method or Patella-BTB grafts. However the small sample size limits the results therefore further studies are necessary.

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15

Vishnyakov, G. N., and O. I. Mashevskaya. "Investigation of the Precision of an Algebraic Algorithm for the Reconstruction of Tomograms from Projections Given in a Limited Range of Angles." Measurement Techniques 48, no. 8 (August 2005): 784–88. http://dx.doi.org/10.1007/s11018-005-0221-y.

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16

Song, Liyao, and Haiwei Li. "Multi-Level Spectral Attention Network for Hyperspectral BRDF Reconstruction from Multi-Angle Multi-Spectral Images." Remote Sensing 17, no. 5 (February 28, 2025): 863. https://doi.org/10.3390/rs17050863.

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With the rapid development of hyperspectral applications using unmanned aerial vehicles (UAVs), the traditional assumption that ground objects exhibit Lambertian reflectance is no longer sufficient to meet the high-precision requirements for quantitative inversion and airborne hyperspectral data applications. Therefore, it is necessary to establish a hyperspectral bidirectional reflectance distribution function (BRDF) model suitable for the area of imaging. However, obtaining multi-angle information from UAV push-broom hyperspectral data is difficult. Achieving uniform push-broom imaging and flexibly acquiring multi-angle data is challenging due to spatial distortions, particularly under heightened roll or pitch angles, and the need for multiple flights; this extends acquisition time and exacerbates uneven illumination, introducing errors in BRDF model construction. To address these issues, we propose leveraging the advantages of multi-spectral cameras, such as their compact size, lightweight design, and high signal-to-noise ratio (SNR) to reconstruct hyperspectral multi-angle data. This approach enhances spectral resolution and the number of bands while mitigating spatial distortions and effectively captures the multi-angle characteristics of ground objects. In this study, we collected UAV hyperspectral multi-angle data, corresponding illumination information, and atmospheric parameter data, which can solve the problem of existing BRDF modeling not considering outdoor ambient illumination changes, as this limits modeling accuracy. Based on this dataset, we propose an improved Walthall model, considering illumination variation. Then, the radiance consistency of BRDF multi-angle data is effectively optimized, the error caused by illumination variation in BRDF modeling is reduced, and the accuracy of BRDF modeling is improved. In addition, we adopted Transformer for spectral reconstruction, increased the number of bands on the basis of spectral dimension enhancement, and conducted BRDF modeling based on the spectral reconstruction results. For the multi-level Transformer spectral dimension enhancement algorithm, we added spectral response loss constraints to improve BRDF accuracy. In order to evaluate BRDF modeling and quantitative application potential from the reconstruction results, we conducted comparison and ablation experiments. Finally, we solved the problem of difficulty in obtaining multi-angle information due to the limitation of hyperspectral imaging equipment, and we provide a new solution for obtaining multi-angle features of objects with higher spectral resolution using low-cost imaging equipment.

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17

Di Jianglei, 邸江磊, 林俊成 Lin Juncheng, 钟丽云 Zhong Liyun, 钱克矛 Qian Kemao та 秦玉文 Qin Yuwen. "基于深度学习的稀疏或有限角度CT重建方法研究综述". Laser & Optoelectronics Progress 60, № 8 (2023): 0811002. http://dx.doi.org/10.3788/lop230488.

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18

Rothkamm, Oliver, Johannes Gürtler, Jürgen Czarske, and Robert Kuschmierz. "Dense U-Net for Limited Angle Tomography of Sound Pressure Fields." Applied Sciences 11, no. 10 (May 17, 2021): 4570. http://dx.doi.org/10.3390/app11104570.

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Tomographic reconstruction allows for the recovery of 3D information from 2D projection data. This commonly requires a full angular scan of the specimen. Angular restrictions that exist, especially in technical processes, result in reconstruction artifacts and unknown systematic measurement errors. We investigate the use of neural networks for extrapolating the missing projection data from holographic sound pressure measurements. A bias flow liner was studied for active sound dampening in aviation. We employed a dense U-Net trained on synthetic data and compared reconstructions of simulated and measured data with and without extrapolation. In both cases, the neural network based approach decreases the mean and maximum measurement deviations by a factor of two. These findings can enable quantitative measurements in other applications suffering from limited angular access as well.

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Yuan Wei, 袁伟, 席雅睿 Xi Yarui, 谭川东 Tan Chuandong, 刘川江 Liu Chuanjiang, 朱国荣 Zhu Guorong та 刘丰林 Liu Fenglin. "基于Swin-Transformer迭代展开的有限角CT图像重建用于PTCT成像". Acta Optica Sinica 44, № 8 (2024): 0834001. http://dx.doi.org/10.3788/aos231823.

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20

Jaffe, J. S. "Limited angle reconstruction using stabilized algorithms." IEEE Transactions on Medical Imaging 9, no. 3 (1990): 338–44. http://dx.doi.org/10.1109/42.57772.

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21

Krisch, Isabell, Jörn Ungermann, Peter Preusse, Erik Kretschmer, and Martin Riese. "Limited angle tomography of mesoscale gravity waves by the infrared limb-sounder GLORIA." Atmospheric Measurement Techniques 11, no. 7 (July 23, 2018): 4327–44. http://dx.doi.org/10.5194/amt-11-4327-2018.

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Abstract. Three-dimensional measurements of gravity waves are required in order to quantify their direction-resolved momentum fluxes and obtain a better understanding of their propagation characteristics. Such 3-D measurements of gravity waves in the lowermost stratosphere have been provided by the airborne Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) using full angle tomography. Closed flight patterns of sufficient size are needed to acquire the full set of angular measurements for full angle tomography. These take about 2 h and are not feasible everywhere due to scientific reasons or air traffic control restrictions. Hence, this paper investigates the usability of limited angle tomography for gravity wave research based on synthetic observations. Limited angle tomography uses only a limited set of angles for tomographic reconstruction and can be applied to linear flight patterns. A synthetic end-to-end simulation has been performed to investigate the sensitivity of limited angle tomography to gravity waves with different wavelengths and orientations with respect to the flight path. For waves with wavefronts roughly perpendicular to the flight path, limited angle tomography and full angle tomography can derive wave parameters like wavelength, amplitude, and wave orientation with similar accuracy. For waves with a horizontal wavelength above 200 km and vertical wavelength above 3 km, the wavelengths can be retrieved with less than 10 % error, the amplitude with less than 20 % error, and the horizontal wave direction with an error below 10∘. This is confirmed by a comparison of results obtained from full angle tomography and limited angle tomography for real measurements taken on 25 January 2016 over Iceland. The reproduction quality of gravity wave parameters with limited angle tomography, however, depends strongly on the orientation of the waves with respect to the flight path. Thus, full angle tomography might be preferable in cases in which the orientation of the wave cannot be predicted or waves with different orientations exist in the same volume and thus the flight path cannot be adjusted accordingly. Also, for low-amplitude waves and short-scale waves full angle tomography has advantages due to its slightly higher resolution and accuracy.

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Zhang, Lingli, Li Zeng, Chengxiang Wang, and Yumeng Guo. "A non-smooth and non-convex regularization method for limited-angle CT image reconstruction." Journal of Inverse and Ill-posed Problems 26, no. 6 (December 1, 2018): 799–820. http://dx.doi.org/10.1515/jiip-2017-0042.

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Abstract Restricted by the practical applications and radiation exposure of computed tomography (CT), the obtained projection data is usually incomplete, which may lead to a limited-angle reconstruction problem. Whereas reconstructing an object from limited-angle projection views is a challenging and ill-posed inverse problem. Fortunately, the regularization methods offer an effective way to deal with that. Recently, several researchers are absorbed in {\ell_{1}} regularization to address such problem, but it has some problems for suppressing the limited-angle slope artifacts around edges due to incomplete projection data. In this paper, in order to surmount the ill-posedness, a non-smooth and non-convex method that is based on {\ell_{0}} and {\ell_{1}} regularization is presented to better deal with the limited-angle problem. Firstly, the splitting technique is utilized to deal with the presented approach called LWPC-ST-IHT. Afterwards, some propositions and convergence analysis of the presented approach are established. Numerical implementations show that our approach is more capable of suppressing the slope artifacts compared with the classical and state of the art iterative reconstruction algorithms.

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23

Liang, Zhiting, Yong Guan, Gang Liu, Xiangyu Chen, Fahu Li, Pengfei Guo, and Yangchao Tian. "A modified discrete algebraic reconstruction technique for multiple grey image reconstruction for limited angle range tomography." Journal of Synchrotron Radiation 23, no. 2 (February 20, 2016): 606–16. http://dx.doi.org/10.1107/s1600577516000564.

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The `missing wedge', which is due to a restricted rotation range, is a major challenge for quantitative analysis of an object using tomography. With prior knowledge of the grey levels, the discrete algebraic reconstruction technique (DART) is able to reconstruct objects accurately with projections in a limited angle range. However, the quality of the reconstructions declines as the number of grey levels increases. In this paper, a modified DART (MDART) was proposed, in which each independent region of homogeneous material was chosen as a research object, instead of the grey values. The grey values of each discrete region were estimated according to the solution of the linear projection equations. The iterative process of boundary pixels updating and correcting the grey values of each region was executed alternately. Simulation experiments of binary phantoms as well as multiple grey phantoms show that MDART is capable of achieving high-quality reconstructions with projections in a limited angle range. The interesting advancement of MDART is that neither prior knowledge of the grey values nor the number of grey levels is necessary.

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Möller, Gregor, and Daniel Landskron. "Atmospheric bending effects in GNSS tomography." Atmospheric Measurement Techniques 12, no. 1 (January 3, 2019): 23–34. http://dx.doi.org/10.5194/amt-12-23-2019.

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Abstract. In Global Navigation Satellite System (GNSS) tomography, precise information about the tropospheric water vapor distribution is derived from integral measurements like ground-based GNSS slant wet delays (SWDs). Therefore, the functional relation between observations and unknowns, i.e., the signal paths through the atmosphere, have to be accurately known for each station–satellite pair involved. For GNSS signals observed above a 15∘ elevation angle, the signal path is well approximated by a straight line. However, since electromagnetic waves are prone to atmospheric bending effects, this assumption is not sufficient anymore for lower elevation angles. Thus, in the following, a mixed 2-D piecewise linear ray-tracing approach is introduced and possible error sources in the reconstruction of the bended signal paths are analyzed in more detail. Especially if low elevation observations are considered, unmodeled bending effects can introduce a systematic error of up to 10–20 ppm, on average 1–2 ppm, into the tomography solution. Thereby, not only the ray-tracing method but also the quality of the a priori field can have a significant impact on the reconstructed signal paths, if not reduced by iterative processing. In order to keep the processing time within acceptable limits, a bending model is applied for the upper part of the neutral atmosphere. It helps to reduce the number of processing steps by up to 85 % without significant degradation in accuracy. Therefore, the developed mixed ray-tracing approach allows not only for the correct treatment of low elevation observations but is also fast and applicable for near-real-time applications.

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25

Reeds, J. A., and L. A. Shepp. "Limited Angle Reconstruction in Tomography via Squashing." IEEE Transactions on Medical Imaging 6, no. 2 (June 1987): 89–97. http://dx.doi.org/10.1109/tmi.1987.4307808.

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26

Liu, Jianhong, Yong Guan, Liang Chen, Haobo Bai, Wenbin Wei, Yangchao Tian, and Gang Liu. "Locating the 'missing wedge' artifacts from limited-angle CT reconstruction." Microscopy and Microanalysis 24, S2 (August 2018): 140–41. http://dx.doi.org/10.1017/s1431927618013089.

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Abstract:'Missing wedge' problem exists in some kind of CT imaging situations, such as electron microscopy, x-ray nano-CT image, etc. Method such as iterative reconstruction algorithms, total variation based method were applied to improve the reconstruction quality, but the 'missing wedge' artifacts are still inevitable. In this paper, a method based on image processing technique was proposed to locate the 'missing wedge' artifacts in CT reconstruction. The result showed good performance on locating the artifacts, which also showed the potential in CT reconstruction and image analysis in nano-CT.

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27

Lu, Fan, Haruka Inamoto, Shuto Takeishi, Shingo Tamaki, Sachie Kusaka, and Isao Murata. "Development of a New Image Reconstruction Method Using Bayesian Estimation with Limited View-Angle Projection Data for BNCT-SPECT." Applied Sciences 14, no. 20 (October 15, 2024): 9411. http://dx.doi.org/10.3390/app14209411.

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Boron Neutron Capture Therapy (BNCT) is an emerging radiation treatment for cancer, and its challenges are being explored. Systems capable of capturing real-time observations of this treatment’s effectiveness, particularly BNCT-SPECT methods that measure gamma rays emitted instantaneously from outside the body during nuclear reactions and that reconstruct images using Single Photon Emission Computed Tomography (SPECT) techniques, remain unavailable. BNCT-SPECT development is hindered by two main factors, the first being the projection angle. Unlike conventional SPECT, the projection angle range which is achievable by rotating a detector array cannot exceed approximately 90 degrees. Consequently, Fourier-based image reconstruction methods, requiring projections from at least 180 degrees, do not apply to BNCT-SPECT. The second limitation is the measurement time. Given these challenges, we developed a new sequential approximation image reconstruction method using Bayesian estimation, which is effective under the stringent BNCT-SPECT conditions. We also compared the proposed method with the existing Maximum Likelihood-Expectation Maximization (ML-EM) image reconstruction method. Numerical experiments were conducted by obtaining BNCT-SPECT projection data from true images and reconstructing images using both the proposed and ML-EM methods from the resulting sinograms. Performance comparisons were conducted using a dedicated program applying Bayesian estimation and this showed promise as a new image reconstruction method useful under BNCT-SPECT conditions.

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28

Hoyle, C., M. Sutcliffe, P. Charlton, S. Mosey, and I. Cooper. "Limited-angle ultrasonic tomography back-projection imaging." Insight - Non-Destructive Testing and Condition Monitoring 63, no. 1 (January 1, 2021): 20–28. http://dx.doi.org/10.1784/insi.2021.63.1.20.

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Ultrasonic inspection of through-transmission is limited due to the inability to obtain defect depth information. Loss of signal is used as the only indicator, providing lateral defect information. This is often a problem in ultrasonic inspection. Radiographic acquisition techniques, where the X-ray source acts as the transmitter and the detector as the receiver, are conceptionally similar to ultrasonic through-transmission. In the latter, the tomography back-projection method is used to reconstruct images of an object that has been subjected to a minimum of 180° of rotation, to allow for full coverage of the item. In this paper, a novel approach based on back-projection is presented to improve image resolution and defect detectability. Two ultrasonic transducers in through-transmission configuration are utilised to capture data for image processing. The rotation of the transmitter and receiver is not possible in this set-up and, therefore, the reconstruction relies on the artificial generation of a limited rotation. Two probes are aligned either side of the material and are used to gather the ultrasonic signals. These signals are processed before the reconstruction algorithm is applied to them. Various processing and imaging reconstruction algorithms are explored, building on the basic back-projection method to obtain images that are better focused. This technique could be used within materials where there are high attenuation levels and, therefore, traditional pulse-echo is not feasible.

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29

Wang, Chengxiang, Li Zeng, Lingli Zhang, Yumeng Guo, and Wei Yu. "An adaptive iteration reconstruction method for limited-angle CT image reconstruction." Journal of Inverse and Ill-posed Problems 26, no. 6 (December 1, 2018): 771–87. http://dx.doi.org/10.1515/jiip-2017-0034.

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Abstract The limited-angle computed tomography (CT) reconstruction problem is an ill-posed inverse problem, and the parameter selection for limited-angle CT iteration reconstruction is a difficult issue in practical application. In this paper, to alleviate the instability of limited-angle CT reconstruction problem and automatize the reconstruction process, we propose an adaptive iteration reconstruction method that the regularization parameter is chosen adaptively via the plot of the normalized wavelet coefficients fitting residual versus that the {\ell_{0}} regularization part. The experimental results show that the reconstructed images using the method with adapted regularization parameter are almost as good as that using the non-adapted parameter method in terms of visual inspection, in addition, our method has an advantage in adaptively choosing the regularization parameter.

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30

Guo, Jingyu, Hongliang Qi, Yuan Xu, Zijia Chen, Shulong Li, and Linghong Zhou. "Iterative Image Reconstruction for Limited-Angle CT Using Optimized Initial Image." Computational and Mathematical Methods in Medicine 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/5836410.

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Limited-angle computed tomography (CT) has great impact in some clinical applications. Existing iterative reconstruction algorithms could not reconstruct high-quality images, leading to severe artifacts nearby edges. Optimal selection of initial image would influence the iterative reconstruction performance but has not been studied deeply yet. In this work, we proposed to generate optimized initial image followed by total variation (TV) based iterative reconstruction considering the feature of image symmetry. The simulated data and real data reconstruction results indicate that the proposed method effectively removes the artifacts nearby edges.

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31

Wang, Jiaxi, Li Zeng, Chengxiang Wang, and Yumeng Guo. "ADMM-based deep reconstruction for limited-angle CT." Physics in Medicine & Biology 64, no. 11 (May 29, 2019): 115011. http://dx.doi.org/10.1088/1361-6560/ab1aba.

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32

Tomitani, T., and M. Hirasawa. "Image reconstruction from limited angle Compton camera data." Physics in Medicine and Biology 47, no. 12 (June 6, 2002): 2129–45. http://dx.doi.org/10.1088/0031-9155/47/12/309.

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33

Qu, Gang-rong, and Ming Jiang. "Landweber iterative methods for angle-limited image reconstruction." Acta Mathematicae Applicatae Sinica, English Series 25, no. 2 (March 17, 2009): 327–34. http://dx.doi.org/10.1007/s10255-008-8132-8.

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34

BaniOdeh, Doaa, and Mohammad Hjouj. "An advanced approach to reconstruct CT images from limited-angle projections, reducing radiation dose and tube load." Journal of Physics: Conference Series 2701, no. 1 (February 1, 2024): 012027. http://dx.doi.org/10.1088/1742-6596/2701/1/012027.

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Abstract The process of reconstructing CT scan images from limited angle projections is critical and requires strict adherence to the ALARA principle. This principle is designed to minimize radiation exposure while maintaining image quality. Our study utilized filter back-projection (FBP) and algebraic iterative reconstruction (IR) algorithms to reconstruct brain CT images from 200 projection lines and a 100 × 100 matrix size. By combining the results of a MATLAB function with the insights of a radiologist, we can produce high-quality images that decrease radiation dose and tube load. Our findings reveal that the algebraic method is superior to the filter back-projection in preserving image quality when utilizing limited-angle projections.

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35

Wang, Ruonan, Zhaocheng Wang, Yu Chen, Hailong Kang, Feng Luo, and Yingxi Liu. "Target Recognition in SAR Images Using Complex-Valued Network Guided with Sub-Aperture Decomposition." Remote Sensing 15, no. 16 (August 14, 2023): 4031. http://dx.doi.org/10.3390/rs15164031.

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Synthetic aperture radar (SAR) images have special physical scattering characteristics owing to their unique imaging mechanism. Traditional deep learning algorithms usually extract features from real-valued SAR images in a purely data-driven manner, which may ignore some important physical scattering characteristics and sacrifice some useful target information in SAR images. This undoubtedly limits the improvement in performance for SAR target recognition. To take full advantage of the physical information contained in SAR images, a complex-valued network guided with sub-aperture decomposition (CGS-Net) for SAR target recognition is proposed. According to the fact that different targets have different physical scattering characteristics at different angles, the sub-aperture decomposition is used to improve accuracy with a multi-task learning strategy. Specifically, the proposed method includes main and auxiliary tasks, which can improve the performance of the main task by learning and sharing useful information from the auxiliary task. Here, the main task is the target recognition task, and the auxiliary task is the target reconstruction task. In addition, a complex-valued network is used to extract the features from the original complex-valued SAR images, which effectively utilizes the amplitude and phase information in SAR images. The experimental results obtained using the MSTAR dataset illustrate that the proposed CGS-Net achieved an accuracy of 99.59% (without transfer learning or data augmentation) for the ten-classes targets, which is superior to the other popular deep learning methods. Moreover, the proposed method has a lightweight network structure, which is suitable for SAR target recognition tasks because SAR images usually lack a large number of labeled data. Here, the experimental results obtained using the small dataset further demonstrate the excellent performance of the proposed CGS-Net.

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36

Park, Maxwell C., Charles Lin, Adam Kantor, Yasuo Itami, Michelle H. McGarry, and Thay Q. Lee. "Anterior Cable Reconstruction Using the Proximal Biceps Tendon for Large Rotator Cuff Defects Limits Superior Migration and Subacromial Contact Without Restricting Range of Motion." Orthopaedic Journal of Sports Medicine 6, no. 7_suppl4 (July 1, 2018): 2325967118S0016. http://dx.doi.org/10.1177/2325967118s00168.

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Objectives: Large rotator cuff defects involving the supraspinatus and infraspinatus tendons, either due to irreparability or after partial repair lack superior capsule support. Any remaining tendon is at risk for tear progression as the tendon must function as both a dynamic tendon and static ligamentous structure. Our purpose was to biomechanically assess an anterior cable reconstruction (ACR) using autologous biceps tendon. We hypothesized that ACR will normalize superior migration and subacromial contact, without limiting range of motion. Methods: Nine cadaveric shoulders were tested using a custom testing system. Glenohumeral kinematics and subacromial contact pressure were measured using a MicroScribe 3DLX and a Tekscan pressure sensor. Each specimen was tested in five conditions: Intact, Stage 2 tear (supraspinatus), Stage 2 tear + ACR, Stage 3 tear (supraspinatus + anterior half of infraspinatus), Stage 3 tear + ACR. ACR involved a biceps tendon tenotomy at the transverse humeral ligament preserving its labral attachment. ACR included “loop-around” suture fixation using two side-to-side sutures and an anchor at the articular margin in order to restore anatomy and secure the tendon along the anterior edge of the cuff defect. ACR was performed in glenohumeral 20° abduction and 60° external rotation. Specimens were tested at 0°, 20°, and 40° of glenohumeral abduction. Total rotational range of motion was measured with 2.2 Nm of torque under a physiologic muscle load. A superiorly unbalanced load was applied to measure superior translation and contact pressure. Repeated measures analysis of variance was used for statistical significance (P < 0.05). Results: The average specimen age was 58 years (range 33-77). Stage 2 and 3 tears showed increased total range of motion at all abduction angles (P < 0.007). ACR after both Stage 2 and 3 tears showed greater total range of motion at 20° abduction (P = 0.035 and P = 0.040) and 40° abduction (P = 0.003 and P < 0.001). The ACR conditions showed significantly higher total ranges of motion compared to Intact (P ≤ 0.007). Superior translation increased significantly from Intact for Stage 2 tears at 7/12 positions (P ≤ 0.014) and Stage 3 tears at all positions except 40° abduction, 90° external rotation (ER) (P < 0.001). At 0° abduction, ACR significantly decreased superior translation for Stage 2 tears at 0°, 30°, and 60° ER (P < 0.01) and Stage 3 tears at 0° and 30° ER (P < 0.001). At 20° abduction, ACR significantly reduced superior translation for Stage 2 tears at 0°, 30°, and 60° ER (P < 0.013) and Stage 3 tears at 0° and 30° ER (P < 0.004). At 40° abduction, ACR significantly decreased superior translation only for Stage 3 tears at 0° ER (P = 0.006). Peak contact pressure significantly increased with Stage 3 tears at 7/12 positions (P ≤ 0.023). ACR significantly reduced peak subacromial contact pressure for Stage 3 tears at: 0° abduction, 30° and 60° ER (P < 0.007); 20° abduction, 30° ER (P < 0.041); 40° abduction, 30° and 60° (peak only) ER (P < 0.024). Conclusion: ACR using autologous biceps tendon can biomechanically normalize superior migration and subacromial contact pressure, without limiting range of motion, similar to superior capsule reconstruction. ACR may improve rotator cuff tendon longevity by providing basic static ligamentous support while helping to maintain normal glenohumeral kinematics.

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37

Shi, Lei, and Gangrong Qu. "Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving." Journal of X-Ray Science and Technology 30, no. 2 (March 15, 2022): 319–31. http://dx.doi.org/10.3233/xst-211069.

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BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.

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38

Nielsen, Leonard C., Torne Tänzer, Irene Rodriguez-Fernandez, Paul Erhart, and Marianne Liebi. "Investigating the missing-wedge problem in small-angle X-ray scattering tensor tomography across real and reciprocal space." Journal of Synchrotron Radiation 31, no. 5 (August 28, 2024): 1327–39. http://dx.doi.org/10.1107/s1600577524006702.

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Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

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39

Wang, Chao, Min Tao, James G. Nagy, and Yifei Lou. "Limited-Angle CT Reconstruction via the $L_1/L_2$ Minimization." SIAM Journal on Imaging Sciences 14, no. 2 (January 2021): 749–77. http://dx.doi.org/10.1137/20m1341490.

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40

Turpin, Léonard, Stéphane Roux, Olivier Caty, and Sébastien Denneulin. "A Phase Field Approach to Limited-angle Tomographic Reconstruction." Fundamenta Informaticae 172, no. 2 (February 8, 2020): 203–19. http://dx.doi.org/10.3233/fi-2020-1901.

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41

Fujieda, I., K. Heiskanen, and V. Perez-Mendez. "Versatility of the CFR algorithm for limited angle reconstruction." IEEE Transactions on Nuclear Science 37, no. 2 (April 1990): 585–88. http://dx.doi.org/10.1109/23.106681.

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42

Yufang, Cai, Fu Fanping, Wang Jue, and Cheng Yan. "Optimization reconstruction of biregular term from limited-angle projections." IOP Conference Series: Earth and Environmental Science 332 (November 5, 2019): 042002. http://dx.doi.org/10.1088/1755-1315/332/4/042002.

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43

Rantala, M., S. Vanska, S. Jarvenpaa, M. Kalke, M. Lassas, J. Moberg, and S. Siltanen. "Wavelet-based reconstruction for limited-angle X-ray tomography." IEEE Transactions on Medical Imaging 25, no. 2 (February 2006): 210–17. http://dx.doi.org/10.1109/tmi.2005.862206.

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44

Ye, Yangbo, Hengyong Yu, and Ge Wang. "Exact Interior Reconstruction from Truncated Limited-Angle Projection Data." International Journal of Biomedical Imaging 2008 (2008): 1–6. http://dx.doi.org/10.1155/2008/427989.

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Using filtered backprojection (FBP) and an analytic continuation approach, we prove that exact interior reconstruction is possible and unique from truncated limited-angle projection data, if we assume a prior knowledge on a subregion or subvolume within an object to be reconstructed. Our results show that (i) the interior region-of-interest (ROI) problem and interior volume-of-interest (VOI) problem can be exactly reconstructed from a limited-angle scan of the ROI/VOI and a 180 degree PI-scan of the subregion or subvolume and (ii) the whole object function can be exactly reconstructed from nontruncated projections from a limited-angle scan. These results improve the classical theory of Hamaker et al. (1980).

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45

Xie, En, Peijun Ni, Rongfan Zhang, and Xiongbing Li. "Limited-Angle CT Reconstruction with Generative Adversarial Network Sinogram Inpainting and Unsupervised Artifact Removal." Applied Sciences 12, no. 12 (June 20, 2022): 6268. http://dx.doi.org/10.3390/app12126268.

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High-quality limited-angle computed tomography (CT) reconstruction is in high demand in the medical field. Being unlimited by the pairing of sinogram and the reconstructed image, unsupervised methods have attracted wide attention from researchers. The reconstruction limit of the existing unsupervised reconstruction methods, however, is to use [0°, 120°] of projection data, and the quality of the reconstruction still has room for improvement. In this paper, we propose a limited-angle CT reconstruction generative adversarial network based on sinogram inpainting and unsupervised artifact removal to further reduce the angle range limit and to improve the image quality. We collected a large number of CT lung and head images and Radon transformed them into missing sinograms. Sinogram inpainting network is developed to complete missing sinograms, based on which the filtered back projection algorithm can output images with most artifacts removed; then, these images are mapped to artifact-free images by using artifact removal network. Finally, we generated reconstruction results sized 512×512 that are comparable to full-scan reconstruction using only [0°, 90°] of limited sinogram projection data. Compared with the current unsupervised methods, the proposed method can reconstruct images of higher quality.

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46

Wu, Chenning, Martin Hutton, and Manuchehr Soleimani. "Limited Angle Electrical Resistance Tomography in Wastewater Monitoring." Sensors 20, no. 7 (March 29, 2020): 1899. http://dx.doi.org/10.3390/s20071899.

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Electrical resistance tomography (ERT) has been investigated in monitoring conductive flows due to its high speed, non-intrusive and no radiation hazard advantages. Recently, we have developed an ERT system for the novel application of smart wastewater metering. The dedicated low cost and high-speed design of the reported ERT device allows for imaging pipes with different flow constituents and monitoring the sewer networks. This work extends the capability of such a system to work with partially filled lateral pipes where the incomplete data issue arises due to the electrodes losing contact with the conductive medium. Although the ERT for such a limited region has been developed for many years, there is no study on imaging content within these limited regions. For wastewater monitoring, this means imaging the wastewater and solid inclusions at the same time. This paper has presented a modified ERT system that has the capacity to image inclusions within the conductive region using limited data. We have adjusted the ERT hardware to register the information of the non-contact electrodes and hence the valid measurements. A limited region image reconstruction method based on Jacobian reformulation is applied to gain robustness when it comes to inclusion recovery in limited data ERT. Both simulation and experimental results have demonstrated an enhanced performance brought by the limited region method in comparison to the global reconstruction.

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47

Wang, Jia, Mingzhe Li, Junxia Cheng, Zhenyan Guo, Dangjuan Li, and Shenjiang Wu. "Exact reconstruction condition for angle-limited computed tomography of chemiluminescence." Applied Optics 60, no. 15 (May 12, 2021): 4273. http://dx.doi.org/10.1364/ao.420223.

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48

Kinoshita, Fujimi, Masamichi Yanagisawa, Hirokazu Turuoka, and Toshiyuki Nakayama. "76. Evaluation of limited angle SPECT reconstruction for myocardial SPECT." Japanese Journal of Radiological Technology 50, no. 2 (1994): 195. http://dx.doi.org/10.6009/jjrt.kj00003534558.

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49

Yao, Lei, and Huabei Jiang. "Photoacoustic image reconstruction from few-detector and limited-angle data." Biomedical Optics Express 2, no. 9 (August 19, 2011): 2649. http://dx.doi.org/10.1364/boe.2.002649.

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50

Wang, Ting, Katsuhiro Nakamoto, Heye Zhang, and Huafeng Liu. "Reweighted Anisotropic Total Variation Minimization for Limited-Angle CT Reconstruction." IEEE Transactions on Nuclear Science 64, no. 10 (October 2017): 2742–60. http://dx.doi.org/10.1109/tns.2017.2750199.

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