Restoration of missing data in limited angle tomography based on Helgason–Ludwig consistency conditions

Huang, Yixing; Huang, Xiaolin; Taubmann, Oliver; Xia, Yan; Haase, Viktor; Hornegger, Joachim; Lauritsch, Guenter; Maier, Andreas

doi:10.1088/2057-1976/aa71bf

Cited by 32 publications

(20 citation statements)

References 45 publications

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“…Using the projection data of a bamboo culm and parasol tree branch acquired with a prototype microscopic CBCT, the investigation verifies that the proposed approach works very well for misalignment correction in microscopic CBCT. For convenience in carrying out the experiments, only botanical specimens were used, but the success of applying the Grangeat Epipolar Consistency Condition for geometry misalignment correction in this work, along with its utility in other applications, encourage us to explore more applications in clinical and preclinical CT imaging with the Grangeat Epipolar Consistency Condition as the foundation.…”

Section: Discussionmentioning

confidence: 99%

Data sustained misalignment correction in microscopic cone beam CT via optimization under the Grangeat Epipolar consistency condition

et al. 2019

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Purpose The misalignment correction in cone beam computed tomography (CBCT), which is usually carried out in an offline manner, is a difficult and tedious process. It becomes even more challenging in microscopic CBCT due to the much higher requirements on spatial resolution. In practice, however, an offline approach for misalignment correction may not be readily implementable, especially in the situations where either time is of the essence or the process needs to be carried out repetitively. Thus, an online self‐calibration (i.e., data sustained misalignment correction without the involvement of specific alignment phantom) would be more practical. In this work, we investigate the data sustained misalignment correction in microscopic CBCT via optimization under the Grangeat Epipolar Consistence Condition and evaluate its performance via phantom and specimen studies. Methods With the cost function defined according to the Grangeat Epipolar Consistency Condition (G‐ECC) and by minimizing the cost function using the simplex‐simulated annealing algorithm (SIMPSA), we evaluate and verify the G‐ECC optimization‐based online self‐calibration method's performance. Performance is measured in sensitivity, robustness, and accuracy using the projection data of phantoms generated by computer simulation and botanical specimens acquired by a prototype microscopic CBCT. Results The online data sustained misalignment correction in microscopic CBCT via G‐ECC optimization works very well in sensitivity and robustness, in addition to its accuracy of 0.27%, 0.48%, and 0.34% relative errors, respectively, in obtaining the three geometric parameters that are the most critical to image reconstruction in CBCT. Quantitatively, the performance in meeting the requirements on spatial resolution is comparable to, if not better than, that of the offline misalignment correction method, in which a specific alignment phantom has to be used. Conclusions The G‐ECC optimization‐based online self‐calibration approach provides a practical solution (as long as no latitudinal (lateral) data truncation occurs) for misalignment correction in microscopic CBCT, an application that demands high accuracy in geometric alignment for biological (cellular) imaging at super high spatial resolutions in the order of micrometers (2.1 µm).

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Section: Discussionmentioning

confidence: 99%

Data sustained misalignment correction in microscopic cone beam CT via optimization under the Grangeat Epipolar consistency condition

et al. 2019

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“…Tomographic reconstruction algorithms such as filtered back projection require a measurement from different scan angle positions in the range of 180 • [9]. Limitations of the angular scanning range result in artifacts such as diagonal lines in the local reconstruction field and disappearance of sharp edges outside the scan angle range occurs [1][2][3]14,15]. Furthermore, an unknown systematic measurement error occurs, i.e., the absolute values of the reconstruction are strongly distorted [16,17].…”

Section: Introductionmentioning

confidence: 99%

Dense U-Net for Limited Angle Tomography of Sound Pressure Fields

et al. 2021

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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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“…The reconstruction of missing-wedge tomography suffers from strong artefacts that generate erroneous structures of the object. These artefacts can be reduced from pre-processing of the sinogram (Kudo & Saito, 1991;Huang et al, 2017), during reconstruction (Kupsch et al, 2016), or post-processing of the reconstruction. Pre-processing often involves filling in the missing projections of the sinogram.…”

Section: Introductionmentioning

confidence: 99%

Tomographic reconstruction with a generative adversarial network

Yang

Kahnt

Brückner

et al. 2020

J Synchrotron Radiat

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This paper presents a deep learning algorithm for tomographic reconstruction (GANrec). The algorithm uses a generative adversarial network (GAN) to solve the inverse of the Radon transform directly. It works for independent sinograms without additional training steps. The GAN has been developed to fit the input sinogram with the model sinogram generated from the predicted reconstruction. Good quality reconstructions can be obtained during the minimization of the fitting errors. The reconstruction is a self‐training procedure based on the physics model, instead of on training data. The algorithm showed significant improvements in the reconstruction accuracy, especially for missing‐wedge tomography acquired at less than 180° rotational range. It was also validated by reconstructing a missing‐wedge X‐ray ptychographic tomography (PXCT) data set of a macroporous zeolite particle, for which only 51 projections over 70° could be collected. The GANrec recovered the 3D pore structure with reasonable quality for further analysis. This reconstruction concept can work universally for most of the ill‐posed inverse problems if the forward model is well defined, such as phase retrieval of in‐line phase‐contrast imaging.

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Restoration of missing data in limited angle tomography based on Helgason–Ludwig consistency conditions

Cited by 32 publications

References 45 publications

Data sustained misalignment correction in microscopic cone beam CT via optimization under the Grangeat Epipolar consistency condition

Data sustained misalignment correction in microscopic cone beam CT via optimization under the Grangeat Epipolar consistency condition

Dense U-Net for Limited Angle Tomography of Sound Pressure Fields

Tomographic reconstruction with a generative adversarial network

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