In various branches of engineering and science, one is confronted with measurements resulting in incomplete spectral data. The problem of the reconstruction of an imagefrom such a data set can be formulated in terms ...
In various branches of engineering and science, one is confronted with measurements resulting in incomplete spectral data. The problem of the reconstruction of an imagefrom such a data set can be formulated in terms of an integral equation of the first kind. Consequently, this equation can be converted into an equivalent integral equation of the second kind which can be solved by a Neumann-type iterative method. It is shown that this Neumann expansion is an error-reducing method and that it is equivalent to the Papoulis-Gerchberg algorithm for bandlimited signal extrapolation. The integral equation can also be solved by employing a conjugate gradient iterative scheme. Again, convergence of this scheme is demonstrated. Finally a number of illustrative numerical examples are presented and discussed.
Symmetry provides a source of redundancy which can be exploited in imagereconstruction. In particular, internal symmetries in molecules can help to compensate for the loss of Fourier phase information in macromolecul...
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ISBN:
(纸本)9780819482969
Symmetry provides a source of redundancy which can be exploited in imagereconstruction. In particular, internal symmetries in molecules can help to compensate for the loss of Fourier phase information in macromolecular x-ray crystallography. Symmetry projections are incorporated into iterative projection algorithms for reconstruction of macromolecular electron densities from x-ray diffraction amplitudes from crystals. The effects of interpolation are studied and the algorithms are applied to reconstruction of an icosahedral virus.
The possibility to design wearable devices based on electrical impedance tomography (EIT) has recently given a boost to this technology. However, the coverage of the sensor array will vary with the size difference of ...
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The possibility to design wearable devices based on electrical impedance tomography (EIT) has recently given a boost to this technology. However, the coverage of the sensor array will vary with the size difference of the measured object, resulting in an incomplete measurement set. If this measurement set is directly invested in the solution of the inverse problem, the imaging quality will be significantly degraded. In this case, it is necessary to take measures to reduce the impact of missing measurement data on reconstruction. In this article, a new method (MinR-DFF) is proposed which provides a novel solution to the problem of local measurement information loss due to incomplete electrode arrays and achieves high-quality imagereconstruction. The effectiveness of the proposed method is verified by numerical simulation and solid-liquid two-phase experiments. By using this method, the correct images of the phantoms are successfully recovered with an incomplete electrode array and both the correlation coefficients (CORs) and the relative errors (REs) do not differ from the results using the complete measurement set by more than 5%.
Cardiac X-ray computed tomography (CT) has been limited due to scanning times which are considerably longer (1 s) than required to resolve the beating heart (0.1 s). The otherwise attractive convolution-backprojection...
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Cardiac X-ray computed tomography (CT) has been limited due to scanning times which are considerably longer (1 s) than required to resolve the beating heart (0.1 s). The otherwise attractive convolution-backprojection algorithm is not suited for CT imagereconstructionfrom measurements comprising an incomplete set of projection data. In this paper, an iterative reconstruction-reprojection (IRR) algorithm is proposed for limited projection data CT imagereconstruction. At each iteration, the missing views are estimated based on reprojection, which is a software substitute for the scanning process. The standard fan-beam convolution-backprojection algorithm is then used for imagereconstruction. The proposed IRR algorithm enables the use of convolution-backprojection in limited angle of view and in limited field of view CT cases. The potential of this method for cardiac CT reconstruction is demonstrated using computer simulated data.
Diffraction tomography (DT) is an established imaging technique for use with diffracting wavefields, which represents a generalized form of x-ray tomography. In this work, we revisit the three-dimensional reconstructi...
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ISBN:
(纸本)0819463957
Diffraction tomography (DT) is an established imaging technique for use with diffracting wavefields, which represents a generalized form of x-ray tomography. In this work, we revisit the three-dimensional reconstruction problem of DT for variable density acoustic media. Novel reconstruction algorithms are developed for reconstructing separate images that depict a weakly scattering object's compressibility and density variations. If tomographic measurement data are acquired at four distinct temporal frequencies, we demonstrate that the effects of object dispersion can be accounted for completely by use of analytic reconstruction formulas. Computer-simulation studies are conducted to demonstrate the developed imagereconstruction methods.
In this paper, we address the problem of generating and enhancing Passive Gamma Emission Tomography (PGET) datafrom a deep learning perspective. The PGET instrument has been developed for the verification of spent nu...
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In this paper, we address the problem of generating and enhancing Passive Gamma Emission Tomography (PGET) datafrom a deep learning perspective. The PGET instrument has been developed for the verification of spent nuclear fuel and relies on imagereconstruction and analysis algorithms to detect missing or substituted fuel pins. Such techniques are sensitive to the quality of the input data: noisy or incomplete sinograms yield to poor reconstructions and, consequently, to low-confidence results. The development and validation of these algorithms is based on complex Monte Carlo simulations that are time-consuming and computationally-demanding. We propose the use of Convolutional Neural Networks (CNNs) for enhancing PGET data. Our technique learns the mapping between incomplete or noisy sinograms and their corresponding full representation. It effectively exploits the high degree of redundancy of the measurements, i.e . the contribution of a single pin can be observed from many different directions, to learn the underlying model of the data and to make informed predictions. The two main applications of our approach are: (1) accelerating Monte Carlo simulations and (2) pre-processing real measurements to enhance them before running the standard imagereconstruction and analysis techniques. The experimental evaluation was performed with both, simulated and real measurements. Results show how effectively CNNs can learn and exploit the structure of the data. For the two use cases evaluated, denoising sinograms and inpainting incomplete ones, our technique achieved state-of-the-art performance with execution times in the order of milliseconds.
Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks so...
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Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error, This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related, The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method, The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques fromincompletedata. The application of this method to a case of two-dimensional (2-D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error.
Photoacoustic imaging is a new non-destructive biomedical imaging method. When limited independent data is available, the restoration of the initial pressure rise distribution is often an ill-posed problem. In this pa...
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Photoacoustic imaging is a new non-destructive biomedical imaging method. When limited independent data is available, the restoration of the initial pressure rise distribution is often an ill-posed problem. In this paper, based on the study of photoacoustic effects, the sparse prior information of photoacoustic images is integrated into the reconstruction process by using the compressed sensing (CS) theory and the L-2 norm optimization technique, combining the augmented Langrange weighting of the alternating direction method of multipliers (ADMM) with the total variation (TV) minimization problem, and the reconstruction artifacts are effectively eliminated. The simulation datafrom the real numerical model show that compared with the common time reversal algorithm, interpolation algorithm and truncated back projection algorithm, the total variational regularization method based on ADMM can effectively improve the quality of reconstructed images under the condition of limited viewing angles and incomplete projection data.
The acquisition of laser range measurements can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many range ...
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The acquisition of laser range measurements can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many range measurement applications. Acquiring such data through a dynamically small subset of measurement locations can address this problem. In such a case, the measured information can be regarded as incomplete, which necessitates the application of special reconstruction tools to recover the original data set. The reconstruction can be performed based on the concept of sparse signal representation. Recovering signals and images from their sub-Nyquist measurements forms the core idea of compressive sensing (CS). A new saliency-guided CS-based algorithm for improving the reconstruction of range imagefrom sparse laser range measurements has been developed. This system samples the object of interest through an optimized probability density function derived based on saliency rather than a uniform random distribution. Particularly, we demonstrate a saliency-guided sampling method for simultaneously sensing and coding range image, which requires less than half the samples needed by conventional CS while maintaining the same reconstruction performance, or alternatively reconstruct range image using the same number of samples as conventional CS with a 16 dB improvement in signal-to-noise ratio. For example, to achieve a reconstruction SNR of 30 dB, the saliency-guided approach required 30% of the samples in comparison to the standard CS approach that required 90% of the samples in order to achieve similar performance. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.
Propagation-based X-ray phase-contrast tomography (PCT) seeks to reconstruct information regarding the complex-valued refractive index distribution of an object. In many applications, a boundary-enhanced image is soug...
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Propagation-based X-ray phase-contrast tomography (PCT) seeks to reconstruct information regarding the complex-valued refractive index distribution of an object. In many applications, a boundary-enhanced image is sought that reveals the locations of discontinuities in the real-valued component of the refractive index distribution. We investigate two iterative algorithms for few-view imagereconstruction in boundary-enhanced PCT that exploit the fact that a boundary-enhanced PCT image, or its gradient, is often sparse. In order to exploit object sparseness, the reconstruction algorithms seek to minimize the l(1)-norm or TV-norm of the image, subject to data consistency constraints. We demonstrate that the algorithms can reconstruct accurate boundary-enhanced images from highly incomplete few-view projection data. (c) 2010 Optical Society of America
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