The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solutio...The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solution does not depend on the measured data continuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regularization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at differentresolutions.展开更多
The geometry of joints has a significant influence on the mechanical properties of rocks.To simplify the curved joint shapes in rocks,the joint shape is usually treated as straight lines or planes in most laboratory e...The geometry of joints has a significant influence on the mechanical properties of rocks.To simplify the curved joint shapes in rocks,the joint shape is usually treated as straight lines or planes in most laboratory experiments and numerical simulations.In this study,the computerized tomography (CT) scanning and photogrammetry were employed to obtain the internal and surface joint structures of a limestone sample,respectively.To describe the joint geometry,the edge detection algorithms and a three-dimensional (3D) matrix mapping method were applied to reconstruct CT-based and photogrammetry-based jointed rock models.For comparison tests,the numerical uniaxial compression tests were conducted on an intact rock sample and a sample with a joint simplified to a plane using the parallel computing method.The results indicate that the mechanical characteristics and failure process of jointed rocks are significantly affected by the geometry of joints.The presence of joints reduces the uniaxial compressive strength (UCS),elastic modulus,and released acoustic emission (AE) energy of rocks by 37%–67%,21%–24%,and 52%–90%,respectively.Compared to the simplified joint sample,the proposed photogrammetry-based numerical model makes the most of the limited geometry information of joints.The UCS,accumulative released AE energy,and elastic modulus of the photogrammetry-based sample were found to be very close to those of the CT-based sample.The UCS value of the simplified joint sample (i.e.38.5 MPa) is much lower than that of the CT-based sample (i.e.72.3 MPa).Additionally,the accumulative released AE energy observed in the simplified joint sample is 3.899 times lower than that observed in the CT-based sample.CT scanning provides a reliable means to visualize the joints in rocks,which can be used to verify the reliability of photogrammetry techniques.The application of the photogrammetry-based sample enables detailed analysis for estimating the mechanical properties of jointed rocks.展开更多
This paper initially applied the non-destructive evaluation-computerized tomography and the fractal theory to research the feature of wood fracture. Pinus elliottii, Populus×canadensis cv. ‘I-214’ and Larix gme...This paper initially applied the non-destructive evaluation-computerized tomography and the fractal theory to research the feature of wood fracture. Pinus elliottii, Populus×canadensis cv. ‘I-214’ and Larix gmelinii were choosed as samples. The author established the logarithm-logarithm relationship between the section area of wood fracture and its location, then defined the slope-D_L regressed by the two factors above as the section variation fractal dimension of wood fracture. The results showed: the non-destructive evaluation-computerized tomography can effectively analysis the feature of wood fracture. All the samples exist an marked linear relationship between the section area of fracture and its location, D_L is a new effective parameter to quantitatively characterize the feature of wood fracture, the delta of -2 described the complexity of fracture surface of wood. Due to the anisotropy and variation of wood properties, D_L is the statistically fractal dimension. All the results are tested by the statistic software——SARS, there exists remarkable difference between the D_L from different species. The average fractal dimension of fracture surface of Pinus elliottii is 2.25, Populus×canadensis cv. ‘I-214’ is 2.46, Larix gmelinii is 2.65.展开更多
基金the support of the German Research Foundation,projects BU 2327/19-1 and MO 2962/7-1support from the EPSRC grant EP/R513106/1support from the Alan Turing Institute.
文摘The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography(CT).As the(naive)solution does not depend on the measured data continuously,regularization is needed to reestablish a continuous dependence.In this work,we investigate simple,but yet still provably convergent approaches to learning linear regularization methods from data.More specifically,we analyze two approaches:one generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work,and one tailored approach in the Fourier domain that is specific to CT-reconstruction.We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on.Finally,we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically,discuss their advantages and disadvantages and investigate the effect of discretization errors at differentresolutions.
基金supported by the National Natural Science Foundation of China(Grant Nos.42277150,41977219)Henan Provincial Science and Technology Research Project(Grant No.222102320271).
文摘The geometry of joints has a significant influence on the mechanical properties of rocks.To simplify the curved joint shapes in rocks,the joint shape is usually treated as straight lines or planes in most laboratory experiments and numerical simulations.In this study,the computerized tomography (CT) scanning and photogrammetry were employed to obtain the internal and surface joint structures of a limestone sample,respectively.To describe the joint geometry,the edge detection algorithms and a three-dimensional (3D) matrix mapping method were applied to reconstruct CT-based and photogrammetry-based jointed rock models.For comparison tests,the numerical uniaxial compression tests were conducted on an intact rock sample and a sample with a joint simplified to a plane using the parallel computing method.The results indicate that the mechanical characteristics and failure process of jointed rocks are significantly affected by the geometry of joints.The presence of joints reduces the uniaxial compressive strength (UCS),elastic modulus,and released acoustic emission (AE) energy of rocks by 37%–67%,21%–24%,and 52%–90%,respectively.Compared to the simplified joint sample,the proposed photogrammetry-based numerical model makes the most of the limited geometry information of joints.The UCS,accumulative released AE energy,and elastic modulus of the photogrammetry-based sample were found to be very close to those of the CT-based sample.The UCS value of the simplified joint sample (i.e.38.5 MPa) is much lower than that of the CT-based sample (i.e.72.3 MPa).Additionally,the accumulative released AE energy observed in the simplified joint sample is 3.899 times lower than that observed in the CT-based sample.CT scanning provides a reliable means to visualize the joints in rocks,which can be used to verify the reliability of photogrammetry techniques.The application of the photogrammetry-based sample enables detailed analysis for estimating the mechanical properties of jointed rocks.
文摘This paper initially applied the non-destructive evaluation-computerized tomography and the fractal theory to research the feature of wood fracture. Pinus elliottii, Populus×canadensis cv. ‘I-214’ and Larix gmelinii were choosed as samples. The author established the logarithm-logarithm relationship between the section area of wood fracture and its location, then defined the slope-D_L regressed by the two factors above as the section variation fractal dimension of wood fracture. The results showed: the non-destructive evaluation-computerized tomography can effectively analysis the feature of wood fracture. All the samples exist an marked linear relationship between the section area of fracture and its location, D_L is a new effective parameter to quantitatively characterize the feature of wood fracture, the delta of -2 described the complexity of fracture surface of wood. Due to the anisotropy and variation of wood properties, D_L is the statistically fractal dimension. All the results are tested by the statistic software——SARS, there exists remarkable difference between the D_L from different species. The average fractal dimension of fracture surface of Pinus elliottii is 2.25, Populus×canadensis cv. ‘I-214’ is 2.46, Larix gmelinii is 2.65.
