Numerical Inversion of Three-Dimensional Geodesic X-Ray Transform Arising from Travel Time Tomography

2019 ◽  
Vol 12 (3) ◽  
pp. 1296-1323
Author(s):  
T. S. Au Yeung ◽  
Eric T. Chung ◽  
Gunther Uhlmann
Keyword(s):  
Travel Time ◽  
Three Dimensional ◽  
Numerical Inversion ◽  
X Ray ◽  
Ray Transform ◽  
Travel Time Tomography

Three-Dimensional Acoustic Travel-Time Tomography of the Atmosphere

2008 ◽  
Vol 94 (3) ◽  
pp. 349-358 ◽  
Author(s):  
Sergey N. Vecherin ◽  
Vladimir E. Ostashev ◽  
Keith D. Wilson
Keyword(s):  
Travel Time ◽  
Three Dimensional ◽  
Travel Time Tomography ◽  
Acoustic Travel Time

scholarly journals The X-Ray Transform Projection of 3D Mother Wavelet Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiangyu Yang ◽  
Jiqiang Guo ◽  
Li Lu ◽  
Li Zeng
Keyword(s):  
Wavelet Transform ◽  
Three Dimensional ◽  
Computation Time ◽  
Projection Data ◽  
3D Image ◽  
Mother Wavelet ◽  
X Ray ◽  
Ray Transform ◽  
3D Wavelet Transform ◽  
Ray Projection

As we all know, any practical computed tomography (CT) projection data more or less contains noises. Hence, it will be inconvenient for the postprocessing of a reconstructed 3D image even when the noise in the projection data is white. The reason is that the noise in the reconstructed image may be nonwhite. X-ray transform can be applied to the three dimensional (3D) CT, depicting the relationship between material density and ray projection. In this paper, nontensor product relationship between the two dimensional (2D) mother wavelet and 3D mother wavelet is obtained by taking X-ray transform projection of 3D mother wavelet. We proved that the projection of the 3D mother wavelet is a 2D mother wavelet if the 3D mother wavelet satisfies certain conditions. So, the 3D wavelet transform of a 3D image can be implemented by the 2D wavelet transform of its X-ray transform projection and it will contribute to the reduction complexity and computation time during image processing. What is more, it can also avoid noise transfer and amplification during the processing of CT image reconstruction.

Ribosome Structural Organization

1974 ◽  
Vol 32 ◽  
pp. 332-333
Author(s):  
James A. Lake
Keyword(s):  
Ribosomal Proteins ◽  
Structural Organization ◽  
Three Dimensional ◽  
Small Subunit ◽  
Structural Studies ◽  
X Ray Diffraction ◽  
Specific Antibodies ◽  
X Ray ◽  
E Coli ◽  
Complete Sequences

The understanding of ribosome structure has advanced considerably in the last several years. Biochemists have characterized the constituent proteins and rRNA's of ribosomes. Complete sequences have been determined for some ribosomal proteins and specific antibodies have been prepared against all E. coli small subunit proteins. In addition, a number of naturally occuring systems of three dimensional ribosome crystals which are suitable for structural studies have been observed in eukaryotes. Although the crystals are, in general, too small for X-ray diffraction, their size is ideal for electron microscopy.

3-D reconstruction of molecular shape from microcrystal thin sections

1983 ◽  
Vol 41 ◽  
pp. 748-749
Author(s):  
S. Cusack ◽  
J.-C. Jésior
Keyword(s):  
Three Dimensional ◽  
Molecular Shape ◽  
Biological Molecules ◽  
Fourier Space ◽  
Single Particles ◽  
Thin Sections ◽  
Standard Methods ◽  
X Ray ◽  
X Ray Crystallography ◽  
Dimensional Reconstruction

Three-dimensional reconstruction techniques using electron microscopy have been principally developed for application to 2-D arrays (i.e. monolayers) of biological molecules and symmetrical single particles (e.g. helical viruses). However many biological molecules that crystallise form multilayered microcrystals which are unsuitable for study by either the standard methods of 3-D reconstruction or, because of their size, by X-ray crystallography. The grid sectioning technique enables a number of different projections of such microcrystals to be obtained in well defined directions (e.g. parallel to crystal axes) and poses the problem of how best these projections can be used to reconstruct the packing and shape of the molecules forming the microcrystal.Given sufficient projections there may be enough information to do a crystallographic reconstruction in Fourier space. We however have considered the situation where only a limited number of projections are available, as for example in the case of catalase platelets where three orthogonal and two diagonal projections have been obtained (Fig. 1).

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