منابع مشابه
The X-ray Transform and its Application in Nano Crystallography
In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...
متن کامل3D discrete X-ray transform
The analysis of 3D discrete volumetric data becomes increasingly important as computation power increases. 3D analysis and visualization applications are expected to be especially relevant in areas like medical imaging and nondestructive testing, where elaborated continuous theory exists. However, this theory is not directly applicable to discrete datasets. Therefore, we have to establish theor...
متن کاملThe Fast Wavelet X-Ray Transform
The wavelet X-ray transform computes one-dimensional wavelet transforms along lines in Euclidian space in order to perform a directional time-scale analysis of functions in several variables. A fast algorithm is proposed which executes this transformation starting with values given on a cartesian grid that represent the underlying function. The algorithm involves a rotation step and wavelet ana...
متن کاملTwo Bounds for the X-ray Transform
We use the arithmetic-combinatorial method of Katz and Tao to give mixed-norm estimates for the x-ray transform on R when d ≥ 4. As an application, we obtain an improved estimate for the Hausdorff dimension of (d, k) sets, which are subsets of R containing a translate of every k-plane.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1976
ISSN: 0022-247X
DOI: 10.1016/0022-247x(76)90008-1