Finding discontinuities from tomographic data
نویسندگان
چکیده
منابع مشابه
Finding Discontinuities from Tomographic Data*
A method for derivation of inversion formulas for the Radon transform of f (x) is given. This method allows one to construct functions ψ(x) which are easy to compute and which have the same wave fronts as f (x). This, in turn, allows one to calculate the singular support S of f (x) by computing ψ(x) given tomographic data. A simple geometrical relation between the singular supports of f andˆf ,...
متن کاملNew methods for finding discontinuities of functions from local tomographic data
A survey of the author’s results in the area of local tomography is given. The basic problem is to find discontinuities of functions from local tomographic data. Methods for finding the location of the discontinuities and the sizes of the jumps of a function from its local tomographic data are given. A class of pseudodifferential operators which generate local tomography operators is characteri...
متن کاملMultidimensional Algorithm for Finding Discontinuities of Signals from Noisy Discrete Data
Algorithms are given for finding discontinuity surfaces of a signal specified with random errors at a regular grid in Rp, p ≥ 1. For each position of a sliding window one arranges points from it in ascending order of the measured values of the signal and divides them into two groups. One group contains points with larger values than the other. The division is made according to the nature of the...
متن کاملTomographic reconstruction from limited data
Introduction At present, image reconstruction in micro-CT imaging is typically performed using the FDK algorithm. This algorithm, which is similar to the Filtered Backprojection algorithm for singleslice tomography, is capable of computing accurate reconstructions in a relatively short time, provided that the acquired dataset satisfies certain requirements: (i) a large number of projection imag...
متن کاملFinding Discontinuities of Piecewise-smooth Functions
Formulas for stable differentiation of piecewise-smooth functions are given. The data are noisy values of these functions. The locations of discontinuity points and the sizes of the jumps across these points are not assumed known, but found stably from the noisy data.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1273517-6