NDLI: Optimal recovery of 3D X-ray tomographic data via shearlet decomposition

Content Provider	Springer Nature Link
Author	Labate, Demetrio Guo, Kanghui
Copyright Year	2012
Abstract	This paper introduces a new decomposition of the 3D X-ray transform based on the shearlet representation, a multiscale directional representation which is optimally efficient in handling 3D data containing edge singularities. Using this decomposition, we derive a highly effective reconstruction algorithm yielding a near-optimal rate of convergence in estimating piecewise smooth objects from 3D X-ray tomographic data which are corrupted by white Gaussian noise. This algorithm is achieved by applying a thresholding scheme on the 3D shearlet transform coefficients of the noisy data which, for a given noise level ε, can be tuned so that the estimator attains the essentially optimal mean square error rate O(log(ε − 1)ε 2/3), as ε→0. This is the first published result to achieve this type of error estimate, outperforming methods based on Wavelet-Vaguelettes decomposition and on SVD, which can only achieve MSE rates of O(ε 1/2) and O(ε 1/3), respectively.
Ending Page	255
Page Count	29
Starting Page	227
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	2
Volume Number	39
Language	English
Publisher	Springer US
Publisher Date	2012-08-05
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Shearlets Numeric Computing Mathematics Theory of Computation Wavelets and other special systems Wavelets Inverse problems Algebra Computed tomography Calculus of Variations and Optimal Control; Optimization X-ray transform Radon transform X-ray tomography General harmonic expansions, frames
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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