منابع مشابه
Radon Transform Inversion using the Shearlet Representation
The inversion of the Radon transform is a classical ill-posed inverse problem where some method of regularization must be applied in order to accurately recover the objects of interest from the observable data. A well-known consequence of the traditional regularization methods is that some important features to be recovered are lost, as evident in imaging applications where the regularized reco...
متن کاملA Fast and Accurate Multilevel Inversion of the Radon Transform
A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N2 logN) algorithm, where the image consists of N×N pixels, while the backprojection is an O(N3) algorithm, thus constituting the major computational burden of the convolution backprojection method. An O(N2 logN) multilevel backprojection ...
متن کاملInversion of noisy Radon transform by SVD based needlets
Article history: Received 29 July 2008 Revised 29 May 2009 Accepted 3 June 2009 Available online 12 June 2009 Communicated by W.R. Madych A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established i...
متن کاملFlexible, inversion-based Matlab implementation of the Radon transform
This study reviews the theory, programming designs and merits of two new Matlab-based routines for the forward and inverse Radon transform. These routines offer users flexible choices of integration path functions to take advantage of improved Radon-domain identification and isolation of seismic phases. Least-squares inversion of frequency components and judicious choices of regularization tech...
متن کاملInversion of the circular Radon transform on an annulus
The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest towards these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some n...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1992
ISSN: 0893-9659
DOI: 10.1016/0893-9659(92)90109-m