Adaptive wavelet-Galerkin methods for limited angle tomography

Authors:
Xiaoqiang Lu;Yi Sun;Gangfeng Bai
Affiliations:
School of Electronic and Information Engineering, Dalian University of Technology, Dalian, Liaoning Province 116023, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian, Liaoning Province 116023, PR China;School of Electronic and Information Engineering, Dalian University of Technology, Dalian, Liaoning Province 116023, PR China
Venue:
Image and Vision Computing
Year:
2010

Citing 8
Cited 4

Incomplete data problems in X-ray computerized tomography. I. Singular value decomposition of the limited angle transform

Numerische Mathematik
Nonlinear total variation based noise removal algorithms

Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Singularities of the X-ray transform and limited data tomography in R2 and R3

SIAM Journal on Mathematical Analysis
Mathematical methods in image reconstruction

Mathematical methods in image reconstruction
The mathematics of computerized tomography

The mathematics of computerized tomography
Kaczmarz extended algorithm for tomographic image reconstruction from limited-data

Mathematics and Computers in Simulation
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

IEEE Transactions on Information Theory
Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography

IEEE Transactions on Image Processing

Image reconstruction by an alternating minimisation

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Optimization for limited angle tomography in medical image processing

Pattern Recognition
Local tomography based on grey model

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A wavelet multiscale iterative regularization method for the parameter estimation problems of partial differential equations

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Abstract

This paper studied incomplete data problems of computed tomography that frequently occur in medical or industrial imaging, for example, when the high-density region of objects can only be penetrated by X-rays at a limited angular range. When projection data are available only in an angular range, the incomplete data problem can be attributed to the limited angle problem, which is a severely ill-posed inverse problem. In this paper, a numerical method for the treatment of inverse problems based on an adaptive wavelet-Galerkin method is introduced and investigated. The paper focuses especially on how to avoid inverse crimes in numerical simulations. The method used here combines numerical simplicity and characteristics of adapting to the unknown smoothness of a reconstructed image, which leads to significant reduction in the computational cost. The reconstruction strategy has a comparable performance with a significant reduction in computational time.