A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT)

Wang, Qi; Wang, Huaxiang

doi:10.1016/j.isatra.2010.11.001

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…Reconstruction method for inversion problems in an acoustic tomography based temperature distribution measurement Sha Liu , Shi Liu and Guowei Tong involve the Tikhonov regularization method [16,17], the singular value decomposition (SVD) method [18], etc. Although non-iterative methods can achieve an online measurement, the reconstruction accuracy (RA) is barely satisfactory.…”

Section: Measurement Science and Technologymentioning

confidence: 99%

Reconstruction method for inversion problems in an acoustic tomography based temperature distribution measurement

Shi

Tong

2017

Meas. Sci. Technol.

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In industrial areas, temperature distribution information provides a powerful data support for improving system efficiency, reducing pollutant emission, ensuring safety operation, etc. As a noninvasive measurement technology, acoustic tomography (AT) has been widely used to measure temperature distribution where the efficiency of the reconstruction algorithm is crucial for the reliability of the measurement results. Different from traditional reconstruction techniques, in this paper a two-phase reconstruction method is proposed to ameliorate the reconstruction accuracy (RA). In the first phase, the measurement domain is discretized by a coarse square grid to reduce the number of unknown variables to mitigate the ill-posed nature of the AT inverse problem. By taking into consideration the inaccuracy of the measured time-of-flight data, a new cost function is constructed to improve the robustness of the estimation, and a grey wolf optimizer is used to solve the proposed cost function to obtain the temperature distribution on the coarse grid. In the second phase, the Adaboost.RT based BP neural network algorithm is developed for predicting the temperature distribution on the refined grid in accordance with the temperature distribution data estimated in the first phase. Numerical simulations and experiment measurement results validate the superiority of the proposed reconstruction algorithm in improving the robustness and RA.

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Section: Measurement Science and Technologymentioning

confidence: 99%

Reconstruction method for inversion problems in an acoustic tomography based temperature distribution measurement

Shi

Tong

2017

Meas. Sci. Technol.

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“…Consequently, the solution of a transient nonlinear inverse heat conduction problem is difficult, especially if multi-dimensions and measurement errors are concerned. IHCPs have been extensively studied [3][4][5][6][7][8][9][10][11][12][13][14] and many methods have been proposed [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems

Cui

Duan

Gao

2015

International Journal of Heat and Mass Transfer

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“…[3] Computerized tomography (CT) imaging is used to reconstruct the source distribution in the interior of an object after collection of externally acquired projection data in different directions. [4,5] Nevertheless, emission tomography is always a highly limited data set problem, due to the limited availability of projection angles, the coarse sampling, [6] and other practical constraints brought about by imaging hardware, scanning geometry or ionizing radiation exposure; [7] or because of limited projection data obtained from a few-view CT system to meet the requirement for high temporal resolution. [8] The challenge is how to reconstruct the source distribution by using under-sampled projection data, which is obviously mathematically ill-posed and additional knowledge is needed to help achieve reasonable reconstruction results.…”

Section: Introductionmentioning

confidence: 99%

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

Liu¹,

Zheng²,

Zhou³

2015

Chinese Phys. B

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In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.

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A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT)

Cited by 7 publications

References 12 publications

Reconstruction method for inversion problems in an acoustic tomography based temperature distribution measurement

Reconstruction method for inversion problems in an acoustic tomography based temperature distribution measurement

A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

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