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Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method.

Yu H, Chen Z, Zhang H, Wong KK, Chen Y, Liu H - PLoS ONE (2015)

Bottom Line: To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS).Experiments based on Monte Carlo simulated data and real data are conducted as validations.The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).

View Article: PubMed Central - PubMed

Affiliation: Department of Optical Engineering, Zhejiang University, Hangzhou, Zhejiang, China.

ABSTRACT
This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).

No MeSH data available.


The regions of phantom and profile lines.The yellow lines mark the lateral displacement profiles. The colorful blocks demonstrate the regions of interest in the phantom.
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pone.0138483.g005: The regions of phantom and profile lines.The yellow lines mark the lateral displacement profiles. The colorful blocks demonstrate the regions of interest in the phantom.

Mentions: Since these experiments are based on Monte Carlo simulations, we can get the true activity distributions at any time exactly. In order to analyze the reconstruction results quantitatively, we define the measurements as follows:bias=1n∑i=1n(ui-u^iu^i),(20)variance=1n∑i=1n(ui-u¯nu^i)2(21)where ui, and represent the estimated activity value of pixel i, the true activity value of pixel i, and the average estimated value of all the n pixels in one ROI respectively. Furthermore, we compute the contrast recovery coefficient (CRC), which is calculated byCRC=(Contrast)measure(Contrast)theory=(S/B)measure-1(S/B)theory-1,(22)where S is the mean activity of the region of interest and B is the mean activity of the white matter region (background) in the reconstructed image. Fig 4 gives the true activity distributions and reconstructed images of the center slice by DF and BOSVS. Table 1 calculates the bias and variance between true activity distributions and reconstruction results by DF and BOSVS respectively. Fig 5 shows the regions of phantom and profile lines. And Fig 6 shows the profiles of reconstruction results by DF and BOSVS compared with the ground truth. Fig 7 gives the details of our selected area in the image reconstructed by two methods. We can obviously see that BOSVS show better recovery of activity distributions than DF.


Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method.

Yu H, Chen Z, Zhang H, Wong KK, Chen Y, Liu H - PLoS ONE (2015)

The regions of phantom and profile lines.The yellow lines mark the lateral displacement profiles. The colorful blocks demonstrate the regions of interest in the phantom.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4580435&req=5

pone.0138483.g005: The regions of phantom and profile lines.The yellow lines mark the lateral displacement profiles. The colorful blocks demonstrate the regions of interest in the phantom.
Mentions: Since these experiments are based on Monte Carlo simulations, we can get the true activity distributions at any time exactly. In order to analyze the reconstruction results quantitatively, we define the measurements as follows:bias=1n∑i=1n(ui-u^iu^i),(20)variance=1n∑i=1n(ui-u¯nu^i)2(21)where ui, and represent the estimated activity value of pixel i, the true activity value of pixel i, and the average estimated value of all the n pixels in one ROI respectively. Furthermore, we compute the contrast recovery coefficient (CRC), which is calculated byCRC=(Contrast)measure(Contrast)theory=(S/B)measure-1(S/B)theory-1,(22)where S is the mean activity of the region of interest and B is the mean activity of the white matter region (background) in the reconstructed image. Fig 4 gives the true activity distributions and reconstructed images of the center slice by DF and BOSVS. Table 1 calculates the bias and variance between true activity distributions and reconstruction results by DF and BOSVS respectively. Fig 5 shows the regions of phantom and profile lines. And Fig 6 shows the profiles of reconstruction results by DF and BOSVS compared with the ground truth. Fig 7 gives the details of our selected area in the image reconstructed by two methods. We can obviously see that BOSVS show better recovery of activity distributions than DF.

Bottom Line: To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS).Experiments based on Monte Carlo simulated data and real data are conducted as validations.The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).

View Article: PubMed Central - PubMed

Affiliation: Department of Optical Engineering, Zhejiang University, Hangzhou, Zhejiang, China.

ABSTRACT
This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).

No MeSH data available.