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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.


Results comparison in different ROIs.(A) Measurements (left: bias, right: variance) of ROIs marked in Fig 5 reconstructed with DF and BOSVS versus counting rate. (B) CRC of different ROIs (left: ROI1 right: ROI2) versus counting rate. Note that we take ROI1 and ROI2 for example.
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pone.0138483.g010: Results comparison in different ROIs.(A) Measurements (left: bias, right: variance) of ROIs marked in Fig 5 reconstructed with DF and BOSVS versus counting rate. (B) CRC of different ROIs (left: ROI1 right: ROI2) versus counting rate. Note that we take ROI1 and ROI2 for example.

Mentions: Different regions in phantom may have different physiological and physical property, and reconstruction of a small target in the presence of background activity can be a challenge in PET imaging, as small targets may either be visually obstructed by noise in a regularized reconstruction or be over-smoothed by regularization. In this section we compare two reconstruction methods aimed at different regions. Take ROI1 and ROI2 for example, Fig 10(A) gives the image of bias and variance versus counting rate in different ROIs of phantom, and more details are shown in Table 2. Fig 10(B) compares the contrast recovery coefficient (CRC) versus counting rate by different methods for two regions of interest (ROI). The plots show that the proposed method achieves a better performance than DF in different regions, even sinogram is in low counting level.


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)

Results comparison in different ROIs.(A) Measurements (left: bias, right: variance) of ROIs marked in Fig 5 reconstructed with DF and BOSVS versus counting rate. (B) CRC of different ROIs (left: ROI1 right: ROI2) versus counting rate. Note that we take ROI1 and ROI2 for example.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0138483.g010: Results comparison in different ROIs.(A) Measurements (left: bias, right: variance) of ROIs marked in Fig 5 reconstructed with DF and BOSVS versus counting rate. (B) CRC of different ROIs (left: ROI1 right: ROI2) versus counting rate. Note that we take ROI1 and ROI2 for example.
Mentions: Different regions in phantom may have different physiological and physical property, and reconstruction of a small target in the presence of background activity can be a challenge in PET imaging, as small targets may either be visually obstructed by noise in a regularized reconstruction or be over-smoothed by regularization. In this section we compare two reconstruction methods aimed at different regions. Take ROI1 and ROI2 for example, Fig 10(A) gives the image of bias and variance versus counting rate in different ROIs of phantom, and more details are shown in Table 2. Fig 10(B) compares the contrast recovery coefficient (CRC) versus counting rate by different methods for two regions of interest (ROI). The plots show that the proposed method achieves a better performance than DF in different regions, even sinogram is in low counting level.

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.