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Sparse CT reconstruction based on multi-direction anisotropic total variation (MDATV).

Li H, Chen X, Wang Y, Zhou Z, Zhu Q, Yu D - Biomed Eng Online (2014)

Bottom Line: The numerical and real data experiments demonstrate that MDATV based iterative reconstruction improved the quality of restored image.MDATV regularization can sufficiently use the prior information of image sparsity and edge information simultaneously.By incorporating more prior information, MDATV based approach could reconstruct the image more exactly.

View Article: PubMed Central - HTML - PubMed

Affiliation: College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, People's Republic of China. xdchen@tju.edu.cn.

ABSTRACT

Background: The sparse CT (Computed Tomography), inspired by compressed sensing, means to introduce a prior information of image sparsity into CT reconstruction to reduce the input projections so as to reduce the potential threat of incremental X-ray dose to patients' health. Recently, many remarkable works were concentrated on the sparse CT reconstruction from sparse (limited-angle or few-view style) projections. In this paper we would like to incorporate more prior information into the sparse CT reconstruction for improvement of performance. It is known decades ago that the given projection directions can provide information about the directions of edges in the restored CT image. ATV (Anisotropic Total Variation), a TV (Total Variation) norm based regularization, could use the prior information of image sparsity and edge direction simultaneously. But ATV can only represent the edge information in few directions and lose much prior information of image edges in other directions.

Methods: To sufficiently use the prior information of edge directions, a novel MDATV (Multi-Direction Anisotropic Total Variation) is proposed. In this paper we introduce the 2D-IGS (Two Dimensional Image Gradient Space), and combined the coordinate rotation transform with 2D-IGS to represent edge information in multiple directions. Then by incorporating this multi-direction representation into ATV norm we get the MDATV regularization. To solve the optimization problem based on the MDATV regularization, a novel ART (algebraic reconstruction technique) + MDATV scheme is outlined. And NESTA (NESTerov's Algorithm) is proposed to replace GD (Gradient Descent) for minimizing the TV-based regularization.

Results: The numerical and real data experiments demonstrate that MDATV based iterative reconstruction improved the quality of restored image. NESTA is more suitable than GD for minimization of TV-based regularization.

Conclusions: MDATV regularization can sufficiently use the prior information of image sparsity and edge information simultaneously. By incorporating more prior information, MDATV based approach could reconstruct the image more exactly.

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Restored circles representing the copper filled hole in Figure17.
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Figure 20: Restored circles representing the copper filled hole in Figure17.

Mentions: For the sparse CT reconstruction experiment, 30 views of fan-beam projections are chose uniformly across the range of 360°. Due to the ATV’s poor performance for the sub-ERP projections (volume of projections is less than that required by ERP), we only compare TV and MDATV based methods. The reconstruction methods used in the experiments are ART-TV-GD, ART-MDATV-GD, and ART-MDATV-NESTA. The step sizes of GD used in the reconstructions are 92 for TV and 10 for MDATV, which are estimated from an approximate synthetic phantom. The iteration times of NESTA for MDATV is 40.In Figure 17, we show the reconstructions after 5 iterations (top row) and 100 iterations (bottom row) with three methods (from left to right): ART-TV-GD, ART-MDATV-GD, ART-MDATV-NESTA. In the restored images, the holes filled with air and copper are distinct, while the hole filled with corn is undistinguishable. To further visualize the difference among various methods, horizontal profiles of restored images were drawn across the 63rd row (for the air and corn filled holes) and 127th row (for the copper filled hole), from the 10th column to the 160th column. The profiles of restored images after 5 and 100 iteration are shown in Figure 18. Since the projection data is not sufficient, the FBP reconstructions abound with artifacts, but the FBP reconstructions clearly depict the boundaries of the air and copper filled holes. And the observations from Figure 18 indicate that MDATV-NESTA profiles matches the FBP profiles best.The regions of holes filled with air and copper (in the red rectangles in Figure 17) are zoomed in and shown in Figures 19 and 20 respectively. To increase the contrast of Figures 19 and 20, 5% of data is saturated at low and high intensities of the original image. Figures 19 and 20 indicate that ART-MDATV-GD method gave the best results. Since the restored circles by ART-MDATV-GD are the most round. The restored circles of ART-MDATV-NESTA are more round than that of ART-TV-GD. The radial artifacts in the restored images are metal artifacts, which can be removed by some off-the-shelf methods.


Sparse CT reconstruction based on multi-direction anisotropic total variation (MDATV).

Li H, Chen X, Wang Y, Zhou Z, Zhu Q, Yu D - Biomed Eng Online (2014)

Restored circles representing the copper filled hole in Figure17.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4127084&req=5

Figure 20: Restored circles representing the copper filled hole in Figure17.
Mentions: For the sparse CT reconstruction experiment, 30 views of fan-beam projections are chose uniformly across the range of 360°. Due to the ATV’s poor performance for the sub-ERP projections (volume of projections is less than that required by ERP), we only compare TV and MDATV based methods. The reconstruction methods used in the experiments are ART-TV-GD, ART-MDATV-GD, and ART-MDATV-NESTA. The step sizes of GD used in the reconstructions are 92 for TV and 10 for MDATV, which are estimated from an approximate synthetic phantom. The iteration times of NESTA for MDATV is 40.In Figure 17, we show the reconstructions after 5 iterations (top row) and 100 iterations (bottom row) with three methods (from left to right): ART-TV-GD, ART-MDATV-GD, ART-MDATV-NESTA. In the restored images, the holes filled with air and copper are distinct, while the hole filled with corn is undistinguishable. To further visualize the difference among various methods, horizontal profiles of restored images were drawn across the 63rd row (for the air and corn filled holes) and 127th row (for the copper filled hole), from the 10th column to the 160th column. The profiles of restored images after 5 and 100 iteration are shown in Figure 18. Since the projection data is not sufficient, the FBP reconstructions abound with artifacts, but the FBP reconstructions clearly depict the boundaries of the air and copper filled holes. And the observations from Figure 18 indicate that MDATV-NESTA profiles matches the FBP profiles best.The regions of holes filled with air and copper (in the red rectangles in Figure 17) are zoomed in and shown in Figures 19 and 20 respectively. To increase the contrast of Figures 19 and 20, 5% of data is saturated at low and high intensities of the original image. Figures 19 and 20 indicate that ART-MDATV-GD method gave the best results. Since the restored circles by ART-MDATV-GD are the most round. The restored circles of ART-MDATV-NESTA are more round than that of ART-TV-GD. The radial artifacts in the restored images are metal artifacts, which can be removed by some off-the-shelf methods.

Bottom Line: The numerical and real data experiments demonstrate that MDATV based iterative reconstruction improved the quality of restored image.MDATV regularization can sufficiently use the prior information of image sparsity and edge information simultaneously.By incorporating more prior information, MDATV based approach could reconstruct the image more exactly.

View Article: PubMed Central - HTML - PubMed

Affiliation: College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, People's Republic of China. xdchen@tju.edu.cn.

ABSTRACT

Background: The sparse CT (Computed Tomography), inspired by compressed sensing, means to introduce a prior information of image sparsity into CT reconstruction to reduce the input projections so as to reduce the potential threat of incremental X-ray dose to patients' health. Recently, many remarkable works were concentrated on the sparse CT reconstruction from sparse (limited-angle or few-view style) projections. In this paper we would like to incorporate more prior information into the sparse CT reconstruction for improvement of performance. It is known decades ago that the given projection directions can provide information about the directions of edges in the restored CT image. ATV (Anisotropic Total Variation), a TV (Total Variation) norm based regularization, could use the prior information of image sparsity and edge direction simultaneously. But ATV can only represent the edge information in few directions and lose much prior information of image edges in other directions.

Methods: To sufficiently use the prior information of edge directions, a novel MDATV (Multi-Direction Anisotropic Total Variation) is proposed. In this paper we introduce the 2D-IGS (Two Dimensional Image Gradient Space), and combined the coordinate rotation transform with 2D-IGS to represent edge information in multiple directions. Then by incorporating this multi-direction representation into ATV norm we get the MDATV regularization. To solve the optimization problem based on the MDATV regularization, a novel ART (algebraic reconstruction technique) + MDATV scheme is outlined. And NESTA (NESTerov's Algorithm) is proposed to replace GD (Gradient Descent) for minimizing the TV-based regularization.

Results: The numerical and real data experiments demonstrate that MDATV based iterative reconstruction improved the quality of restored image. NESTA is more suitable than GD for minimization of TV-based regularization.

Conclusions: MDATV regularization can sufficiently use the prior information of image sparsity and edge information simultaneously. By incorporating more prior information, MDATV based approach could reconstruct the image more exactly.

Show MeSH