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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 iamges from 120 views of fan-beam projections with FBP. The display gray scale window is [80,400].
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Figure 16: Restored iamges from 120 views of fan-beam projections with FBP. The display gray scale window is [80,400].

Mentions: In the experiment, the detector has 1024 bins, and the physical size of each bin is 0.05 millimeters. Therefore, the raw sinogram of one view has 1024 pixels, and each pixel represents the physical length of 0.05 millimeters. However, the computation load of the iterative reconstruction is very heavy for the high resolution sinogram. Thus the high resolution sinogram is down sampled by the ratio of 4. And the low resolution sinogram of one view has 256 = 1024 ÷ 4 pixels. To maintain the physical length of the projection geometry, each pixel in the low resolution sinogram represents the physical length of 0.2 = 0.05 × 4 millimetres. Actually, in this down sampling, four neighboring pixels in the raw sinogram of one view is averaged as one pixel in the low resolution sinogram of one view.In this experiment, restrained by the micro-CT machine, the whole projection data contains 120 views of fan-beam projection uniformly distributed across 360°. Its FBP reconstruction is shown in Figure 16. Compare Figure 15 and 16, it is easy to distinguish the air and copper filled holes from the background organic glass, while the corn filled hole is hard to distinguish from the background organic glass. This is because that the attenuation coefficient of corn flour is very similar to that of the organic glass, while the attenuation coefficients of air and copper are very different from that of the organic glass.


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 iamges from 120 views of fan-beam projections with FBP. The display gray scale window is [80,400].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 16: Restored iamges from 120 views of fan-beam projections with FBP. The display gray scale window is [80,400].
Mentions: In the experiment, the detector has 1024 bins, and the physical size of each bin is 0.05 millimeters. Therefore, the raw sinogram of one view has 1024 pixels, and each pixel represents the physical length of 0.05 millimeters. However, the computation load of the iterative reconstruction is very heavy for the high resolution sinogram. Thus the high resolution sinogram is down sampled by the ratio of 4. And the low resolution sinogram of one view has 256 = 1024 ÷ 4 pixels. To maintain the physical length of the projection geometry, each pixel in the low resolution sinogram represents the physical length of 0.2 = 0.05 × 4 millimetres. Actually, in this down sampling, four neighboring pixels in the raw sinogram of one view is averaged as one pixel in the low resolution sinogram of one view.In this experiment, restrained by the micro-CT machine, the whole projection data contains 120 views of fan-beam projection uniformly distributed across 360°. Its FBP reconstruction is shown in Figure 16. Compare Figure 15 and 16, it is easy to distinguish the air and copper filled holes from the background organic glass, while the corn filled hole is hard to distinguish from the background organic glass. This is because that the attenuation coefficient of corn flour is very similar to that of the organic glass, while the attenuation coefficients of air and copper are very different from that of the organic glass.

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