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Accelerated Compressed Sensing Based CT Image Reconstruction.

Hashemi S, Beheshti S, Gill PR, Paul NS, Cobbold RS - Comput Math Methods Med (2015)

Bottom Line: Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors.Simulation results are shown for phantoms and a patient.Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

View Article: PubMed Central - PubMed

Affiliation: Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada M5S 3G9.

ABSTRACT
In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

No MeSH data available.


Related in: MedlinePlus

(a) Pseudopolar grids: red lines are basically horizontal (BH) and the black lines are basically vertical (BV). (b) Polar grids (red dots) on the pseudopolar grids (gray dots).
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fig1: (a) Pseudopolar grids: red lines are basically horizontal (BH) and the black lines are basically vertical (BV). (b) Polar grids (red dots) on the pseudopolar grids (gray dots).

Mentions: An equally sloped tomography (EST) method was originally proposed for electron beam tomography [20–22] to improve the DFR-based algorithms. EST is an iterative method that makes use of the pseudopolar Fourier transform (PPFT) [23]. It calculates the Fourier coefficients of an image directly on pseudopolar grids, which contain two types of samples: basically horizontal (BH) and basically vertical (BV), as can be seen in Figure 1. To reconstruct an N × N image from its PPFT coefficients, 4N2 samples are needed (2N samples on 2N equally sloped radial lines). A fast algorithm has been proposed by Averbuch et al. [23] to calculate the PPFT and its adjoint with complexity of O(N2logN). This algorithm can then be used to implement a fast and efficient 2D Radon transform on the equally sloped radial lines. The PPFT has three important properties which makes it a good alternative to conventional DFR methods: (1) it is closer to a polar (equiangular line) grid than to a Cartesian grid, which significantly decreases the gridding error, (2) it has both a fast forward and a fast backward calculation algorithm [23], which enables our proposed algorithm to avoid the regridding step used in iterative non-Cartesian Fourier based reconstruction methods, and (3) it has an analytical adjoint function. As a result, it can efficiently be used in iterative algorithms, including compressed sensing [24, 25]. However, it should be noted that Fourier-based reconstruction algorithms, for example, ESR and DFR, are only valid for parallel X-ray projections.


Accelerated Compressed Sensing Based CT Image Reconstruction.

Hashemi S, Beheshti S, Gill PR, Paul NS, Cobbold RS - Comput Math Methods Med (2015)

(a) Pseudopolar grids: red lines are basically horizontal (BH) and the black lines are basically vertical (BV). (b) Polar grids (red dots) on the pseudopolar grids (gray dots).
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4489012&req=5

fig1: (a) Pseudopolar grids: red lines are basically horizontal (BH) and the black lines are basically vertical (BV). (b) Polar grids (red dots) on the pseudopolar grids (gray dots).
Mentions: An equally sloped tomography (EST) method was originally proposed for electron beam tomography [20–22] to improve the DFR-based algorithms. EST is an iterative method that makes use of the pseudopolar Fourier transform (PPFT) [23]. It calculates the Fourier coefficients of an image directly on pseudopolar grids, which contain two types of samples: basically horizontal (BH) and basically vertical (BV), as can be seen in Figure 1. To reconstruct an N × N image from its PPFT coefficients, 4N2 samples are needed (2N samples on 2N equally sloped radial lines). A fast algorithm has been proposed by Averbuch et al. [23] to calculate the PPFT and its adjoint with complexity of O(N2logN). This algorithm can then be used to implement a fast and efficient 2D Radon transform on the equally sloped radial lines. The PPFT has three important properties which makes it a good alternative to conventional DFR methods: (1) it is closer to a polar (equiangular line) grid than to a Cartesian grid, which significantly decreases the gridding error, (2) it has both a fast forward and a fast backward calculation algorithm [23], which enables our proposed algorithm to avoid the regridding step used in iterative non-Cartesian Fourier based reconstruction methods, and (3) it has an analytical adjoint function. As a result, it can efficiently be used in iterative algorithms, including compressed sensing [24, 25]. However, it should be noted that Fourier-based reconstruction algorithms, for example, ESR and DFR, are only valid for parallel X-ray projections.

Bottom Line: Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors.Simulation results are shown for phantoms and a patient.Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

View Article: PubMed Central - PubMed

Affiliation: Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada M5S 3G9.

ABSTRACT
In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

No MeSH data available.


Related in: MedlinePlus