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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

Algorithm used to solve (19).
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alg1: Algorithm used to solve (19).

Mentions: To solve the proposed formulation, a fast composite splitting algorithm (FCSA) [41–43] is used to decompose (19) into two simpler subproblems given by(20)x^1=arg⁡minx⁡f1x,f1x=12y−AxC2+μ1WTxq,x^2=arg⁡minx⁡f2x,f2x=12y−AxC2+μ2TVf,in which y is the measured data interpolated/rebinned on the equally sloped lines, A is the PPFT-based Radon transform, and AT is its adjoint. By calculating and , the FCSA method proposes that the solution to the problem can be obtained by a linear combination of the solutions of the two subproblems; that is,(21)x^=Δx^1+1−Δx^2,in which Δ = f2/(f1 + f2) is a function of the values of the objective functions of the two subproblems. Each of these subproblems can be solved by a subgradient-projection based method [44]. The pseudocode of the proposed recovery is shown in Algorithm 1, in which prox{g(x), z} = arg minxg(x) + (1/2)‖x − z‖22. To find , the optimization problem in step (2) of this algorithm can be solved by a wavelet soft thresholding algorithm [36]. Moreover, to calculate in step (3), the split Bregman TV based denoising algorithm as proposed in [45] was used. Finally, to estimate in the kth iteration, (21) was used.


Accelerated Compressed Sensing Based CT Image Reconstruction.

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

Algorithm used to solve (19).
© Copyright Policy
Related In: Results  -  Collection

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

alg1: Algorithm used to solve (19).
Mentions: To solve the proposed formulation, a fast composite splitting algorithm (FCSA) [41–43] is used to decompose (19) into two simpler subproblems given by(20)x^1=arg⁡minx⁡f1x,f1x=12y−AxC2+μ1WTxq,x^2=arg⁡minx⁡f2x,f2x=12y−AxC2+μ2TVf,in which y is the measured data interpolated/rebinned on the equally sloped lines, A is the PPFT-based Radon transform, and AT is its adjoint. By calculating and , the FCSA method proposes that the solution to the problem can be obtained by a linear combination of the solutions of the two subproblems; that is,(21)x^=Δx^1+1−Δx^2,in which Δ = f2/(f1 + f2) is a function of the values of the objective functions of the two subproblems. Each of these subproblems can be solved by a subgradient-projection based method [44]. The pseudocode of the proposed recovery is shown in Algorithm 1, in which prox{g(x), z} = arg minxg(x) + (1/2)‖x − z‖22. To find , the optimization problem in step (2) of this algorithm can be solved by a wavelet soft thresholding algorithm [36]. Moreover, to calculate in step (3), the split Bregman TV based denoising algorithm as proposed in [45] was used. Finally, to estimate in the kth iteration, (21) was used.

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