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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

An example of calculating the interpolation error in the error adaptation weight (EAW).
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fig3: An example of calculating the interpolation error in the error adaptation weight (EAW).

Mentions: The value of ϵi represents the error of the interpolated samples. If the interpolated sample is close to the original measurements, the value of ϵi is small and the confidence about the interpolated value is high. If the angular distance of the measured data from the interpolated line is more than the angular difference of the equally sloped lines, the interpolation error is considered to be high (ϵi → ∞): this follows from the fact that the distance of points on the line from the true measured values is maximal and therefore the error is maximal. Using (18), this condition corresponds to ci → 0. The closer the equally sloped lines are to the rays on which the measurements are made, the smaller the interpolation error will be, so that ϵis on that line get closer to zero. Finally, if the desired equally sloped rays are exactly on the polar lines, the interpolation error ei is zero, which is equivalent to ϵi = 0. This process is illustrated in Figure 3.


Accelerated Compressed Sensing Based CT Image Reconstruction.

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

An example of calculating the interpolation error in the error adaptation weight (EAW).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig3: An example of calculating the interpolation error in the error adaptation weight (EAW).
Mentions: The value of ϵi represents the error of the interpolated samples. If the interpolated sample is close to the original measurements, the value of ϵi is small and the confidence about the interpolated value is high. If the angular distance of the measured data from the interpolated line is more than the angular difference of the equally sloped lines, the interpolation error is considered to be high (ϵi → ∞): this follows from the fact that the distance of points on the line from the true measured values is maximal and therefore the error is maximal. Using (18), this condition corresponds to ci → 0. The closer the equally sloped lines are to the rays on which the measurements are made, the smaller the interpolation error will be, so that ϵis on that line get closer to zero. Finally, if the desired equally sloped rays are exactly on the polar lines, the interpolation error ei is zero, which is equivalent to ϵi = 0. This process is illustrated in Figure 3.

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