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Analysis of iterative region-of-interest image reconstruction for x-ray computed tomography.

Sidky EY, Kraemer DN, Roth EG, Ullberg C, Reiser IS, Pan X - J Med Imaging (Bellingham) (2014)

Bottom Line: In order to characterize this optimization problem, we apply it to computer-simulated two-dimensional fan-beam CT data, using both ideal noiseless data and realistic data containing a level of noise comparable to that of the breast CT application.The proposed method is demonstrated for both complete field-of-view and ROI imaging.To demonstrate the potential utility of the proposed ROI imaging method, it is applied to actual CT scanner data.

View Article: PubMed Central - PubMed

Affiliation: University of Chicago, Department of Radiology, 5841 South Maryland Avenue, Chicago, Illinois 60637, United States.

ABSTRACT

One of the challenges for iterative image reconstruction (IIR) is that such algorithms solve an imaging model implicitly, requiring a complete representation of the scanned subject within the viewing domain of the scanner. This requirement can place a prohibitively high computational burden for IIR applied to x-ray computed tomography (CT), especially when high-resolution tomographic volumes are required. In this work, we aim to develop an IIR algorithm for direct region-of-interest (ROI) image reconstruction. The proposed class of IIR algorithms is based on an optimization problem that incorporates a data fidelity term, which compares a derivative of the estimated data with the available projection data. In order to characterize this optimization problem, we apply it to computer-simulated two-dimensional fan-beam CT data, using both ideal noiseless data and realistic data containing a level of noise comparable to that of the breast CT application. The proposed method is demonstrated for both complete field-of-view and ROI imaging. To demonstrate the potential utility of the proposed ROI imaging method, it is applied to actual CT scanner data.

No MeSH data available.


Maximum and minimum singular values for the combined system matrix  for a two-dimensional CT configuration with image pixel array  and projection data set consisting of  projections over a  scanning arc and a linear detector array with  detection elements. The solid circles represent singular values arrived at through direct SVD of a small system with  ranging from 18 to 64. The solid diamond represents extrapolation to the case of interest at . The linear fitting model is displayed in the legend of each graph.
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f6: Maximum and minimum singular values for the combined system matrix for a two-dimensional CT configuration with image pixel array and projection data set consisting of projections over a scanning arc and a linear detector array with detection elements. The solid circles represent singular values arrived at through direct SVD of a small system with ranging from 18 to 64. The solid diamond represents extrapolation to the case of interest at . The linear fitting model is displayed in the legend of each graph.

Mentions: In order to understand the phantom recovery, we apply singular value decomposition (SVD) in a manner similar to that of Ref. 14. We note that under ideal noiseless conditions, the minimizer of with and satisfies the following linear equation: DuXf=DuXf0,(16)where is the test phantom. If the combined system matrix is left-invertible then this equation can be reduced to and the minimizer of with and is the test phantom . The system matrix is left-invertible if its condition number is finite. We demonstrate this by performing SVD on smaller systems with the same sampling ratio, computing the corresponding condition numbers, and extrapolating to the system size of interest. The present sampling ratio takes the form of projections onto a detector of bins for an image represented on an pixel grid, where . The largest and smallest singular values for systems with the same sampling ratio are shown in Fig. 6 for varying between 18 and 64. Assuming a linear relationship between the logarithm of these singular values and the logarithm of , a condition number of 8.87 is estimated for the present system corresponding to . Thus, is left-invertible and the minimizer of is , thereby explaining the accurate phantom recovery shown in Fig. 5.


Analysis of iterative region-of-interest image reconstruction for x-ray computed tomography.

Sidky EY, Kraemer DN, Roth EG, Ullberg C, Reiser IS, Pan X - J Med Imaging (Bellingham) (2014)

Maximum and minimum singular values for the combined system matrix  for a two-dimensional CT configuration with image pixel array  and projection data set consisting of  projections over a  scanning arc and a linear detector array with  detection elements. The solid circles represent singular values arrived at through direct SVD of a small system with  ranging from 18 to 64. The solid diamond represents extrapolation to the case of interest at . The linear fitting model is displayed in the legend of each graph.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4326078&req=5

f6: Maximum and minimum singular values for the combined system matrix for a two-dimensional CT configuration with image pixel array and projection data set consisting of projections over a scanning arc and a linear detector array with detection elements. The solid circles represent singular values arrived at through direct SVD of a small system with ranging from 18 to 64. The solid diamond represents extrapolation to the case of interest at . The linear fitting model is displayed in the legend of each graph.
Mentions: In order to understand the phantom recovery, we apply singular value decomposition (SVD) in a manner similar to that of Ref. 14. We note that under ideal noiseless conditions, the minimizer of with and satisfies the following linear equation: DuXf=DuXf0,(16)where is the test phantom. If the combined system matrix is left-invertible then this equation can be reduced to and the minimizer of with and is the test phantom . The system matrix is left-invertible if its condition number is finite. We demonstrate this by performing SVD on smaller systems with the same sampling ratio, computing the corresponding condition numbers, and extrapolating to the system size of interest. The present sampling ratio takes the form of projections onto a detector of bins for an image represented on an pixel grid, where . The largest and smallest singular values for systems with the same sampling ratio are shown in Fig. 6 for varying between 18 and 64. Assuming a linear relationship between the logarithm of these singular values and the logarithm of , a condition number of 8.87 is estimated for the present system corresponding to . Thus, is left-invertible and the minimizer of is , thereby explaining the accurate phantom recovery shown in Fig. 5.

Bottom Line: In order to characterize this optimization problem, we apply it to computer-simulated two-dimensional fan-beam CT data, using both ideal noiseless data and realistic data containing a level of noise comparable to that of the breast CT application.The proposed method is demonstrated for both complete field-of-view and ROI imaging.To demonstrate the potential utility of the proposed ROI imaging method, it is applied to actual CT scanner data.

View Article: PubMed Central - PubMed

Affiliation: University of Chicago, Department of Radiology, 5841 South Maryland Avenue, Chicago, Illinois 60637, United States.

ABSTRACT

One of the challenges for iterative image reconstruction (IIR) is that such algorithms solve an imaging model implicitly, requiring a complete representation of the scanned subject within the viewing domain of the scanner. This requirement can place a prohibitively high computational burden for IIR applied to x-ray computed tomography (CT), especially when high-resolution tomographic volumes are required. In this work, we aim to develop an IIR algorithm for direct region-of-interest (ROI) image reconstruction. The proposed class of IIR algorithms is based on an optimization problem that incorporates a data fidelity term, which compares a derivative of the estimated data with the available projection data. In order to characterize this optimization problem, we apply it to computer-simulated two-dimensional fan-beam CT data, using both ideal noiseless data and realistic data containing a level of noise comparable to that of the breast CT application. The proposed method is demonstrated for both complete field-of-view and ROI imaging. To demonstrate the potential utility of the proposed ROI imaging method, it is applied to actual CT scanner data.

No MeSH data available.