Program Information
Random Undersampled Cone Beam CT: Theoretical Analysis and a Novel Reconstruction Method
C Shen1*, Y Lou2 , L Chen1 , X Jia1 , (1) The University of Texas Southwestern Medical Center, Dallas, TX, (2) The University of Texas at Dallas, Dallas, Texas
Presentations
WE-AB-207A-4 (Wednesday, August 3, 2016) 7:30 AM - 9:30 AM Room: 207A
Purpose: Reducing x-ray exposure and speeding up data acquisition motived studies on projection data undersampling. It is an important question that for a given undersampling ratio, what the optimal undersampling approach is. In this study, we propose a new undersampling scheme: random-ray undersampling. We will mathematically analyze its projection matrix properties and demonstrate its advantages. We will also propose a new reconstruction method that simultaneously performs CT image reconstruction and projection domain data restoration.
Methods: By representing projection operator under the basis of singular vectors of full projection operator, matrix representations for an undersampling case can be generated and numerical singular value decomposition can be performed. We compared properties of matrices among three undersampling approaches: regular-view undersampling, regular-ray undersampling, and the proposed random-ray undersampling. To accomplish CT reconstruction for random undersampling, we developed a novel method that iteratively performs CT reconstruction and missing projection data restoration via regularization approaches.
Results: For a given undersampling ratio, random-ray undersampling preserved mathematical properties of full projection operator better than the other two approaches. This translates to advantages of reconstructing CT images at lower errors. Different types of image artifacts were observed depending on undersampling strategies, which were ascribed to the unique singular vectors of the sampling operators in the image domain. We tested the proposed reconstruction algorithm on a Forbid phantom with only 30% of the projection data randomly acquired. Reconstructed image error was reduced from 9.4% in a TV method to 7.6% in the proposed method.
Conclusion: The proposed random-ray undersampling is mathematically advantageous over other typical undersampling approaches. It may permit better image reconstruction at the same undersampling ratio. The novel algorithm suitable for this random-ray undersampling was able to reconstruct high-quality images.
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