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Techn. Fakultät Willkommen am Institut für Informatik FAU-Logo

Yixing Huang M. Sc.

Researcher in the Analytic Reconstruction and Consistency (ARC) group at the Pattern Recognition Lab of the Friedrich-Alexander-Universität Erlangen-Nürnberg

Yixing Huang

Limited Angle Reconstruction with Iterative Reweighted Total Variation Minimization

In 2D fan beam computed tomography, the x ray source needs to rotate at least Π+2γmax in order to get complete data. However, in limited angle tomography, the scan angle is less than than Π+2γmax and thus artefacts occur with Filtered Backprojection (FBP) algorithm due to data loss, as Fig 1 shows.
Recently, the compressed sensing (CS) technologies attract significant attention and a variety of total variation (TV) minimization algorithms are applied in medical imaging processing. Here the iterative reweighted total variation (wTV) algorithm proposed by Candes et al is used for limited angle reconstruction and it proves to be very powerful to remove the artefacts while keeping the image resolution.

     Fig 1: FBP reconstruction                                   Fig 2: wTV reconstruction

 

 
 
Missing Data Restoration in Limited Angle Tomography based on Helgason-Ludwig Consistency Conditions
In limited angle tomography, missing data in an insufficient angular scan will cause streak artifacts 
in the reconstructed images. Correspondingly, in the frequency domain representation of the imaged 
object, a double wedge-shaped region is missing. In this paper, we perform a regression in sinogram 
domain and an image fusion in frequency domain to restore the missing data. We first convert the 
sinogram restoration problem into a regression problem based on the Helgason-Ludwig consistency 
conditions. Due to its severe ill-posedness, regression only partially recovers the correct frequency 
components, especially lower frequency components, and will introduce erroneous ones, particularly 
higher frequencies. Bilateral filtering is utilized to retain the most prominent high frequency 
components and suppress erroneous ones. Afterwards, a fusion in the frequency domain utilizes the 
restored frequency components to fill the missing double wedge region. The proposed method is 
evaluated in a parallel-beam study on both numerical and clinical phantoms. The results show that our 
method is promising in streak reduction and intensity offset compensation in both noise-free and noisy 
situations.