Z-Index Parameterization (ZIP) for Volumetric CT Image Reconstruction via 3D Dictionary Learning

Ti Bai, Hao Yan, Xun Jia, Steve Jiang, Ge Wang, Xuanqin Mou

Research output: Contribution to journalArticle

10 Scopus citations


Despite the rapid developments of x-ray cone-beam CT (CBCT), image noise still remains a major issue for the low dose CBCT. To suppress the noise effectively while retain the structures well for low dose CBCT image, in this work, a sparse constraint based on the 3D dictionary is incorporated into a regularized iterative reconstruction framework, defining the 3DDL method. In addition, by analyzing the sparsity level curve associated with different regularization parameters, a new adaptive parameter selection strategy is proposed to facilitate our 3DDL method. To justify the proposed method, we first analyze the distributions of the representation coefficients associated with the 3D dictionary and the conventional 2D dictionary to compare their efficiencies in representing volumetric images. Then, multiple real data experiments are conducted for performance validation. Based on these results, we found: (1) the 3D dictionary based sparse coefficients have three orders narrower Laplacian distribution compared to the 2D dictionary, suggesting the higher representation efficiencies of the 3D dictionary; (2) the sparsity level curve demonstrates a clear Z-shape, and hence referred to as Z-curve in this paper; (3) the parameter associated with the maximum curvature point of the Z-curve suggests a nice parameter choice, which could be adaptively located with the proposed Z-index parameterization (ZIP) method; (4) the proposed 3DDL algorithm equipped with the ZIP method could deliver reconstructions with the lowest root mean squared errors (RMSE) and the highest structural similarity (SSIM) index compared to the competing methods; (5) similar noise performance as the regular dose FDK reconstruction regarding the standard deviation metric could be achieved with the proposed method using 1/2 / 1/4 / 1/8 dose level projections. The contrast-noise ratio (CNR) is improved by ~ 2.5/3.5 times with respect to two different cases under the 1/8 dose level compared to the low dose FDK reconstruction. The proposed method is expected to reduce the radiation dose by a factor of 8 for CBCT, considering the voted strongly discriminated low contrast tissues.

Original languageEnglish (US)
JournalIEEE Transactions on Medical Imaging
StateAccepted/In press - Oct 4 2017


  • Computed tomography
  • cone-beam CT
  • Dictionaries
  • Dictionary learning
  • Image reconstruction
  • Machine learning
  • Matching pursuit algorithms
  • noise suppression
  • regularization parameter
  • sparse representation
  • Three-dimensional displays
  • Two dimensional displays

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

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