title: Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions.
abstract: OBJECTIVE
  The purpose of this work is to combine two areas of active research in tomographic x-ray imaging. The first one is the use of iterative reconstruction (IR) techniques. The second one is differential phase contrast imaging (DPCI).
  
  
  METHODS
  The authors derive a maximum likelihood (ML) reconstruction algorithm with regularization for DPCI. Forward and back-projection are implemented using spherically symmetric basis functions (blobs) and differential footprints, thus completely avoiding the need for numerical differentiation throughout the reconstruction process. The method is applied to the problem of reconstruction of an object from sparsely sampled projections.
  
  
  RESULTS
  The results show that the proposed method can handle the sparsely sampled data efficiently. In particular no streak artifacts are visible which are present in images obtained by filtered back-projection (FBP).
  
  
  CONCLUSIONS
  IR algorithms have a wide spectrum of proven advantages in the area of conventional computed tomography. The present work describes for the first time, how a matched forward and back-projection can be implemented for DPCI, which is furthermore free of any heuristics. The newly developed ML reconstruction algorithm for DPCI shows that for the case of sparsely sampled projection data, an improvement in image quality is obtained that is qualitatively comparable to a corresponding situation in conventional x-ray imaging. Based on the proposed operators for forward and back-projection, a large variety of IR algorithms is thus made available for DPCI.
authors.forename: Thomas
authors.initials: T
authors.lastname: Köhler
authors.forename: Bernhard
authors.initials: B
authors.lastname: Brendel
authors.forename: Ewald
authors.initials: E
authors.lastname: Roessl
mesh_terms: D000465:Algorithms; D006801:Humans; D016013:Likelihood Functions; D019047:Phantoms, Imaging; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D014057:Tomography, X-Ray Computed / Q000706:statistics & numerical data*