title: Penalized maximum likelihood reconstruction for x-ray differential phase-contrast tomography.
abstract: OBJECTIVE
  The purpose of this work is to propose a cost function with regularization to iteratively reconstruct attenuation, phase, and scatter images simultaneously from differential phase contrast (DPC) acquisitions, without the need of phase retrieval, and examine its properties. Furthermore this reconstruction method is applied to an acquisition pattern that is suitable for a DPC tomographic system with continuously rotating gantry (sliding window acquisition), overcoming the severe smearing in noniterative reconstruction.
  
  
  METHODS
  We derive a penalized maximum likelihood reconstruction algorithm to directly reconstruct attenuation, phase, and scatter image from the measured detector values of a DPC acquisition. The proposed penalty comprises, for each of the three images, an independent smoothing prior. Image quality of the proposed reconstruction is compared to images generated with FBP and iterative reconstruction after phase retrieval. Furthermore, the influence between the priors is analyzed. Finally, the proposed reconstruction algorithm is applied to experimental sliding window data acquired at a synchrotron and results are compared to reconstructions based on phase retrieval.
  
  
  RESULTS
  The results show that the proposed algorithm significantly increases image quality in comparison to reconstructions based on phase retrieval. No significant mutual influence between the proposed independent priors could be observed. Further it could be illustrated that the iterative reconstruction of a sliding window acquisition results in images with substantially reduced smearing artifacts.
  
  
  CONCLUSIONS
  Although the proposed cost function is inherently nonconvex, it can be used to reconstruct images with less aliasing artifacts and less streak artifacts than reconstruction methods based on phase retrieval. Furthermore, the proposed method can be used to reconstruct images of sliding window acquisitions with negligible smearing artifacts.
authors.affiliation: Research Laboratories, Philips GmbH Innovative Technologies, Hamburg D-22335, Germany.
authors.forename: Bernhard
authors.initials: B
authors.lastname: Brendel
authors.affiliation: Lehrstuhl für Biomedizinische Physik, Physik-Department und Institut für Medizintechnik, Technische Universität München, Garching D-85748, Germany.
authors.forename: Maximilian
authors.initials: M
authors.lastname: von Teuffenbach
authors.affiliation: Department of Radiology, Technische Universität München, Munich D-80333, Germany.
authors.forename: Peter B
authors.initials: PB
authors.lastname: Noël
authors.affiliation: Lehrstuhl für Biomedizinische Physik, Physik-Department und Institut für Medizintechnik, Technische Universität München, Garching D-85748, Germany and Department of Radiology, Technische Universität München, Munich D-80333, Germany.
authors.forename: Franz
authors.initials: F
authors.lastname: Pfeiffer
authors.affiliation: Research Laboratories, Philips GmbH Innovative Technologies, Hamburg D-22335, Germany and Institute for Advanced Study, Technische Universität München, Garching D-85748, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Koehler
mesh_terms: D000818:Animals; D016477:Artifacts; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016013:Likelihood Functions; D051381:Rats; D014054:Tomography; D014965:X-Rays