title: Total variation minimization approach in in-line x-ray phase-contrast tomography.
abstract: The reconstruction problem in in-line X-ray Phase-Contrast Tomography is usually approached by solving two independent linearized sub-problems: phase retrieval and tomographic reconstruction. Both problems are often ill-posed and require the use of regularization techniques that lead to artifacts in the reconstructed image. We present a novel reconstruction approach that solves two coupled linear problems algebraically. Our approach is based on the assumption that the frequency space of the tomogram can be divided into bands that are accurately recovered and bands that are undefined by the observations. This results in an underdetermined linear system of equations. We investigate how this system can be solved using three different algebraic reconstruction algorithms based on Total Variation minimization. These algorithms are compared using both simulated and experimental data. Our results demonstrate that in many cases the proposed algebraic algorithms yield a significantly improved accuracy over the conventional L2-regularized closed-form solution. This work demonstrates that algebraic algorithms may become an important tool in applications where the acquisition time and the delivered radiation dose must be minimized.
authors.affiliation: Department of Imaging Science & Technology, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
authors.forename: Alexander
authors.initials: A
authors.lastname: Kostenko
authors.forename: K Joost
authors.initials: KJ
authors.lastname: Batenburg
authors.forename: Andrew
authors.initials: A
authors.lastname: King
authors.forename: S Erik
authors.initials: SE
authors.lastname: Offerman
authors.forename: Lucas J
authors.initials: LJ
authors.lastname: van Vliet
mesh_terms: D000465:Algorithms; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*