title: Combined mixed approach algorithm for in-line phase-contrast x-ray imaging.
abstract: OBJECTIVE
  In the past decade, phase-contrast imaging (PCI) has been applied to study different kinds of tissues and human body parts, with an increased improvement of the image quality with respect to simple absorption radiography. A technique closely related to PCI is phase-retrieval imaging (PRI). Indeed, PCI is an imaging modality thought to enhance the total contrast of the images through the phase shift introduced by the object (human body part); PRI is a mathematical technique to extract the quantitative phase-shift map from PCI. A new phase-retrieval algorithm for the in-line phase-contrast x-ray imaging is here proposed.
  
  
  METHODS
  The proposed algorithm is based on a mixed transfer-function and transport-of-intensity approach (MA) and it requires, at most, an initial approximate estimate of the average phase shift introduced by the object as prior knowledge. The accuracy in the initial estimate determines the convergence speed of the algorithm. The proposed algorithm retrieves both the object phase and its complex conjugate in a combined MA (CMA).
  
  
  RESULTS
  Although slightly less computationally effective with respect to other mixed-approach algorithms, as two phases have to be retrieved, the results obtained by the CMA on simulated data have shown that the obtained reconstructed phase maps are characterized by particularly low normalized mean square errors. The authors have also tested the CMA on noisy experimental phase-contrast data obtained by a suitable weakly absorbing sample consisting of a grid of submillimetric nylon fibers as well as on a strongly absorbing object made of a 0.03 mm thick lead x-ray resolution star pattern. The CMA has shown a good efficiency in recovering phase information, also in presence of noisy data, characterized by peak-to-peak signal-to-noise ratios down to a few dBs, showing the possibility to enhance with phase radiography the signal-to-noise ratio for features in the submillimetric scale with respect to the attenuation-based imaging.
  
  
  CONCLUSIONS
  It has been shown that phase-retrieved radiographies can be used both to have quantitative phase information about soft tissues, complementary to the attenuation information, and to enhance the visibility of details inside soft tissues, with higher efficiency with respect to phase radiography.
authors.affiliation: Istituto di Cristallografia-Consiglio Nazionale delle Ricerche (IC-CNR), via Amendola 122/0, 1-70125 Bari, Italy. liberato.decaro@ic.cnr.it
authors.forename: Liberato
authors.initials: L
authors.lastname: De Caro
authors.forename: Francesco
authors.initials: F
authors.lastname: Scattarella
authors.forename: Cinzia
authors.initials: C
authors.lastname: Giannini
authors.forename: Sabina
authors.initials: S
authors.lastname: Tangaro
authors.forename: Luigi
authors.initials: L
authors.lastname: Rigon
authors.forename: Renata
authors.initials: R
authors.lastname: Longo
authors.forename: Roberto
authors.initials: R
authors.lastname: Bellotti
mesh_terms: D000042:Absorption; D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted; D014965:X-Rays