title: Exact and approximate Fourier rebinning algorithms for the solution of the data truncation problem in 3-D PET.
abstract: This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.
authors.affiliation: Montpellier II University, Mathematics and Modeling Institute, Place Eugène Bataillon, Montpellier 34095 Cedex 5, France. faybenb@hotmail.com
authors.forename: Fayçal Ben
authors.initials: FB
authors.lastname: Bouallègue
authors.forename: Jean-François
authors.initials: JF
authors.lastname: Crouzet
authors.forename: Claude
authors.initials: C
authors.lastname: Comtat
authors.forename: Marjolaine
authors.initials: M
authors.lastname: Fourcade
authors.forename: Bijan
authors.initials: B
authors.lastname: Mohammadi
authors.forename: Denis
authors.initials: D
authors.lastname: Mariano-Goulart
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000000981:diagnostic imaging*; D005583:Fourier Analysis; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D049268:Positron-Emission Tomography / Q000379:methods*; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity