title: Cone-beam and fan-beam image reconstruction algorithms based on spherical and circular harmonics.
abstract: A cone-beam image reconstruction algorithm using spherical harmonic expansions is proposed. The reconstruction algorithm is in the form of a summation of inner products of two discrete arrays of spherical harmonic expansion coefficients at each cone-beam point of acquisition. This form is different from the common filtered backprojection algorithm and the direct Fourier reconstruction algorithm. There is no re-sampling of the data, and spherical harmonic expansions are used instead of Fourier expansions. As a special case, a new fan-beam image reconstruction algorithm is also derived in terms of a circular harmonic expansion. Computer simulation results for both cone-beam and fan-beam algorithms are presented for circular planar orbit acquisitions. The algorithms give accurate reconstructions; however, the implementation of the cone-beam reconstruction algorithm is computationally intensive. A relatively efficient algorithm is proposed for reconstructing the central slice of the image when a circular scanning orbit is used.
authors.affiliation: Utah Center for Advanced Imaging Research, University of Utah, 729 Arapeen Drive, Salt Lake City, Utah 84108, USA. larry@ucair.med.utah.edu
authors.forename: Gengsheng L
authors.initials: GL
authors.lastname: Zeng
authors.forename: Grant T
authors.initials: GT
authors.lastname: Gullberg
mesh_terms: D000465:Algorithms; D005240:Feasibility Studies; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D036542:Tomography, Spiral Computed / Q000295:instrumentation / Q000379:methods*