2015/10/24 by Jürgen Frikel, Frikel, Jürgen, Eric Todd Quinto +1
Computer Science · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Radiation Dose and Imaging
paper · pdf · doi:10.48550/arxiv.1510.07151
openalex publication_date 2015/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the generalized Radon transform (defined in terms of smooth\nweight functions) on hyperplanes in \ℝn. We analyze general filtered\nbackprojection type reconstruction methods for limited data with filters given\nby general pseudodifferential operators. We provide microlocal\ncharacterizations of visible and added singularities in \ℝn and\ndefine modified versions of reconstruction operators that do not generate added\nartifacts. We calculate the symbol of our general reconstruction operators as\npseudodifferential operators, and provide conditions for the filters under\nwhich the reconstruction operators are elliptic for the visible singularities.\nIf the filters are chosen according to those conditions, we show that almost\nall visible singularities can be recovered reliably. Our work generalizes the\nresults for the classical line transforms in \ℝ2 and the classical\nreconstruction operators (that use specific filters). In our proofs, we employ\na general paradigm that is based on the calculus of Fourier integral operators.\nSince this technique does not rely on explicit expressions of the\nreconstruction operators, it enables us to analyze more general imaging\nsituations.\n