2015/12/03 by Linh V. Nguyen, Nguyen, Linh V.
Engineering · Mathematics · Medicine · #35S05 #35S30 #44A12 #92C55 #Advanced X-ray and CT Imaging #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Medical Imaging Techniques and Applications #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1512.01287
openalex publication_date 2015/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study the limited angle problem for the weighted X-ray\ntransform. We consider the approximate reconstructions by applying two filtered\nback projection formulas to the limited data. We prove that each resulted\noperator can be decomposed into the sum of three Fourier integral operators\nwhose symbols are of types ( varrho,\δ) \≠ (1,0). The first operator,\nbeing a pseudo-differential operator, is responsible for the reconstruction of\nvisible singularities. The other two are responsible for the generation of the\nartifacts. The theory of Fourier integral operators then implies, in\nparticular, the continuity of the reconstruction operator and geometry of the\nartifacts. We then extend the technique developed by the author in [Inverse\nProblems 31 (2015) 055003] to obtain more refined microlocal estimates for the\nstrength of the artifacts.\n