TY - JOUR
T1 - A parametrix method in integral geometry
AU - Palamodov, V. P.
N1 - Publisher Copyright:
© 2015, Hebrew University Magnes Press.
PY - 2015/1
Y1 - 2015/1
N2 - The objective of reconstructive integral geometry is to recover a function from its integrals over a set of subvarieties. A parametrix is a method of reconstruction of a function from its integral data up to a smoothing operator. In the simplest case, a parametrix recovers a function with a jump singularity along a curve (surface) up to a continuous function, which can be quite informative in medical imaging. We provide an explicit construction for a wide class of acquisition geometries. The case of photo-acoustic geometry is of special interest.
AB - The objective of reconstructive integral geometry is to recover a function from its integrals over a set of subvarieties. A parametrix is a method of reconstruction of a function from its integral data up to a smoothing operator. In the simplest case, a parametrix recovers a function with a jump singularity along a curve (surface) up to a continuous function, which can be quite informative in medical imaging. We provide an explicit construction for a wide class of acquisition geometries. The case of photo-acoustic geometry is of special interest.
UR - http://www.scopus.com/inward/record.url?scp=84922531560&partnerID=8YFLogxK
U2 - 10.1007/s11854-015-0011-7
DO - 10.1007/s11854-015-0011-7
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AN - SCOPUS:84922531560
SN - 0021-7670
VL - 125
SP - 353
EP - 370
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -