TY - JOUR
T1 - Inversion formula for the conical Radon transform arising in a single first semicircle second Compton camera with rotation
AU - Moon, Sunghwan
AU - Kwon, Kiwoon
N1 - Publisher Copyright:
© 2019, The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - Since a Compton camera and its data type were introduced, several types of conical Radon transforms have been studied. To increase the accuracy, new Compton camera designs have been proposed (Smith, Technologies 3(4):219–237, 2015). Among these, we consider the Single First Semicircle Second (SFSS) camera design consisting of a first (scattering) detector element and a second (absorption) detector shaped as a semicircle. Here we introduce a new type of a conical Radon transform which this SFSS Compton camera design brings about. To obtain sufficient data, we rotate the SFSS camera around the object of interest. Also, we provide an inversion formula for this conical Radon transform and generalize this result to an n-dimensional conical Radon transform. To demonstrate our suggested algorithm, numerical simulations for the 3-dimensional case are presented.
AB - Since a Compton camera and its data type were introduced, several types of conical Radon transforms have been studied. To increase the accuracy, new Compton camera designs have been proposed (Smith, Technologies 3(4):219–237, 2015). Among these, we consider the Single First Semicircle Second (SFSS) camera design consisting of a first (scattering) detector element and a second (absorption) detector shaped as a semicircle. Here we introduce a new type of a conical Radon transform which this SFSS Compton camera design brings about. To obtain sufficient data, we rotate the SFSS camera around the object of interest. Also, we provide an inversion formula for this conical Radon transform and generalize this result to an n-dimensional conical Radon transform. To demonstrate our suggested algorithm, numerical simulations for the 3-dimensional case are presented.
KW - Compton camera
KW - Conical Radon transform
KW - Inversion
KW - Tomography
UR - http://www.scopus.com/inward/record.url?scp=85070335423&partnerID=8YFLogxK
U2 - 10.1007/s13160-019-00379-x
DO - 10.1007/s13160-019-00379-x
M3 - Article
AN - SCOPUS:85070335423
SN - 0916-7005
VL - 36
SP - 989
EP - 1004
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 3
ER -