Abstract
In recent articles Metz and Pan have introduced a large class of methods for inverting the exponential Radon transform that are parametrized by a function ω of two variables. We show that when ω satisfies a certain constraint, the corresponding inversion method uses projection to the range of the transform. The addition of another constraint on ω makes this projection orthogonal with respect to a weighted inner product. Their quasi-optimal algorithm uses the projection that is orthogonal with respect to the ordinary inner product.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 563-571 |
| Number of pages | 9 |
| Journal | Inverse Problems |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 1999 |
Fingerprint
ASJC Scopus subject areas
- Applied Mathematics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Projections onto the range of the exponential Radon transform and reconstruction algorithms. / Clarkson, Eric W.
In: Inverse Problems, Vol. 15, No. 2, 04.1999, p. 563-571.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Projections onto the range of the exponential Radon transform and reconstruction algorithms
AU - Clarkson, Eric W
PY - 1999/4
Y1 - 1999/4
N2 - In recent articles Metz and Pan have introduced a large class of methods for inverting the exponential Radon transform that are parametrized by a function ω of two variables. We show that when ω satisfies a certain constraint, the corresponding inversion method uses projection to the range of the transform. The addition of another constraint on ω makes this projection orthogonal with respect to a weighted inner product. Their quasi-optimal algorithm uses the projection that is orthogonal with respect to the ordinary inner product.
AB - In recent articles Metz and Pan have introduced a large class of methods for inverting the exponential Radon transform that are parametrized by a function ω of two variables. We show that when ω satisfies a certain constraint, the corresponding inversion method uses projection to the range of the transform. The addition of another constraint on ω makes this projection orthogonal with respect to a weighted inner product. Their quasi-optimal algorithm uses the projection that is orthogonal with respect to the ordinary inner product.
UR - http://www.scopus.com/inward/record.url?scp=0000017205&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000017205&partnerID=8YFLogxK
U2 - 10.1088/0266-5611/15/2/014
DO - 10.1088/0266-5611/15/2/014
M3 - Article
VL - 15
SP - 563
EP - 571
JO - Inverse Problems
JF - Inverse Problems
SN - 0266-5611
IS - 2
ER -