Jump to main content
US EPA
United States Environmental Protection Agency
Search
Search
Main menu
Environmental Topics
Laws & Regulations
About EPA
Health & Environmental Research Online (HERO)
Contact Us
Print
Feedback
Export to File
Search:
This record has one attached file:
Add More Files
Attach File(s):
Display Name for File*:
Save
Citation
Tags
HERO ID
7234088
Reference Type
Journal Article
Title
STABILITY OF THE INTERIOR PROBLEM FOR POLYNOMIAL REGION OF INTEREST
Author(s)
Katsevich, E; Katsevich, A; Wang, G; ,
Year
2012
Is Peer Reviewed?
Yes
Journal
Inverse Problems
ISSN:
0266-5611
Language
English
PMID
24058227
DOI
10.1088/0266-5611/28/6/065022
Abstract
In many practical applications, it is desirable to solve the interior problem of tomography without requiring knowledge of the attenuation function fa on an open set within the region of interest (ROI). It was proved recently that the interior problem has a unique solution if fa is assumed to be piecewise polynomial on the ROI. In this paper, we tackle the related question of stability. It is well-known that lambda tomography allows one to stably recover the locations and values of the jumps of fa inside the ROI from only the local data. Hence, we consider here only the case of a polynomial, rather than piecewise polynomial, fa on the ROI. Assuming that the degree of the polynomial is known, along with some other fairly mild assumptions on fa , we prove a stability estimate for the interior problem. Additionally, we prove the following general uniqueness result. If there is an open set U on which fa is the restriction of a real-analytic function, then fa is uniquely determined by only the line integrals through U. It turns out that two known uniqueness theorems are corollaries of this result.
Home
Learn about HERO
Using HERO
Search HERO
Projects in HERO
Risk Assessment
Transparency & Integrity