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Related Experiment Video

Updated: May 7, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

STABILITY OF THE INTERIOR PROBLEM FOR POLYNOMIAL REGION OF INTEREST.

E Katsevich¹, A Katsevich, G Wang

¹Princeton University, Princeton, NJ 08544Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA 24061, USA.

Inverse Problems

|September 24, 2013

Summary

This summary is machine-generated.

This study proves stability for the interior problem in tomography when the attenuation function is a polynomial. It also establishes a general uniqueness result for real-analytic functions within the region of interest.

Related Experiment Videos

Last Updated: May 7, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

Medical Imaging
Applied Mathematics
Computational Science

Background:

The interior problem in tomography aims to reconstruct an object's properties from limited internal data.
Previous work showed unique solutions for piecewise polynomial attenuation functions.
Stability analysis is crucial for practical, noisy tomographic reconstructions.

Purpose of the Study:

To investigate the stability of solving the interior tomography problem for polynomial attenuation functions.
To establish a general uniqueness theorem for real-analytic functions in tomography.
To extend existing uniqueness results using new theoretical frameworks.

Main Methods:

Mathematical analysis of the interior tomography problem.
Derivation of stability estimates under polynomial assumptions.
Proof of a general uniqueness result based on real-analytic properties.

Main Results:

A stability estimate is proven for the interior tomography problem with polynomial attenuation functions.
A novel general uniqueness theorem is established for real-analytic functions.
Existing uniqueness theorems are shown to be corollaries of the new result.

Conclusions:

The interior tomography problem exhibits stability for polynomial attenuation functions under specific conditions.
Real-analytic properties of the attenuation function lead to strong uniqueness guarantees.
This research advances the theoretical understanding of tomographic reconstruction from limited data.