Spectrum reconstruction from dose measurements as a linear inverse problem

Benjamin Armbruster, Russell J Hamilton, Arthur K. Kuehl

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

There are three ways to determine the spectrum of a clinical photon beam: direct measurement, modelling the source and reconstruction from ion-chamber measurements. We focus on reconstruction because the necessary equipment is readily available and it provides independent confirmation of source models for a given machine. Reconstruction methods involve measuring the dose in an ion chamber after the beam passes through an attenuator. We gain information about the spectrum from measurements using attenuators of differing compositions and thicknesses since materials have energy dependent attenuation. Unlike the procedures used in other papers, we do not discretize or parametrize the spectrum. With either of these two approximations, reconstruction is a least squares problem. The forward problem of going from a spectrum to a series of dose measurements is a linear operator, with the composition and thickness of the attenuators as parameters. Hence the singular value decomposition (SVD) characterizes this operator. The right singular vectors form a basis for the spectrum, and, at first approximation, only those corresponding to singular values above a threshold are measurable. A more rigorous error analysis shows with what confidence different components of the spectrum can be measured. We illustrate this theory with simulations and an example utilizing six sets of dose measurements with water and lead as attenuators.

Original languageEnglish (US)
Pages (from-to)5087-5099
Number of pages13
JournalPhysics in Medicine and Biology
Volume49
Issue number22
DOIs
StatePublished - Nov 21 2004

Fingerprint

Inverse problems
attenuators
Ions
dosage
Least-Squares Analysis
Photons
Ionization chambers
ionization chambers
Equipment and Supplies
Water
linear operators
Singular value decomposition
Chemical analysis
Error analysis
photon beams
error analysis
Dosimetry
Light sources
approximation
confidence

ASJC Scopus subject areas

  • Biomedical Engineering
  • Physics and Astronomy (miscellaneous)
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology

Cite this

Spectrum reconstruction from dose measurements as a linear inverse problem. / Armbruster, Benjamin; Hamilton, Russell J; Kuehl, Arthur K.

In: Physics in Medicine and Biology, Vol. 49, No. 22, 21.11.2004, p. 5087-5099.

Research output: Contribution to journalArticle

Armbruster, Benjamin ; Hamilton, Russell J ; Kuehl, Arthur K. / Spectrum reconstruction from dose measurements as a linear inverse problem. In: Physics in Medicine and Biology. 2004 ; Vol. 49, No. 22. pp. 5087-5099.
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