Invertibility of multi-energy X-ray transform.

ABSTRACT:

Purpose

The goal is to provide a sufficient condition for the invertibility of a multi-energy (ME) X-ray transform. The energy-dependent X-ray attenuation profiles can be represented by a set of coefficients using the Alvarez-Macovski (AM) method. An ME X-ray transform is a mapping from N AM coefficients to N noise-free energy-weighted measurements, where N≥2 .

Methods

We apply a general invertibility theorem to prove the equivalence of global and local invertibility for an ME X-ray transform. We explore the global invertibility through testing whether the Jacobian of the mapping J(A) has zero values over the support of the mapping. The Jacobian of an arbitrary ME X-ray transform is an integration over all spectral measurements. A sufficient condition for J(A)≠0 for all A is

SUBMITTER: Ding Y 

PROVIDER: S-EPMC8568641 | biostudies-literature | 2021 Oct

REPOSITORIES: biostudies-literature