XCOM intrinsic dimensionality for low-Z elements at diagnostic energies

Area of Science:

• Medical Physics
• Computational Physics

Background:

• Linear attenuation coefficients (LACs) are crucial for X-ray imaging.
• Understanding the intrinsic dimensionality of LACs informs data analysis and model development.
• XCOM provides reference data for elemental photon interactions.

Purpose of the Study:

• To determine the intrinsic dimensionality of LACs for low atomic number elements (Z=1-20).
• To assess this dimensionality at diagnostic X-ray energies (25-120 keV).

Main Methods:

• Principal Component Analysis (PCA) was used to project LACs.
• Wild bootstrap was applied to handle non-i.i.d. residuals.
• Credible regions for eigenvalues determined statistical significance.

Main Results:

• The intrinsic dimensionality of low-Z XCOM data at diagnostic energies was found to be four.
• This was determined by testing the hypothesis that LACs are spanned by q bases.

Conclusions:

• The presented method determines statistically significant dimensionality in noisy data.
• A dimensionality of four for low-Z LACs may impact parametrization schemes and X-ray imaging techniques.
• This finding suggests potential for improved tissue characterization with higher model dimensionality in advanced X-ray systems.