XCOM intrinsic dimensionality for low‐Z elements at diagnostic energies

摘要: Purpose: To determine the intrinsic dimensionality of linear attenuation coefficients (LACs) from XCOM for elements with low atomic number (Z = 1-20) at diagnostic x-ray energies (25-120 keV). H{sub 0}{sup q}, hypothesis that space LACs is spanned by q bases, tested various q-values. Methods: Principal component analysis first applied and are projected onto principal bases. The residuals model values vs data determined all numbers. Heteroscedasticity invalidates prerequisite i.i.d. errors necessary bootstrapping residuals. Instead wild bootstrap applied, which, not mixing residuals, allows effect non-i.i.d to be reflected in result. Credible regions eigenvalues correlation matrix bootstrapped LAC determined. If subsequent credible overlap, corresponding considered represent true structure but noise. this happens l + 1, any l{<=}q, q} rejected. Results: largest value which nonrejectable 5%-level 4. This indicates statistically significantmore » low-Z four. Conclusions: method presented determination significant noisy subspace. Knowledge such interest making assumptions on evaluating results reference data. For LACs, knowledge might relevant when parametrization schemes tuned imaging techniques based basis decomposition (Alvarez Macovski, Phys. Med. Biol. 21, 733-744, 1976), an underlying two commonly assigned human tissue energies. finding a higher thus raises question whether assumed (now feasible advent multibin systems) also practically relevant, i.e., if better characterization can obtained.« less