To estimate detected x-ray spectra from transmission measurements of known attenuators that allow to accurately simulate the transmission in unknown attenuators.Methods:
Starting from the established spectrum estimation method using the truncated singular value decomposition (TSVD) we extended the algorithm by incorporating prior knowledge about the statistical nature of the transmission data and about high-frequency spectral components like characteristic peaks. Thereby our proposed approach requires only minimal prior knowledge, namely the energy positions of characteristic peaks or k-edges, which are typically well-known. This ensures that the final spectrum is not biased towards a given prior spectrum which is often observed in other methods. The new approach, prior truncated singular value decomposition (PTSVD), is compared to TSVD as well as the expectation–maximization (EM) method in a simulation and a measurement study. The resulting spectra are evaluated according to their ability to reproduce transmission data of attenuators that have not been included into the estimation process.Results:
In case of noiseless simulated data, the PTSVD approach outperforms the existing methods in both, estimating the shape of the spectrum as well as providing a spectrum that reproduces the transmission data. Not surprisingly for increasing noise the ability of PTSVD to estimate the spectral shape worsens while it still performs best in reproducing the transmission data. This finding is also confirmed in the measurement study.Conclusion:
Our new approach allows to estimate detected x-ray spectra that accurately reproduce both transmission measurements that have and have not been included into the estimation process. It is less prone to noise compared to the established TSVD method and potentially leads to smaller transmission errors compared to EM for accurate transmission data while being less biased towards the given prior information.