Application of Bayesian estimation to X-ray fluorescent image

Matsuyama, Tsugufumi*; Igarashi, Momo*; Yasuda, Sora*; Murakami, Masashi  ; Yoshida, Yukihiko; Hayashi, Kazunori*; Machida, Masahiko  ; Tsuji, Koichi*

Micro-X-ray fluorescence (M-XRF) image is applied for obtaining elemental images of various samples. When elemental distributions are obtained by M-XRF analysis, a long measurement time is required. In this study, Bayesian estimation was applied to M-XRF analysis for clear elemental distribution. Bayesian estimation is based on the conditional probability, its prediction is performed by the likelihood function and prior distribution. Likelihood function and prior distribution were defined as Poisson distribution and the relationship between the count rate and its frequency, respectively. Prior distribution was prepared from the sum spectrum. For obtaining the optimal value, the expected value of the posterior distribution was selected. 2-euro and Japanese 500-yen coins were measured by M-XRF analysis. To evaluate this method, mean squared errors (MSEs) and peak signal to noise ratios (PSNRs) were calculated for elemental images with and without Bayesian estimation. Elemental distributions in a long-time measurement were selected as right elemental distribution for MSE and PSNR. MSE and PSNR values of elemental distributions of 2-euro coin were improved by using Bayesian estimation compared to those without Bayesian estimation. We can obtain the similar results for 500-yen coin. Therefore, it was seen that a quality of elemental distributions was improved by applying M-XRF images to Bayesian estimation.