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Figure 8
Reconstruction of concentration profiles for two levels of acquisition noise: panels (a) and (b) very low (σk = 0.01, SNR = [{{{\bb{E}}\,[I_{k}^{\,m}]^{2}}/{\sigma_{k}^{\,2}}}\,\in\,[250\times10^{3},16\times10^{6}]]), and panels (c) and (d) very high (σk = 0.5, SNR ∈ [100, 6400]). In panels (a) and (c) the profile reconstructions are plotted in blue ([\hat{\rho}|A^{m}\!,{\bf y}]), orange ([\hat{\rho}|A^{m}\!,{\bf y}_{0}]) and red ([\hat{\rho}|A^{m}_{0},{\bf y}]) with their respective variabilities as shaded areas. In panels (b) and (d) the a posteriori [[{\cal P}(\rho|A^{m}\!,{\bf y})]] is represented in blue and the marginals in orange [[{\cal P}(\rho|A^{m}\!,{\bf y}_{0})]] and red [[{\cal P}(\rho|A^{m}_{0},{\bf y})]]. For the noise variability ρ|Am, y0 and the noise marginal [{\cal P}(\rho|A^{m}\!,{\bf y}_{0})], the true values of λe have been used to emphasize the effect of uncertain attenuation lengths.

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Volume 30| Part 5| September 2023| Pages 941-961
https://doi.org/10.1107/S1600577523006124
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