Optimization-Based Approach for Joint X-Ray Fluorescence and Transmission Tomographic Inversion

Abstract

Fluorescence tomographic reconstruction, based on the detection of photons coming from fluorescent emission, can be used for revealing the internal elemental composition of a sample. On the other hand, conventional X-ray transmission tomography can be used for reconstructing the spatial distribution of the absorption coefficient inside a sample. In this work, we integrate both X-ray fluorescence and X-ray transmission data modalities and formulate a nonlinear optimization-based approach for reconstruction of the elemental composition of a given object. This model provides a simultaneous reconstruction of both the quantitative spatial distribution of all elements and the absorption effect in the sample. Mathematically speaking, we show that compared with the single-modality inversion (i.e., the X-ray transmission or fluorescence alone), the joint inversion provides a better-posed problem, which implies a better recovery. Therefore, the challenges in X-ray fluorescence tomography arising mainly from the effects of self absorption in the sample are partially mitigated. The use of this technique is demonstrated on the reconstruction of several synthetic samples.

Joint reconstruction of x-ray fluorescence and transmission tomography

“…Guided by the multimodal analysis methodology developed in [30], we apply a joint-inversion framework to solve XRF reconstruction problem more accurately by incorporating a second data modality as XRT. We investigate the correlations between XRF and XRT data, and estab- Intensity (counts/sec) Fig.…”

“…We start from an earlier approach [30], which we extend considerably here to include a different model of XRF self-absorption effect and the ability to better balance differences in variability of acquired data. We use θ ∈ Θ and τ ∈ T to denote, respectively, the index of the x-ray beam angle and discretized beamlet from a collection of |Θ| angles and |T | beamlets.…”

“…The calculation of the remaining derivatives ∂ ∂W v , e F j (W W W) is described in our previous paper [30].…”

Monte Carlo Simulation for Polychromatic X-Ray Fluorescence Computed Tomography with Sheet-Beam Geometry

“…According to our results, different algorithms influence the values of CNR, which is similar with conclusion of Zichao.et.al. [22] Thirdly, X-ray detector with higher energy resolution is used during the process.…”

Simultaneous Sensing Error Recovery and Tomographic Inversion Using an Optimization-Based Approach

“…Potential approaches to this problem include the incorporation of prior knowledge into the reconstruction process using Bayesian frameworks [17,33,34] and the use of regularizers to promote sparsity or smoothness of the reconstruction [14,10,23,30,20]. One can also collect additional data (beyond x-ray projections) that is less sensitive to experimental errors and use this data to help with the reconstruction [7]. Unfortunately, the improvement in tomographic hardware has been so great that these generic approaches, which apply more widely to problems other than CoR drift recovery, are not likely to be sufficient.…”