Conventional x-ray imaging provides little quantitative information due to scatter, beam hardening, and overlaying tissues. A single-shot quantitative x-ray imaging (SSQI) method was previously developed to quantify material-specific densities in x-ray imaging by combining the use of a primary modulator (PM) and dual-layer (DL) detector. The feasibility of this concept was demonstrated with simulations using an iterative patch-based method. In this work, we propose a new algorithm pipeline for SSQI that enables accurate quantification and high computational efficiency. The DL images contain four measurements that are obtained behind the unattenuated and partially attenuated regions of the PM of each layer. Using the low-frequency property of scatter and a precalibrated material decomposition (MD), four unknowns (i.e., two scatter images and two material-specific images) are jointly recovered by directly solving four equations given by the four measurements. We tested this algorithm in simulations and further demonstrated its efficacy on chest phantom experiments. Through simulation, we show that the new method for MD is robust against scatter. Its performance improves with smaller PM pitch size and smaller focal spot blur. The RMSE in material-specific images compared to ground truth reduces by 52%-84% versus without scatter correction. For our experimental study, we successfully separated soft tissue and bone. The computational time for processing each view was ~8 s without optimization. The reported results further strengthen the potential of SSQI for widespread adoption, leading to quantitative imaging not only for x-ray imaging but also for real-time image guidance or cone-beam CT.
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