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This paper expands the LIPR formalism to achieve quantitative material thickness decomposition. Propagation-based phase contrast X-ray imaging with subsequent phase retrieval has been shown to improve the signal-to-noise ratio (SNR) by factors of up to hundreds compared to conventional X-ray imaging. This is a key step in biomedical imaging, where radiation exposure must be kept low without compromising the SNR. However, for a satisfactory phase retrieval from a single measurement, assumptions must be made about the object investigate