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Quantitative X-ray radiographic imaging systems that utilize a charged couple device (CCD) camera connected to a thick, monolithic scintillator can exhibit blur that varies spatially across the field of view, especially for thick scintillators used in pulse-power radiography of dynamically compressed objects. A three-point approach to estimating and accounting for this effect is demonstrated by (a) using a local estimation technique to measure the effect of blurring a calibration object at key locations across the field of view, (b) combining each of the local estimates into a spatially varying blurring function via partitions of unity interpolation, and (c) resolving the effects of that blur on the image by solving an ill-posed inverse problem using a spatially varying regularization term. The technique is demonstrated on synthetic examples and actual radiographs collected at the Naval Research Laboratory's (NRL) Mercury pulsed power facility.

Measure transport is a rich area in applied mathematics that involves the construction of deterministic transformations-known as transport maps-between probability distributions (Santambrogio, 2015). These maps characterize a complex target distribution as a (deterministic) transformation of a simple reference distribution (e.g., a standard Gaussian). In the context of probabilistic modeling, transport maps enable easy generation of samples from the target distribution and direct evaluation of the target probability density function. Monotone triangular maps (Baptista et al., 2022) are a specific class of transport maps endowed with several computational advantages over non-triangular maps, such as easy invertibility and training, and yet sufficiently general to represent any absolutely continuous distribution; they are also the building block of many normalizing flow architectures commonly used in the machine learning community (Papamakarios et al., 2021).

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