A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems

Abstract

One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or ‘spot’. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods – which involve the analysis of blur caused by a structured aperture – can be used to obtain the spot’s spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Synthetic data-sets are used to demonstrate accurate reconstruction, while real data taken with high-energy X-ray imaging systems are used to demonstrate applicability and feasibility.