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.

Localization for MCMC: sampling high-dimensional posterior distributions with local structure

“…We use this example to illustrate that IACT of the Gibbs sampler can remain constant as the dimension of x and the number of observations increase with image size. Many practical difficulties, e.g., estimation of noise and regularization parameters (see, e.g., [3,19,42]), are neglected in this example.…”

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Point Spread Function Estimation in X-Ray Imaging with Partially Collapsed Gibbs Sampling

“…In the probabilistic framework, the solution to (7) is equivalent to a maximum a posteriori (MAP) estimate when the PSF is assumed to be a Gaussian, and taking n = 2 guarantees that the corresponding prior covariance operator is trace class [27]. Since data and estimates are inherently discrete quantities, we proceed by discretizing (5) and (10).…”

An approach to characterizing spatial aspects of image system blur

“…To quantitatively analyze the images captured in this way, it is important to understand how each of these components degrades the signal and introduces blurring artifacts. The size and spatial profile of the radiation source, or "spot" produces a so-called source blur [5,9]. Blur is also caused by X-ray scatter in the scene, through the conversion and scattering of light in the scintillating crystal, optical lensing, and the response of the CCD array recording the visible light [9,19,18].…”