Abstract The quality of high energy flash X‐ray images is crucial to the high‐precision diagnosis of object density. High energy flash X‐ray radiography is susceptible to the system blur, which usually causes the poor quality of static images. In response to this, a novel restoration algorithm using region extrema and kernel optimization (REKO) is presented. Based on the observation that the region extrema distribution of blurred high energy flash X‐ray images deviates from opposite ends of image grey domain, the sparseness‐inducing prior for regularizing image region extrema is applied to construct the restoration model. Considering the sparse characteristics of blur kernels, the sparseness‐inducing regularization is incorporated to constrain blur kernels in the restoration model. The non‐convex and non‐linear objective function is gradually minimized through energy alternating minimization and dually linear approximation. Furthermore, a continuity enforced kernel optimization algorithm is proposed to estimate more accurate blur kernels. The discontinuous kernel elements are suppressed by extracting the main structure of blur kernels and constructing kernel continuity function in cross windows. Experimental results demonstrate that our algorithm can more accurately estimate blur kernels and achieve restoration results with sharper edges on high energy flash X‐ray images.

Flash Radiography inspections stand to gain from inversion to infer density distribution of object based on X-ray transmission image. It is indispensable to be able to reliably provide uncertainties associated with the inversions. Although many inversion algorithms have been devised, they often perform poorly due to either their sensitivity to regularization parameter chosen in variational optimization or prohibitive computation and noisy results in stochastic simulation. In this paper, we present a gradual reconstruction algorithm, called TLE-Gibbs (two-level efficient Gibbs sampling), for flash radiography. At its core, TLE-Gibbs is a stochastic approach based on efficient Gibbs sampling and reconstruction refinement. A two-level scheme is proposed that enables high-resolution image to be constrained with uncertainty estimation from high-level reconstruction. Furthermore, a splitting variant that increases flexibility and precision is considered in the two-level scheme. An efficient Markov chain Monte Carlo (MCMC) endowed with first-order truncated conjugate gradient (CG) optimizer is developed to achieve minimal cost per sample and to approximate the posterior distribution. Finally, we adopt an effective refinement method to remove noises remained in the sample meanwhile maintaining sharp edges. For performance evaluation, TLE-Gibbs is applied on both synthetic data in which the influence of system blur is specially investigated and real data, and comparison with state-of-the-art reconstruction methods demonstrates the superiority of the proposed method.

Image non-blind deblurring is still an ill-posed problem. Uncertainty in solutions occurs when singular vectors of forward model matrix spanning the noise subspace have rather small singular values. This letter proposes a new image deblurring algorithm, called MNBC-Gibbs (multiple norms and boundary constraint enforced Gibbs sampling). To be more specific, the quadratic and sparseness-inducing norms are combined to construct regularization term, and the objective function is gradually minimized without requirement of regularization parameter choice. In particular, we propose an efficient Markov chain Monte Carlo (MCMC) method equipped with closed-form solution, artifacts processing and non-negative constraint to approximate the posterior distribution and estimate uncertainty for the unknown. Satisfactory deblurring results with sharp edges can be generated while maintaining smoothness without raising extra noise. The quantitative evaluations on different blur kernels and comparison with state-of-the-art image deblurring methods demonstrate the superiority of the proposed method. In addition, we show that our method can effectively deal with real blurry images.