Limited data X-ray tomography using accretive operators

Limited Data X-Ray Tomography Using Nonlinear Evolution Equations

A novel approach to the X-ray tomography problem with sparse projection data is proposed. Non-negativity of the X-ray attenuation coefficient is enforced by modelling it as max{Φ(x), 0} where Φ is a smooth function. The function Φ is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods. The reconstruction algorithm is applie...

X-ray Tomography of Large Objects with Limited Measurement Angle

In this paper we present an efficient implementation of an algorithm for reconstructing a 3D volume from limited angle projection data, based on statistical inversion theory. We demonstrate the strength of the method for detecting structural defects in large composite aerospace components, whose dimensions prevent acquiring measurements over the full circle. In comparison with a number of other...

Limited-angle x-ray luminescence tomography: methodology and feasibility study.

X-ray luminescence tomography (XLT) has recently been proposed as a new imaging modality for biological imaging applications. This modality utilizes phosphor nanoparticles which luminesce near-infrared light when excited by x-ray photons. The advantages of this modality are that it uniquely combines the high sensitivity of radioluminescent nanoparticles and the high spatial localization of coll...

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

Numerical Solution of Limited-data Inverse Problems Arising from X-ray Tomography and Acoustic Inverse Scattering