Richard S. C. Cobbold

Hisham Assi, Richard S. C. Cobbold

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for time-domain modeling of elastic wave propagation in an unbounded lossless anisotropic medium. The formulation is based on a second-order approach that has the advantages of, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. Specifically, our formulation uses three second-order equations of the displacement field and nine auxiliary equations, along with the three time histories of the displacement field. The properties of the PML, which are controlled by a complex two-parameter stretch function, are such that it acts as near perfect absorber. Using finite element method (FEM) 3D numerical results are presented for a highly anisotropic medium. An extension of the formulation to the particular case of a Kelvin-Vogit viscoelastic medium is also presented.

SayedMasoud Hashemi, Soosan Beheshti, Patrick R. Gill et al.

Ultra low radiation dose in X-ray Computed Tomography (CT) is an important clinical objective in order to minimize the risk of carcinogenesis. Compressed Sensing (CS) enables significant reductions in radiation dose to be achieved by producing diagnostic images from a limited number of CT projections. However, the excessive computation time that conventional CS-based CT reconstruction typically requires has limited clinical implementation. In this paper, we first demonstrate that a thorough analysis of CT reconstruction through a Maximum a Posteriori objective function results in a weighted compressive sensing problem. This analysis enables us to formulate a low dose fan beam and helical cone beam CT reconstruction. Subsequently, we provide an efficient solution to the formulated CS problem based on a Fast Composite Splitting Algorithm-Latent Expected Maximization (FCSA-LEM) algorithm. In the proposed method we use pseudo polar Fourier transform as the measurement matrix in order to decrease the computational complexity; and rebinning of the projections to parallel rays in order to extend its application to fan beam and helical cone beam scans. The weight involved in the proposed weighted CS model, denoted by Error Adaptation Weight (EAW), is calculated based on the statistical characteristics of CT reconstruction and is a function of Poisson measurement noise and rebinning interpolation error. Simulation results show that low computational complexity of the proposed method made the fast recovery of the CT images possible and using EAW reduces the reconstruction error by one order of magnitude. Recovery of a high quality 512$\times$ 512 image was achieved in less than 20 sec on a desktop computer without numerical optimizations.