A mixed finite element discretisation of linear and nonlinear multivariate splines using the Laplacian penalty based on biorthogonal systems.

We consider a mixed finite element method for a linear multivariate spline using the Laplacian penalty. Our discretisation is based on biorthogonal systems leading to a very simple and efficient finite element scheme. We also extend our approach to a nonlinear case and describe a split Bregman iteration scheme for the resulting nonlinear equations. We apply our numerical schemes to remove the mixture of Gaussian and impulsive noise for some test images.•This paper presents a method of discretising a multivariate spline using a finite element method.•The method uses a biorthogonal system to achieve an efficient finite element method.•The method is extended to cover a discretisation scheme for a nonlinear case, including an adaptation of the split Bregman method for the nonlinear case.

Energy Resolved Neutron Imaging for Strain Reconstruction Using the Finite Element Method.

A novel pulsed neutron imaging technique based on the finite element method is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility of a nondestructive analysis of strain fields with a high spatial resolution. The finite element approach used to reconstruct the strain uses the least square method constrained by the conditions of equilibrium. This inclusion of equilibrium makes the problem well-posed. The procedure is developed and verified by validating for a cantilevered beam problem. It is subsequently demonstrated by reconstructing the strain from experimental data for a ring-and-plug sample, measured at the spallation neutron source RADEN at J-PARC in Japan. The reconstruction is validated by comparison with conventional constant wavelength strain measurements on the KOWARI diffractometer at ANSTO in Australia. It is also shown that the addition of a Tikhonov regularisation scheme further improves the reconstruction.

A proposed method for linear accelerator photon beam steering using EPID.

Beam steering is the process of calibrating the angle and translational position with which a linear accelerator's (linac's) electron beam strikes the x-ray target with respect to the collimator rotation axis. The shape of the dose profile is highly dependent on accurate beam steering and is essential for ensuring correct delivery of the radiotherapy treatment plan. Traditional methods of beam steering utilize a scanning water tank phantom that makes the process user-dependent. This study is the first to provide a methodology for both beam angle steering and beam translational position steering based on EPID imaging of the beam and does not require a phantom. Both the EPID-based beam angle steering and beam translational steering methods described have been validated against IC Profiler measurement. Wide field symmetry agreement was found between the EPID and IC Profiler to within 0.06 ± 0.14% (1 SD) and 0.32 ± 0.11% (1 SD) for flattened and flattening-filter-free (FFF) beams, respectively. For a 1.1% change in symmetry measured by IC Profiler the EPID method agreed to within 0.23%. For beam translational position steering, the EPID method agreed with IC Profiler method to within 0.03 ± 0.05 mm (1 SD) at isocenter. The EPID-based methods presented are quick to perform, simple, accurate and could easily be integrated with the linac, potentially via the MPC application. The methods have the potential to remove user variability and to standardize the process of beam steering throughout the radiotherapy community.