Image Restoration Combining the Second-Order and Fourth-Order PDEs

Compound PDE-Based Image Restoration Algorithm Using Second-Order and Fourth-Order Diffusions

Traveling Wave Solutions of Fourth Order PDEs for Image Processing

Fourth-Order Time-Stepping for Stiff PDEs

A modification of the exponential time-differencing fourth-order Runge–Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competi...

Comparison between fourth and second order DT-MR image segmentations

A second order tensor is usually used to describe the diffusion of water for each voxel within a Diffusion Tensor Magnetic Resonance (DT-MR) images. However, a second order tensor approximation fails to accurately represent complex local tissue structures such as crossing fibers. Therefore, higher order tensors are used to represent more complex diffusivity profiles. In this work we examine and...

Diagnosing Manufacturing Variation Using Second-Order and Fourth-Order Statistics

This article discusses a method that can aid in diagnosing root causes of product and process variability in complex manufacturing processes, when large amounts of multivariate in-process measurement data are available. A linear structured model, similar to the standard factor analysis model, is used to generically represent the variation patterns that result from the root causes. Blind source ...