Numerical Schemes for Linear and Non-linear Enhancement of DW-MRI
نویسندگان
چکیده
We consider left-invariant diffusion processes on DTI data by embedding the data into the space R o S of 3D positions and orientations. We then define and solve the diffusion equation in a moving frame of reference defined using left-invariant derivatives. The diffusion process is made adaptive to the data in order to do Perona-Malik-like edge preserving smoothing, which is necessary to handle fiber structures near regions of large isotropic diffusion such as the ventricles of the brain. The corresponding partial differential systems are solved using finite difference stencils. We include experiments both on synthetic data and on DTI-images of the brain.
منابع مشابه
Computer extended series and HAM for the solution of non-linear Squeezing flow of Casson fluid between parallel plates
The paper presents analysis of two-dimensional non-Newtonian incompressible viscous flow between parallel plates. The governing problem of momentum equations are reduced to NODE using similarity transformations. The resulting equation is solved using series solution and homotopy analysis method. These methods have advantages over pure numerical methods for obtaining the derived quantities accur...
متن کاملNonlinear Numerical Integration Scheme in Strain Space Plasticity
Strains are applied to the integration procedure in nonlinear increments todecrease the errors arising from the linearization of plastic equations. Two deformationvectors are used to achieve this. The first vector is based on the deformations obtained bythe first iteration of the equilibrium step, and the second is acquired from the sum of thesucceeding iterations. By applying these vectors and...
متن کاملThe microscopic dose enhancement factor measurment of bismuth nanoparticles in external radiation therapy using MRI polymer gel dosimetery
Introduction: Bismuth-based nanoparticles having high atomic number and electron density, besides of being utilized as CT contrast agent, stand as a strongly proposed method for dose enhancement in radiotherapy. Embedded nanoparticle in polymer gel dosimeter poses the first step to assess the dose enhancement capability in nanoparticles. To this end, MAGICA gel dosimeter, whic...
متن کاملPreconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملFiber Enhancement in Diffusion-Weighted MRI
Diffusion-Weighted MRI (DW-MRI) measures local water diffusion in biological tissue, which reflects the underlying fiber structure. In order to enhance the fiber structure in the DW-MRI data we consider both (convection-)diffusions and Hamilton-Jacobi equations (erosions) on the space R o S of 3D-positions and orientations, embedded as a quotient in the group SE(3) of 3D-rigid body movements. T...
متن کامل