Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization

摘要: Nonlinear partial differential equations (PDE) are now widely used to regularize images. They allow eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a geometric framework design PDE flows acting on constrained datasets. We focus our interest of matrix-valued functions undergoing orthogonal spectral constraints. The corresponding evolution PDE's found by minimization cost functionals, depend the natural metrics underlying manifolds (viewed Lie groups or homogeneous spaces). Suitable numerical schemes that fit constraints also presented. illustrate theoretical through recent challenging problem in medical imaging: regularization diffusion tensor volumes (DTMRI).