Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systema...

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the s...

We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension and unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, the problem’s weak solution is approximated in space, with finite-difference methods. The rate of co...