Accurate and efficient numerical solutions for elliptic obstacle problems.

Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. In order to solve such problems effectively using finite difference (FD) methods, the article investigates simple iterative algorithms based on the successive over-relaxation (SOR) method. It introduces subgrid FD methods to reduce the accuracy deterioration occurring near the free boundary when the mesh grid does not match with the free boundary.

Curvature interpolation method for image zooming.

We introduce a novel image zooming algorithm, called the curvature interpolation method (CIM), which is partial-differential-equation (PDE)-based and easy to implement. In order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect, the CIM first evaluates the curvature of the low-resolution image. After interpolating the curvature to the high-resolution image domain, the CIM constructs the high-resolution image by solving a linearized curvature equation, incorporating the interpolated curvature as an explicit driving force.

The error-amended sharp edge (EASE) scheme for image zooming.

This paper proposes a new interpolation method, called the error-amended sharp edge (EASE) scheme, which is a modified bilinear method. In order to remove/reduce interpolation artifacts such as image blur and the checkerboard effect (ringing), EASE tries to amend the interpolation error by employing the classical interpolation error theorem in an edge-adaptive fashion. EASE is applied for image zooming by both integer and noninteger magnification factors.

Edge-forming methods for color image zooming.

This paper introduces edge-forming schemes for image zooming of color images by general magnification factors. In order to remove/reduce artifacts arising in image interpolation, such as image blur and the checkerboard effect, an edge-forming method is suggested to be applied as a postprocess of standard interpolation methods. The method is based on nonconvex nonlinear partial differential equations.

PDE-based image restoration: a hybrid model and color image denoising.

The paper is concerned with PDE-based image restoration. A new model is introduced by hybridizing a nonconvex variant of the total variation minimization (TVM) and the motion by mean curvature (MMC) in order to deal with the mixture of the impulse and Gaussian noises reliably. We suggest the essentially nondissipative (ENoD) difference schemes for the MMC component to eliminate the impulse noise with a minimum (ideally no) introduction of dissipation.