Image denoise by fourth-order PDE based on the changes of laplacian

Fourth-order partial differential equation (PDE) proposed by You and Kaveh (You-Kaveh fourth-order PDE), which replaces the gradient operator in classical second-order nonlinear diffusion methods with a Laplacian operator, is able to avoid blocky effects often caused by second-order nonlinear PDEs. However, the equation brought forward by You and Kaveh tends to leave the processed images with isolated black and white speckles. Although You and Kaveh use median filters to filter these speckles, median filters can blur the processed images to some extent, which weakens the result of You-Kaveh fourth-order PDE. In this paper, the reason why You-Kaveh fourth-order PDE can leave the processed images with isolated black and white speckles is analyzed, and a new fourth-order PDE based on the changes of Laplacian (LC fourth-order PDE) is proposed and tested. The new fourth-order PDE preserves the advantage of You-Kaveh fourth-order PDE and avoids leaving isolated black and white speckles. Moreover, the new fourth-order PDE keeps the boundary from being blurred and preserves the nuance in the processed images, so, the processed images look very natural.

Aspects of the in vitro bioactivity of hydraulic calcium (alumino)silicate cement

In response to a burgeoning interest in the prospective clinical applications of hydraulic calcium (alumino)silicate cements, the in vitro bioactivity and dissolution characteristics of a white Portland cement have been investigated. The formation of an apatite layer within 6 h of contact with simulated body fluid was attributed to the rapid dissolution of calcium hydroxide from the cement matrix and to the abundance of pre-existing Si-OH nucleation sites presented by the calcium silicate hydrate phase. A simple kinetic model has been used to describe the rate of apatite formation and an apparent pseudo-second-order rate constant for the removal of HPO42- ions frorn solultion has been calculated (k(2) = 5.8 x 10(-4) g mg(-1)). Aspects of the chemistry of hydraulic cements are also discussed with respect to their potential use in the remedial treatment of living tissue. (C) 2008 Wiley Periodicals, Inc. J Biomed Mater Res 90A: 166-174, 2009