Research on mathematical modelling in image processing

Abstract

One of my concerns is how to solve effectively nonlinear equations. Particularly I aim at solving the noise removal. In this thesis I introduce selective smoothing methods and total variation type methods for noise removal. The methods are being developed. Particularly I am interested in the fourth order partial equation applied to selective smoothing methods, that is an improved method for noise removal more than the previews smoothing methods. Our fourth order selective smoothing method has a unique solution on closed time interval. Furthermore we show numerical evidence of the power of resolution of this model with respect to [1],[2] and [5]. The total variation type methods are introduced and developed by Rudin, Osher and others. But solving total variation type by using Newton method has some problems as we know generally. To overcome this problems I introduce a similar functional to functional that is introduced by Acar and Vogel. From our functional I draw the Euler-Lagrange equation and am going to solve this by using Newton method, that can be viewed as an inexact Newton method(Newton-like Method) for the Euler-Lagrange equation. Experimental results show that the new method has much improved convergence behavior than the Newton method.