TY - THES
T1 - Denoising and enhancement of digital images : variational methods, integrodifferential equations, and wavelets
A1 - Didas,Stephan
Y1 - 2011/04/28
N2 - The topics of this thesis are methods for denoising, enhancement, and simplification of digital image data. Special emphasis lies on the relations and structural similarities between several classes of methods which are motivated from different contexts. In particular, one can distinguish the methods treated in this thesis in three classes: For variational approaches and partial differential equations, the notion of the derivative is the tool of choice to model regularity of the data and the desired result. A general framework for such approaches is proposed that involve all partial derivatives of a prescribed order and experimentally are capable of leading to piecewise polynomial approximations of the given data. The second class of methods uses wavelets to represent the data which makes it possible to understand the filtering as very simple pointwise application of a nonlinear function. To view these wavelets as derivatives of smoothing kernels is the basis for relating these methods to integrodifferential equations which are investigated here. In the third case, values of the image in a neighbourhood are averaged where the weights of this averaging can be adapted respecting different criteria. By refinement of the pixel grid and transfer to scaling limits, connections to partial differential equations become visible here, too. They are described in the framework explained before. Numerical aspects of the simplification of images are presented with respect to the NDS energy function, a unifying approach that allows to model many of the aforementioned methods. The behaviour of the filtering methods is documented with numerical examples.
KW - Rauschen
KW - Glättung
KW - Integrodifferentialgleichung
CY - Saarbrücken
PB - Saarländische Universitäts- und Landesbibliothek
AD - Postfach 151141, 66041 Saarbrücken
UR - http://scidok.sulb.uni-saarland.de/volltexte/2011/3514
ER -