Seminar for Statistics

Patric Müller: Image restoration Blind deconvolution for noised Gaussian blur

Adviser: Prof. Dr. S. van de Geer

February 2009


Blind deconvolution is an inverse problem with one or more unknown parameters.
Nowadays, one of the more common practical applications of deconvoultion is in image analysis, where it is used determining how to restore blurred images. To recover the original image, however, we first have to estimate the unknown parameteres the image  was blurred. In the last years, this topic has attracted significant attention, resulting in numerous studies.

This thesis studies blind deconvolution from theoretical and practical point of view.
On the other side, we provide the necessary tools we will utilise to improve the quality of blurred and noised pictures. Our results give rise to algorithms computing estimations if the aforementioned unknows.
The applicability of the explored techniques then is demonstrated by means of several practical examples.

The thesis is concluded by a brief qualitative analysis of the limits of deconvolution
with regard to image restoration. To this end we show that the process is
ill-conditioned. Thus, it might be at best inefficient, but at worst impossible, to retrieve the original picture from a blurred one.


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