Image processing and topology optimization

Structural optimization, posed as finding the optimal distribution of material and void is well known as a mathematically ill-posed problem. This ill-posedeness nature expresses itself in the lack of compactness of the set of allowed domains and is commonly considered as being the cause of some numerical problems like mesh dependency, for example.
Many solutions have been proposed in order to address this lack of solution and build strong and accurate numerical approximations. In most of these method, the "black-or-white" character of the domain (i.e. material OR void) is replaced with a "gray-level" density function, allowed to take its values between 0 and 1 (0 representing then void while 1, material). Then, one can choose between a penalization of the perimeter of the designed domain (i.e. a penalization of the Total Variation of the density function), a extra bound on the gradient of the density function or the use of a filtering technique.
All these methods are strongly related to the problem known in the image processing domain as "image restoration", i.e. trying to reverse the alterations (noise, blur...) made on an image.
The main goal of the project is the use of image processing knowledges to help understanding the filtering technique, reinforce its theoretical foundations and improve its implementation.