Matching Pursuit Algorithms as a possible topic

I met with Thomas K. today at his office in the 9th district, where he gave me an introduction into the topic of Matching Pursuit Algorithms. It is in general a more linear algebraic sort of thing. You have a set of vectors in a Hilbert space, which is large in relation to the dimension of the space, i.e. there are many linear dependent elements in it. This set of so-called ‘atoms’ is called a dictionary and will be used to describe elements of the space. The aim is to use only those atoms which are ‘near’ (-> inner product) the vector to analyze. These best atoms can be obtained by the so-called Matching Pursuit algorithm. In general, this has nothing to do with Numerical Harmonic Analysis, but the relation to NuHAG’s more central topic, Gabor Analysis, raises when a Gabor dictionary(?) is chosen as a dictionary, which also is an overstuffed set of atoms, which are then called frames(?).

Thomas will mainly give an overview of these algorithms in his master thesis, and his idea was to have me do the ‘applied part’ of this topic in my own thesis. I should have a look at the two papers he sent me, and next week we would meet again to have a look at some applied examples he can find.

As far as I can tell at this point, a topic which is nearer to Gabor Analysis would be of more interest to me. I will have to wait for my decision until HGFei gives me an overview of the second possible direction for my thesis. What argues for working together with Thomas is that he has a similar background as me: He is regularly employed, writes his thesis during his freetime and simply has the finishing of his studies as primary motivation.