Status September 2007

I broke the sound barrier of 70 pages yesterday. I wrote some rather mathematical pages about that tensor products of frames for Hilbert spaces are frames for the (tensor) product space, and that the frame coefficients of a 2D product frame can be computed by applying the individual frame matrices to the left and right of an image. Next, I want to show Gabor thresholding for a separable 2D window on a fully separable 4D lattice. I should also mention that computational speed can be increased when using the STFT code.

The next section will look at separable windows on partially non-separable 4D lattices that are still given as a product Λ=Λ₁×Λ₂. Not much will change here, I can show how a dual looks like and do again some thresholding. I want to start with that two days from now.

Then I’ll come to non-separable windows and show how this case can be reduced to the 1D case if the lattice is fully separable and width and height of the image are relatively prime. I’ll again show a dual and some thresholding. This should be done over the weekend.

Then there will be non-separable windows on partially and truly non-separable lattices. I’ll just use Prinz’ code to show a dual and demonstrate thresholding. I don’t know whether I will show computations on a truly non-separable lattice. Maybe I’ll just mention the idea of image segmentation or down-/upsampling.

So, maybe I can start doing a roundup at Oct. 15th and hand my thesis out to HGFei during that week, as my holidays are starting at Oct. 20th and I’ll return at Nov. 3rd. In the week after my holidays I have time for cleaning it up (minor corrections/additions, preface, appendix), and in the week between Nov. 12th and Nov. 16th I want to hand it out to the print shop. The Master exam is to be scheduled in the mid of December, maybe in the week before the winter family days. This. Must. Work.