hit Signal Image Processing Seminar 2005/2006

The organisers are Dr Inna Kozlov, Dr Anatoly Golberg and Professor Eduard Yakubov. Please contact them to suggest a potential speaker.

The seminar language is English. Unless otherwise is specified, the seminars take place on Wednesdays at 13:00/Fall Term, in the Seminar Room 330/5, Margalit Building. Light refreshments are served quarter an hour before the announced seminar time.

21 Dec 2005

Wednesday 15:00

Room 330/5

We construct multi-resolution ellipsoid covers of R^d that can adapt to the geometry of a given domain or to the point/curve/surface singularities of a given input function. We show that the covers naturally impose anisotropic quasi-distances in R^d. For example, in the bivariate case, one may place long and thin ellipses along the curve singularities of a given function, but cover the areas away from the singularities by disks. In this example, the derived quasi-distance 'warps' the space near the singularities, yet is almost Euclidian away from them. We can also construct covers and quasi-distances using higher order local elements that are 'banana shaped'. Over each level of the ellipsoid cover we place polynomial reproducing bumps that are supported on the ellipsoids and form a partition of unity. Using the framework of spaces of homogeneous type, we then obtain anisotropic wavelet frames, which provide representations in L_p, p > 1. Since the wavelets are essentially supported on the micro-local elements of the cover, they can be highly anisotropic. In these settings we also introduce anisotropic Besov-type spaces that are governed by the anisotropic quasi-distances. Functions with geometric structure, such as curve/surface singularities have higher smoothness in the adaptive Besov-type space we propose.

23 Nov 2005

Wednesday 13:00

Room 330/5

The problem of sparse approximations/representations in redundant frame systems will be discussed. In appropriate settings, this problem is essentially equivalent to all 3 main problems of Coding Theory: data compression (source encoding), error correcting codes (channel encoding), and secret data transmission (cryptography). In addition, such problems as compressed sensing, in-painting, and probably many others can be reduced to sparse approximations.