Reconstruction from Fourier Data by using Compactly Supported Multiscale Systems
Talk by Jackie Ma
Date: 12.11.14 Time: 16.15 - 16.45 Room: Y27H25
The acquisition of Fourier data appears in many real world problems, such as magnetic resonance imaging, X-ray computed tomography, etc. The collected data, can be viewed as a collection of point samples of the Fourier transform of some object of interest, e.g. the human brain. Having these measurements, we are then left with the task to find an approximation of the original object. In this talk we discuss how this sampling and reconstruction task can be modeled using the so-called generalized sampling reconstruction method. In particular, we will present some benchmark results regarding the number of measurements that are needed in order to guarantee stable reconstructions. The results are presented for some compactly supported multiscale systems, such as wavelets and shearlets.