Abstract

If a function is square integrable then we can recover it (in the L2 sense) by knowing all of its Fourier coefficients. In practical situations, such as MRI scanning, we will only be able to sample finitely many coefficients. In certain cases, representing the function in a different basis will allow us to get a better reconstruction than simply truncating the Fourier series. Throughout this talk I shall discuss the method that is used to do this (generalized sampling) when reconstructing with a basis of boundary corrected Daubechies wavelets. A fast reconstruction algorithm will be demonstrated, along with some interesting numerical results.

Little background knowledge will be assumed, and the talk should be accessible to first year CCA students. In particular, a detailed understanding of wavelets is not required and a brief summary of the main ideas will be provided.