Marcelo Zimbres Silva Wuppertal

Denoising of signals on the sphere with a sparse expansion in wavelets. (pdf)

Data analysis commonly concerns data distributed on the real line or images on the plane. But other experiments also acquire data in all directions defined on the sphere. This is notably the case of observations of the cosmic microwave background (CMB) and of cosmic rays by the Pierre Auger observatory. Experimental data sets are always affected by various sources of noise, that may be related with instrumentation. Signals can also originate from various sources, which arises the need for separation of components seeing as signal from those seeing as noise. In this presentation, we intend to show how we can separate the noise from the signal using wavelet techniques. First, we compare wavelet expansion with Fourier expansion of local structures in one dimension, where visualization is easier. After that we jump to simulated data on the sphere where we use the Donoho and Johnstone threshold to filter a point like source immersed in an stochastic background.