Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

In this talk, we discuss the issue of source separation in a signal on the sphere or on the plane, relying on the sparsity of one signal component in a scale-discretized steerable wavelet basis. The steerability of wavelets allows to probe in detail the local morphology of a signal at each analysis scale. It gives access to local measures of signed-intensity, orientation, elongation, etc. The scale discretization of the wavelets allows the reconstruction of the signal analyzed. In this context, local directional features can be identified at any scale from their sparsity in wavelet space, and reconstructed after their separation from other signal components. In cosmology, this approach reveals to be of great interest for the search of topological defects in the cosmic microwave background signal, such as cosmic strings.