Numerical methods for decomposition of 2D signals by rotation and wavelet techniques

Segregation of desirable and undesirable components in a signal given by measurements is a broad subject with many applications of huge importance. We focus on the problem that the signal to be detected is superposed by polluting signals which are characterized by a large amplitude and a few dominant directions. Such problems occur for instance in the analysis of seismic signals. We devise numerical algorithms which combine rotation of the given data with one-dimensional and two-dimensional discrete wavelet decomposition techniques respectively. The numerical algorithms are tested on both real and synthetic datasets and are compared with more classical techniques based on Fourier transforms.