Title: Using bandwidths as scales in multiscale localpolynomial decompositions
Authors: Mohamed Amghar - Universite Libre de Bruxelles (Belgium) [presenting]
Maarten Jansen - ULB Brussels (Belgium)
Abstract: The choice of the bandwidths in a multiscale local polynomial data transform is discussed. The transform adopts the local polynomial smoothing paradigm for the construction of a multiresolution data decomposition, much like a wavelet transform or a Laplacian pyramid. The bandwidths depend on the resolution level, defining for each level the scale of the coefficients. As a result, the scale is not necessarily dyadic as in a discrete wavelet transform, nor is it grid dependent as in second generation wavelet transform. Unlike in a uniscale local polynomial smoothing scheme, the bandwidth in a multiscale data transform is not optimised for data processing, i.e. smoothing, but rather for data transformation. The bandwidth at each level should be chosen in a way that it makes the representation after transformation as suitable as possible for subsequent, non-linear processing. The objective is to find bandwidths that lead to optimal multiscale decomposition, in the sense that the resulting decomposition is as easy to work with. In particular we optimize the bandwidths with respect to sparsity of the decomposition on one hand, and the noise reduction of the decomposition through an orthogonal prefilters on the other hand.