Title:Sparse signal representation and the tunable Qfactor wavelet transform
Abstract:For the sparse wavelet representation of a signal, the Qfactor* of the wavelet transform should be chosen so as to match the signal's oscillatory behavior. This talk describes a new wavelet transform, the 'tunable Qfactor wavelet transform' (TQWT), for which the Qfactor is continuously tunable. Therefore, the wavelet can be chosen according to the oscillatory behavior of the signal, so as to enhance the sparsity of a sparse representation. The TQWT is well suited for iterative algorithms for sparse representation as it is a fullydiscrete Parseval frame which can be efficiently implemented using radix2 FFTs. Sparse TQWT representations obtained by L1norm minimization will be shown. [* The Qfactor of a pulse is defined as the ratio of its center frequency to its bandwidth.]
