February Fourier Talks 2012

For the sparse wavelet representation of a signal, the Q-factor* 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 Q-factor wavelet transform' (TQWT), for which the Q-factor 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 fully-discrete Parseval frame which can be efficiently implemented using radix-2 FFTs. Sparse TQWT representations obtained by L1-norm minimization will be shown. [* The Q-factor of a pulse is defined as the ratio of its center frequency to its bandwidth.]