Basis selection for wavelet processing of sparse signals

The sparsity of a signal in a wavelet domain depends on both the wavelet basis and the exact form of the signal. We consider the selection of a wavelet basis that can efficiently represent a piecewise polynomial signal that is itself sparse in the signal domain. Accounting for the inherent sparsity of the signal allows for the maximum wavelet filter length and number of decomposition levels to be computed so as to guarantee that the resulting wavelet-domain representation is at least as sparse as the original signal, a desirable property for most wavelet processing techniques.