A translation-invariant wavelet representation algorithm with applications

We address the time-varying problem of wavelet transforms, and a new translation-invariant wavelet representation algorithm is proposed. Using the algorithm introduced by Beylkin, we compute the wavelet transform for all the circular time shifts of a length-N signal in 0(N log N) operations. The wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function. We apply the translation-invariant representation algorithm to a geoacoustic data compression application. The results show that the new algorithm can reduce the distortion (the squared error in our case) substantially, if the input signals are transients that are sensitive to time shifts.