On the choice of a wavelet for signal coding and processing

It is argued that a good wavelet for representing a given signal is one that leads to a compact representation of the signal up to a given scale. Unfortunately, minimizing the distance between a given signal and its approximation up to a given scale using any wavelet is a difficult optimization problem. Instead, a tight upper bound on that distance is developed. The bound is an explicit function of the discrete set of coefficients defining the wavelet. By minimizing this upper bound one then obtains a good wavelet for representing the given signal