Representing A Signal By Selected Wavelets

摘要

This paper indroduces an algorithm which decomposes a signal into a linear combination of waveforms that are selected from some wavelet bases. These waveforms are chosen in order to adapt the signal structure. It is proved that representing a signal by the selected wavelets can achieve integrated square error of order O(1/n), where n is the number of selected bases. It is interesting to note that here we use relatively small number of bases compared to the exponential number of bases by common wavelet expansion. We are compensated by the square error order of O(1/n) for the lost information.