Application of Wavelet Transform to the Detection of Signals in Noise

Signal detection based on wavelet transform is studied, and a concept of multiresolution likelihood ratio is put forward. It is shown that there exist some particular spaces in time domain, in which most of the signal energy is conserved while the noise energy is attenuated sharply. Therefore, based on wavelet transform, and by analyzing the likelihood ratio of the particular spaces in time domain, it can be easily determined that whether or not there are some signals mixed in noise