On the correlation property of multiscaling coefficients for signal denoising

The discrete multiwavelet transform (DMWT) enables a signal to be analyzed in a multiresolution and multidimensional way. While the generated multiwavelet coefficients are vectors in nature, it has been generally understood that correlation exists between the vector elements. This feature has been adopted particularly in image coding applications to allow efficient design of VQ codebook. For a multiresolution analysis, the multiwavelet coefficients are generated from the multiscaling coefficients of the upper level. In this paper, we show that many multiwavelet systems cannot give correlated multiscaling vector elements, as different from the multiwavelet vector elements. But for those that can give correlated multiscaling vector elements, they can provide much information to assist in identifying the "blank" regions in a noisy signal. A new denoising algorithm is then proposed based on this feature and is particularly useful for sparse source signals.