Wavelet transform domain filters: a spatially selective noise filtration technique

Wavelet transforms are multiresolution decompositions that can be used to analyze signals and images. They describe a signal by the power at each scale and position. Edges can be located very effectively in the wavelet transform domain. A spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced. A high correlation is used to infer that there is a significant feature at the position that should be passed through the filter. The authors have tested the technique on simulated signals, phantom images, and real MR images. It is found that the technique can reduce noise contents in signals and images by more than 80% while maintaining at least 80% of the value of the gradient at most edges. The authors did not observe any Gibbs' ringing or significant resolution loss on the filtered images. Artifacts that arose from the filtration are very small and local. The noise filtration technique is quite robust. There are many possible extensions of the technique. The authors see its applications in spatially dependent noise filtration, edge detection and enhancement, image restoration, and motion artifact removal. They have compared the performance of the technique to that of the Weiner filter and found it to be superior.