A new method of filtering MR images is presented that uses wavelet transforms instead of Fourier transforms. The new filtering method does not reduce the sharpness of edges. However, the new method does eliminate any small structures that are similar in size to the noise eliminated. There are many possible extensions of the filter.

Wavelet encoding is presented and compared to phase encoding. In wavelet encoding a distribution of spins is excited by a slice selective RF pulse; for each repetition time the distribution excited has the profile of a wavelet at different scale and translation. The spin density can be reconstructed with an inverse wavelet transform. Wavelet encoding has three advantages over phase encoding: (1) there is no Gibb's ringing from partial volume effects, (2) the effective repetition time can be 36 times the repetition time for a 256 x 256 image, and (3) motion artifacts are local and dramatically reduced. Using wavelet encoding, a 256 x 256 T2-weighted projection image can be acquired in 33 s.

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.

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