Noise Reduction By Constrained Reconstructions In The Wavelet-transform Domain

Most filtering techniques involve a trade off between the spatial resolution and the signd-to-noise ratio. Ideally, one wishes to smooth noise while still preserving or enhancing edges. We present a technique of suppressing noise while preserving or even enhancing the sharpness of edges. We have combined Mallat and Zhong’s technique for compact image coding and a modification of Witkin’s edge identification method. We have used the technique to filter MR images; noise power is reduced by 90% or more while the gradients at major edges are 80% to 120% of their original values. Such dual demands are incompatible in conventional filtering techniques. Our technique is an extension of Mallat and Zhong’s work on signal representation and reconstruction from wavelet-transform (WT) maxima [l]. Mallat and Zhong have shown that a signal represented by the WT maxima, which are interpreted as multiscale edges, can be precisely reconstructed by iterative alternating projections. The stable convergence of this reconstruction enables one to slightly perturb the WT maxima representation and maintain nearly lossless coding. Mallat and Zhong have employed this technique in image compression [l, 21. As they point out, the technique can be used to filter noise from images. The key to our technique is the choice of maxima in the WT domain. We have used Witkin’s ”coarse-to-fine tracking” [3] to generate a WT maxima tree representation of an image, which is an extension to Mallat and Zhong’s original WT maxima representation. This work is supported by the Whitaker Foundation.