Noise reduction with a multiscale edge representation and perceptual criteria

The wavelet multiscale edge representation of signals developed by S.G. Mallat and S. Zhong (1991) provides a new tool for signal and image processing. A tree structure was built from wavelet-transform (WT) maxima, and metrics for analyzing the WT maxima tree were developed. These metrics fall into two classes corresponding to two perceptual criteria (scaling and spatial stabilities) for discriminating features from background noise. Identified noisy branches are trimmed off the WT maxima tree. This technique of noise reduction preserves edges well while suppressing noise. The results of processing simulated and medical images with this technique are presented.<<ETX>>

[1]  J. Galayda.  Edge Focusing , 1981, IEEE Transactions on Nuclear Science.

[2]  D Marr,et al.  Bandpass channels, zero-crossings, and early visual information processing. , 1979, Journal of the Optical Society of America.

[3]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[4]  Walter F. Bischof,et al.  Parsing scale-space and spatial stability analysis , 1988, Comput. Vis. Graph. Image Process..

[5]  Dennis M. Healy,et al.  Noise Reduction By Constrained Reconstructions In The Wavelet-transform Domain , 1991, Proceedings of the Seventh Workshop on Multidimensional Signal Processing.

[6]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Azriel Rosenfeld,et al.  Multiresolution image processing and analysis , 1984 .

[8]  Stéphane Mallat,et al.  Compact image coding from edges with wavelets , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[9]  Jan-Olof Eklundh,et al.  On the computation of a scale-space primal sketch , 1991, J. Vis. Commun. Image Represent..

[10]  A. Rosenfeld.  Some Useful Properties of Pyramids , 1984 .

[11]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[12]  S. Zhong.  Edge representation from wavelet transform maxima , 1991 .

[13]  T. Poggio.  Vision by man and machine. , 1984, Scientific American.

[14]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[15]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[16]  Stéphane Mallat,et al.  Zero-crossings of a wavelet transform , 1991, IEEE Trans. Inf. Theory.