Contribution of the fractal dimension to multiscale adaptive filtering of SAR imagery

Radar images can show great variability from pixel to pixel, which is an obstacle to effective processing. This variability, due to speckle created by the radar wave coherence, necessitates the use of more adapted filters. Previous studies have shown that multiresolution wavelet analysis yields better results but produces artefacts due to multiscale decomposition. This paper proposes a method that reduces these effects by introducing the fractal dimension. The resultant filter combines wavelet decomposition and variance change model based on the level of variance estimated by studying the fractal dimension of the image.

[1]  Jelena Kovacevic,et al.  Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn , 1992, IEEE Trans. Inf. Theory.

[2]  Gregory W. Wornell,et al.  Estimation of fractal signals from noisy measurements using wavelets , 1992, IEEE Trans. Signal Process..

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

[4]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[5]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  M. S. Keshner.  1/f noise , 1982, Proceedings of the IEEE.

[7]  Jean-Luc Starck,et al.  1 - Restauration des images multi-échelles par l'algorithme à trous , 1994 .

[8]  Langis Gagnon,et al.  Speckle noise reduction of airborne SAR images with symmetric Daubechies wavelets , 1996, Defense, Security, and Sensing.

[9]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Stefano Giordano,et al.  A wavelet-based approach to the estimation of the Hurst parameter for self-similar data , 1997, Proceedings of 13th International Conference on Digital Signal Processing.

[11]  Jean-Marc Boucher,et al.  Multiscale MAP filtering of SAR images , 2001, IEEE Trans. Image Process..

[12]  Ming-Jun Lai,et al.  Examples of bivariate nonseparable compactly supported orthonormal continuous wavelets , 2000, IEEE Trans. Image Process..

[13]  M. Vetterli.  Multi-dimensional sub-band coding: Some theory and algorithms , 1984 .

[14]  A. Lopes,et al.  A statistical and geometrical edge detector for SAR images , 1988 .

[15]  S. Kay,et al.  Fractional Brownian Motion: A Maximum Likelihood Estimator and Its Application to Image Texture , 1986, IEEE Transactions on Medical Imaging.

[16]  R. Caloz,et al.  Précis de télédétection , 2002 .

[17]  E. Nezry,et al.  Structure detection and statistical adaptive speckle filtering in SAR images , 1993 .

[18]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[19]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .