COHERENT NOISE FILTERING USING RECONSTRUCTED PHASE SPACE

Within the framework of coherent noise attenuation, this paper describes an original filtering approach based on the dynamical system theory. The reconstructed phase space is used to interpret dynamical behavior of image measurements, i.e. of local pixel amplitudes. Originaly developed for time series, the method of delays allows reconstructing steady-state trajectories from measurements of a physical system. This contribution suggests a method of delays adapted to the 2D data issue. The phase space of an image is defined as vectors-axes in a Cartesian plane, containing the pixel amplitude at spatially delayed coordinates, the latter selected according to a directional neighborhood criterion. The space proposed helps to evaluate the statistical properties of local structures within the image. Structures with similar local dynamics occupy nearby locations in phase space. These dynamical properties allow modelling local periodic patterns corrupting the image, such as the coherent noise. The Average Phase Space (APS) is a modified frequency distribution map that consists of the amplitude mean of trajectories points. For the proposed filter, each pixel value of the output image corresponds directly to the APS magnitude at the location associated with the original pixel image. APS method is applied to synthetic and real noisy images. Findings indicate that APS filtering is a low-cost algorithm for coherent noise attenuation that preserves the quality of edges in images.

[1]  K. W. Cattermole.  The Fourier Transform and its Applications , 1965 .

[2]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

[3]  Ioannis A. Kakadiaris,et al.  Towards robust structure-based enhancement and horizon picking in 3-D seismic data , 2004, CVPR 2004.

[4]  E. Crescini.  Journal de Physique , 1895 .

[5]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .

[6]  A. Mackay.  "Textures" , 1987 .

[7]  D. C. Henley.  The Radial Trace Transform: an Effective Domain For Coherent Noise Attenuation And Wavefield Separation , 1999 .

[9]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[10]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[11]  P. Bakker,et al.  Image structure analysis for seismic interpretation , 2002 .

[12]  Antoine Guitton,et al.  Multiple attenuation in complex geology with a pattern-based approach , 2005 .

[13]  Stuart Bennett,et al.  A History of Control Engineering 1930-1955 , 1993 .

[14]  P. Bergé,et al.  L'ordre dans le chaos. , 1984 .

[15]  P. Glendinning.  Chaos in Dynamical Systems., by E. Ott , 1994 .

[16]  Antoine Guitton,et al.  Coherent noise attenuation using Inverse Problems and Prediction Error Filters , 2000 .

[17]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[18]  Joachim Holzfuss,et al.  Approach to error-estimation in the application of dimension algorithms , 1986 .

[19]  David C. Henley,et al.  Coherent noise attenuation in the radial trace domain , 2003 .