COHERENT NOISE FILTERING USING RECONSTRUCTED PHASE SPACE
Résumé
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.
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