25 March 1996 Nonlinear filters based on ordering by FFT structure
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A filter structure formed as a linear combination of a bank of nonlinear filters, in particular, as linear combination of a bank of stack filters, is studied. This type of filter includes many known filter classes, e.g., linear FIR filters and nonlinear threshold Boolean filters, L-filters. An efficient algorithm based on joint distribution functions of stack filters for finding optimal filter coefficients under MSE (mean squared error) criterion is proposed. A subclass of the above filters, called FFT-ordered L-filters (FFT-LF), is studied in detail. In this case the bank of filters is formed according to the generalized structure of the FFT flowgraph. It is shown that FFT-LFs effectively remove mixed Gaussian and impulsive noise. Possessing good characteristics of performance, FFT-LFs are simple in implementation. The most complicated (in the sense of implementation) FFT-LFs are well known L-filters. We suggest an efficient parallel architecture implementing FFT-LFs as well as a family of discrete orthogonal transforms including discrete Fourier, Walsh and other transforms. Both linear and nonlinear L-filter-type filters are implemented effectively on the architecture. Comparison with known architectures implementing both linear and nonlinear filters reveals advantages of the proposed architecture.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Karen O. Egiazarian, Jaakko T. Astola, Samvel M. Atourian, David Zaven Gevorkian, "Nonlinear filters based on ordering by FFT structure", Proc. SPIE 2662, Nonlinear Image Processing VII, (25 March 1996); doi: 10.1117/12.235823; https://doi.org/10.1117/12.235823

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