1 July 1996 Efficient nonlinear transform methods for image processing
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J. of Electronic Imaging, 5(3), (1996). doi:10.1117/12.242907
A filter structure formed as a linear combination of stack filters (L-stack-filters), is studied. This type of filters include many useful filter classes, e.g., linear FIR filters and nonlinear threshold Boolean filters, and L-filters. An efficient algorithm for finding optimal filter coefficients under the mean squared error (MSE) criterion is derived. 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 a generalized structure of the FFT flowchart. It is shown that FFT-LFs effectively remove mixed Gaussian and impulsive noise. While possessing good characteristics of performance, FFT-LFs are simple in implementation. In the sense of implementation the most complicated FFT-LFs are the 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 and Walsh 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. An efficient implementation of L-stack-filters is also proposed.
Samvel M. Atourian, David Zaven Gevorkian, Karen O. Egiazarian, Jaakko T. Astola, "Efficient nonlinear transform methods for image processing," Journal of Electronic Imaging 5(3), (1 July 1996). https://doi.org/10.1117/12.242907

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