1 July 1996 Efficient nonlinear transform methods for image processing
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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, Samvel M. Atourian, David Zaven Gevorkian, David Zaven Gevorkian, Karen O. Egiazarian, Karen O. Egiazarian, Jaakko T. Astola, 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 . Submission:

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