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Stack filters and the mean absolute error criterion

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2 Author(s)
Coyle, E.J. ; Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA ; Lin, J.-H.

A method to determine the stack filter which minimizes the mean absolute error between its output and a desired signal, given noisy observations of this desired signal, is presented. Specifically, an optimal window-width-b stack filter can be determined with a linear program with O(b2b) variables. This algorithm is efficient since the number of different inputs to a window-width-b filter is Mb if the filter has M-valued input and the number of stack filters grows faster than 2 raised to the 2b/2 power. It is shown that optimal stack filtering under the mean-absolute-error criterion is analogous to optimal linear filtering under the mean-squared-error criterion: both linear filters and stack filters are defined by superposition properties, both classes are implementable, and both have tractable procedures for finding the optimal filter under an appropriate error criterion

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:36 ,  Issue: 8 )