Kenneth E. Barner and Gonzalo R. Arce. Permutation filters: A class of nonlinear filters based on set permutations. IEEE Transactions on Signal Processing, 42(4):782--798, 1994. 109 BIBLIOGRAPHY 110  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a trimmed mean. When an abrupt transition is detected, the filter behaves like a median, which preserves edges. Unfortunately, the median filter also destroys fine details, as illustrated in Figure 1.3. Another extension of OSFs to the nonstationary case, called a Permutation Filter or or P filter [10], has apparently not yet been tested on image restoration problems. 1.3.2 Lee s local statistics filter The Lee filter [11] is able to smooth away noise in flat regions, but leave fine details (such as lines and text) unchanged. It uses small windows (3x3,5x5 or 7x7) Within each window, the ....

Kenneth E. Barner and Gonzalo R. Arce. Permutation filters: A class of nonlinear filters based on set permutations. IEEE Transactions on Signal Processing, 42(4):782--798, 1994. 109 BIBLIOGRAPHY 110

....these limitations a cascade of FIR filters followed by a WOS filter, a structure known as FIR WOS hybrid filter, has been proposed [1] While showing improved performance in near Gaussian environments, FIRWOS filters suffer from the constraints on the WOS weights. L [3, 4] and permutation [5, 6] filters overcome this deficiency in that they admit real valued (positive and negative) filter coefficients and, consequently, can be designed to have a wide range of filtering characteristics. Unfortunately, the complexity of L and permutation filters increases very rapidly with the window ....

K. E. Barner and G. R. Arce, "Permutation filters: a class of nonlinear filters based on set permutations," IEEE Transactions on Signal Processing, vol. 42, pp. 782--798, April 1994.

.... Many generalizations of rank order filters have been proposed that incorporate some form of temporal information [2] 6] 7] 8] Still, due to their constrained nature, these methods do not fully utilize the information contained in both the temporal and rank ordering of the observed data [9]. Recently, several filtering methods that operate on the full information contained in the temporal to rank mapping, x 7 x r , have been developed [9] 10] These filters are referred to as Permutation (P) filters because heir output is a function of the permutation that maps x to x r . P ....

.... constrained nature, these methods do not fully utilize the information contained in both the temporal and rank ordering of the observed data [9] Recently, several filtering methods that operate on the full information contained in the temporal to rank mapping, x 7 x r , have been developed [9], 10] These filters are referred to as Permutation (P) filters because heir output is a function of the permutation that maps x to x r . P filters can be derived as either weighted sum or selection type filters. In a selection P filter, the mapping x 7 x r determines which input sample is ....

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K. E. Barner and G. R. Arce, "Permutation filters: A class of non-linear filters based on set peremutations", IEEE Trans. Sig. Proc., vol. 42, no. 4, Apr. 1994.

.... order statistic (GWOS) filters, are two filter classes addressing these issues, both of which extend the threshold decomposition architecture to include cross level links [16, 17] Another filter class recently introduced that addresses these issues is the class of selection permutation filters [1]. While this last class has been shown to overcome the limitations of WOS and stack filters, its implementation is computationally expensive, since N possible permutations must be taken into account in deciding the filter s output value. Approaches that combine ranking or thresholding with ....

....i are assigned the same value regardless of the observation permutation. In the PWOS[N Gamma 1] filter, the complete mapping from location to rank for all samples in the observation vector is used to assign the weights, making it equivalent to the Permutation Filter introduced by Barner and Arce [1]. The following examples illustrate the operation of PWOS filtering. We first present an example where the filter weights are all positive integers. We then present a simple example that describes the replication operator for the case where the weights are real and positive. Consider the PWOS ....

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K. E. Barner, G. R. Arce, "Permutation filters: a class of nonlinear filters based on set permutations," To appear in the IEEE Transactions on Signal Processing, vol. ASSP-42, April 1994.

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