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A framework is effective in restoration of images corrupted with Gaussian noise, and mixed Gaussian and impulse noise. Simulations show that the method efficiently suppresses noise, preserves images and is robust. The output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window controls the filtering operation. The results obtained using different algorithms are discussed.

This paper proposes a median-type fuzzy filter, aiming at the signal estimation in the case where the impulse and white Gaussian noise are superposed on the signal with sudden changes, such as the image signal. The filter is realized by generalizing the fuzzy filter previously proposed by the authors. In the previously proposed fuzzy filter, the signal point to be estimated is taken as the reference point and the signal is estimated by determining the input signals relatively close to the reference point, using the fuzzy clustering; whereas the filter proposed in this paper uses the median value of the input signal sequence as the reference point and the signal is estimated by determining the input signals close to that reference point using the fuzzy clustering. The signal is estimated by determining the center of gravity of the cluster of the points close to the median. Furthermore, in the proposed filter, the optimum design is realized by learning with respect to appropriate training signals. It is in general not possible to decide definitely whether or not the input signal is close to the median, and thus the fuzzy clustering is effective since it takes into consideration the ambiguity of the signal. By introducing the fuzzy clustering, it is shown in particular than an effective signal estimation is realized for the signal with subtle changes. [ABSTRACT FROM AUTHOR]

The authors investigated construction of an extended-order statistic filter to remove non-Gaussian white noise added to image signal. First, they devised a differential-order statistic filter using signal-differential ordering instead of a signal-value ordering and estimated its noise reduction performance. Next, they proposed an extended-order statistic filter which unifies the three-order information of time, signal value, and signal differences obtained from a signal within the filter window. Preparing the 3-dimensionalized filter coefficient space and using filter coefficients chosen sequentially in the three different orders among them allow effective noise reduction performance to be obtained. In addition, as a method for resolving a problem on the design method of filter coefficients, investigation was made using a synthesized training sequence. Extracting parameters necessary to a linear AR model from an objective signal, it is shown that the filter design using a training sequence synthesized from it gives noise reduction performance similar to the one at the optimal design. [ABSTRACT FROM AUTHOR]