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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.

For the purposes of separating the specific components of nonsteady signals, the ℇ-separating nonlinear filter bank is proposed. Previously, the authors proposed a nonlinear digital filter called the ℇ-filter. This filter effectively eliminates the small signal amplitude random noise superimposed on a signal with a large signal changing component. The ℇ-filter bank proposed in this paper consists of these ℇ-filters and separates the components by taking account of both the signal amplitude and frequency. Further, a filter system for beautifying facial images using this filter bank is proposed. The human facial image consists not only of large-signal components such as the frame, eyes, nose, and mouth, but also of small-signal high-frequency components such as fine wrinkles as well as small-signal medium-frequency components such as large wrinkles and blemishes. Additionally, ultrasmall-amplitude high-frequency components expressing the natural roughness of the skin also exist. The present filter bank can eliminate wrinkles and blemishes while maintaining the natural roughness of the skin, allowing beautification of the skin of facial images to be performed effectively. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(4): 52– 62, 2007; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/ecjc.20241 [ABSTRACT FROM AUTHOR]

A novel image-processing technique based on fuzzy rules is proposed. This technique uses human knowledge about how an image should be processed depending on the local characteristics of image. The knowledge is represented by fuzzy rules and is also represented by a multidimensional nonlinear function which can be optimized by training. Efficient noise reduction and edge detection are realized by this fuzzy rule-based method. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 457–461, 1997 [ABSTRACT FROM AUTHOR]

When a random noise is superposed on a non-Gaussian signal with an abruptly changing component, as in the ease of the image signal, it is impossible for the conventional linear filter to eliminate the noise effectively. This is one of the cases where the nonlinear filter should be applied. This paper proposes a nonlinear digital filter based on the layered neural network, including the optimization of the nonlinear function. The proposed filter can effectively eliminate the noise by utilizing the nonlinearity of the layered neural network and its learning function. Another point is that the performance can be improved by the piecewise-linear approximation of the nonlinear function and the automatic design of the optimal nonlinear function. The effectiveness of the proposed filter is demonstrated by eliminating the noise from the two-dimensional image signal. [ABSTRACT FROM AUTHOR]

This paper proposes the median filter based on the fuzzy rules, as a filter that effectively eliminates the impulsive noise without greatly distorting the signal such as image. It is already known that the median filter is effective in eliminating the impulsive noise, but the median filter also distorts the signal waveform itself. To cope with this situation, it is desirable that the filter should operate as the median filter when there exists the impulsive noise and, if not, should only pass the input to the output. In this approach, however, the rule to decide on the existence/nonexistence of the impulsive noise generally is ambiguous. From such as viewpoint, this paper proposes a new type of a median filter where then above decision rule is represented by the fuzzy rules and the output is controlled by the result of the decision. The filter is designed optimally by training. The effectiveness of the filter is demonstrated by actually eliminating the noise from the image. [ABSTRACT FROM AUTHOR]

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]

A digital filter is developed to estimate signals containing discontinuities from observations contaminated with low-amplitude white noise. Called an &epsilon-Kalman filter, this is a Kalman filter combined with a nonlinear function. It is very effective for signals with known statistical properties. Principles of operation and realization of the filter are discussed. It is compared with another nonlinear filter called an ε-filter also proposed by the authors. Results of computer simulations are shown to demonstrate the effectiveness of the new filter. Pictorial examples are also provided. [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]