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The authors propose a new method for restoring images corrupted by high-probability impulsive noise at 10 to 50%. The strength (number of instances) of impulsive noise present in the area adjacent to a processing point is not uniform even in images that are corrupted by high-probability impulsive noise. In addition, when a processing point itself does not represent high-probability impulsive noise, outputting the input signal as is without performing median filter processing is vital to avoid image degradation. Given the above, one approach for restoring images degraded by high-probability impulsive noise is to first determine whether or not a processing point represents impulsive noise, and then perform median filter processing only when it is determined that impulsive noise is present. Second, when performing median filter processing, the amount of impulsive noise adjacent to a processing point must be estimated, the size of the filter window appropriate to that amount must be set, and efforts to preserve the signal must be made. In the proposed method the authors were able to unify three types of fuzzy inference. In addition, the proposed method is superior at handling images degraded by impulsive noise over a probability range of 10 to 50% when the fuzzy sets are fixed by setting the fuzzy sets in the three fuzzy inferences appropriately. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(9): 43–57, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1118 [ABSTRACT FROM AUTHOR]

We propose a method that uses multiple Wiener filters based on region decomposition to restore natural images degraded by Gaussian noise. Usually, a Wiener filter is designed to be optimal for the entire image. However, because natural images are highly nonstationary, an effective method switches to the optimum filter for each local region. In this paper, we consider a method that repeatedly decomposes into four equal parts, the four regions obtained by dividing an image into four equal parts, and design a Wiener filter for each region. As the regions become smaller, the desired Wiener filter is not necessarily obtained because of the drop in reliability of the correlation functions used to find the Wiener filter. Therefore, we first study to what extent the restoration accuracy of a known source image is improved by ideal decomposition that repeatedly decomposes only regions where the accuracy will improve. We then present a practical method that sufficiently improves the restoration accuracy even when the source image is unknown. We next merge similar decomposed regions and investigate how many classes are essential for the decomposition and these class boundaries. Thus, we verify that the proposed decomposition implicitly accounts for properties such as the contours in the image and clearly demonstrate the suitability of the proposed method. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(8): 51–61, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1112 [ABSTRACT FROM AUTHOR]

In this paper, the authors propose a data-dependent weighted average filter (Video-DDWA: Video Data-Dependent Weighted Average) aimed at restoration of dynamic images deteriorated due to Gaussian additive noises. As proposed by the authors, this filter is based on the data-dependent processing, in which the filter weight is varied by multiple local information items derived from the data proximal to the processing point in a still image, with extension of this processing from a spatial filter to a temporal-spatial filter; and then the weight of adjacent frames is determined by detecting presence or absence of motion from the motion information such as new local information. There are several conventional methods of restoration of dynamic images that involve motion compensation with subsequent spatiotemporal filter processing, but they all have limitations as to the filter restoration performance due to noise-affected deterioration of the estimation accuracy of the motion vector. The proposed data-dependent filter using the motion information has among others the following advantages: (1) Because it involves detection of the motion degree at which noise influence is suppressed, it enables restoration of dynamic images featuring a high noise cancellation performance in still areas, without motion deterioration due to filter processing in motion areas—in other words, with processing that does not cause deterioration of movement and (2) the computing load is lower than that with motion-compensated filters. As compared to the conventional methods using motion compensation, this method enables attaining a high restoration performance not only for signals with a low S/N ratio at which the accuracy of the motion compensation estimation vector starts decreasing, but also for signals with a wide range of S/N ratios. The authors demonstrate with various application examples that this method is efficient for restoration of dynamic images. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(4): 1–10, 2001 [ABSTRACT FROM AUTHOR]

Since weighted median filters effective in recovering images belong to the class of stack filters, the authors have proposed a fuzzy weighted median (FWM) filter, which is a weighted median filter defined by a fuzzy Boolean function, and have presented its design method. The design of the FWM filter can be considered in terms of the design of the weight and the design of the fuzzy Boolean function separately. In the design methods developed to date, the fuzzy Boolean functions are sigmoid-type functions and the weights are S-type functions with only the distance from the processing point as a variable, which are approximated and require derivations of four parameters, which is an easy task. Such methods, however, are restricted to the class of designable FWM filters. In this paper, the class of designable FWM filters has been significantly expanded to incorporate nearly all classes of FWM filters by establishing all weights independently and by defining the fuzzy Boolean functions by appropriate functions in addition to the sigmoid-type functions. Thus, a high-performance filter is designed by the filter weight and the fuzzy Boolean function designed for the kinds of added noise for real image processing examples, which change more flexibly as compared with the FWM filters developed in the previous design methods. In addition, a design procedure for realistic cases in which only the images which are targets of processing are known is presented and a design method for an FWM filter, which is effective in practical terms, is presented by showing its performance. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(2): 95–106, 2001 [ABSTRACT FROM AUTHOR]

The stack filter is the most systematic among the nonlinear filters, including the weighted median filter and the morphology filter. The authors undertook to expand the class of stack filters and to increase the number of degrees of freedom in the design. They employed a fuzzy Boolean function in which the output Boolean function takes a continuous value between “0” and “1,” and proposed a fuzzy stack filter defined by that function. Up to the present, the fuzzy median filter and the fuzzy center weighted median filter have been presented as the most fundamental and simplest fuzzy stack filters. This paper proposes a fuzzy weighted median filter in which the weighted median filter, which is a more general nonlinear filter, is given a fuzzy property through the stack filter. The fuzzy weighted median filter changes continuously from the weighted median filter to the weighted average filter by varying the setting of the fuzzy Boolean function. This implies that the fuzzy weighted median filter has a high noise elimination ability for both impulsive and Gaussian noise. The fuzzy weighted median filter can be designed independently for the weight function and the fuzzy Boolean function. This paper aims at a simple design for the weight function and the fuzzy Boolean function, without losing its general character. The weight is approximated by an S-shaped function with only the distance from the processed point as the parameter, and the fuzzy Boolean function is approximated by a sigmoid function. The design is reduced to the determination of four parameters, which is performed by the LMS algorithm. Through application examples, the properties and the effectiveness of the fuzzy weighted median filter are revealed. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(10): 40–49, 1999 [ABSTRACT FROM AUTHOR]

This paper presents a design method of data-dependent filters that uses simplified fuzzy interference. Since the antecedents of fuzzy inference can comprise several local characteristics (i.e., observation values), it is possible for the fuzzy filter to adjust its weights to adapt to local image data. The tuning of membership functions and fuzzy rules of the proposed filter results in a least mean square (LMS)-like algorithm. Thus, local characteristics can be increased for the proposed fuzzy filter optimally. This paper, introduces a new observation value (calculated from local statistics) into the proposed filter. The proposed filter changes filter behavior according to the local properties of signals and provides good noise attenuation in all regions of image, including detail regions while still preserving the details. [ABSTRACT FROM AUTHOR]