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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]

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 enlargement of a digital image is a process of narrowing the sampling interval. Since the image before the enlargement and that after the enlargement have different Nyquist frequencies, it is necessary to predict or estimate the high-frequency components that are lost in the image before processing and to complement these components in the enlargement process. It is noted that the image can be represented as the sum of Gaussian components and Laplacian components in a hierarchical structure (pyramid representation). There exists a strong correlation between the Laplacian images of the layers. Based on that property, Greenspan and Anderson have proposed a nonlinear procedure where the unknown Laplacian image of high resolution (i.e., containing the lost high-frequency components) is estimated from the Laplacian image of low resolution. This paper notes that the Greenspan procedure can be network-structured and proposes an enlargement method for digital images using a neural network (NN) for improving the resolution, based on generalizing the network. It is shown that the enlarged NN can be constructed almost independently of the kind of training image or of the hierarchy (resolution). It is also shown that a better enlarged image can be derived compared with Greenspan's method. In other words, the effectiveness and practical usefulness of the proposed method are demonstrated. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 19–29, 1999 [ABSTRACT FROM AUTHOR]

The authors have previously proposed a fuzzy stack filter that is defined by a fuzzy Boolean function. We have also presented a specific design method (called the fuzzy Boolean function determination method) for the most fundamental fuzzy stack filter, the FCWM (fuzzy center weighted median). By varying the fuzzy Boolean function, we can achieve both an arbitrary CWM filter and a weighted average value filter in which only the weights at arbitrary processing points are varied. Hence, in comparison with the CWM filter, our filter is better at eliminating Gaussian noise. In this paper, to improve the reconstruction accuracy of nonsteady state signals, such as the image signals, a data-dependent FCWM (DD-FCWM) is proposed anew. The data-dependent filter is an adaptive filter in which the filter parameters are varied in response to the nature of the data near the processing point (local information). In a DD-FCWM filter, the fuzzy Boolean function is varied by using local information. We demonstrate that the proposed DD-FCWM filter uses the local signal information to appropriately vary, not only the weights of the processing points, but also the filter mode (average value type or median type). Furthermore, by use of image processing examples, we demonstrate that highly accurate signal reconstruction can be attained. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 27–40, 1998 [ABSTRACT FROM AUTHOR]

An optimal filter in terms of removing noise can be determined for any signal distribution by using an order statistics (OS) filter, a typical nonlinear filter. For restoration of signals degraded by nonstationary signals such as an image signal, nonstationary noise, and mixed noise, an adaptive process in which the filter coefficients are varied in accordance with the local information is indispensable to improving signal accuracy. From these facts, an adaptive OS filter can be considered effective for image restoration. Most of the adaptive OS filters proposed so far have several fixed coefficients which are changed in accordance with the local information. However, for the restoration of signals such as deteriorated image signals, it is ideal to have the adaptive OS filter coefficients continuously change. In this paper, filter window signals are fuzzy-clustered into five predefined typical classes using a fuzzy inference system where three types of local information are the parameters of the antecedent part. Since there is an optimal OS filter for each of the five classes, we obtain the sum of outputs of the proposed filters from the filter output value which is optimal for each class, weighted by the degree of assignment of each filter class. With the proposed adaptive OS filter, the filter coefficients are varied continuously, and improvement of image restoration accuracy is attempted. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(9): 70–80, 1997 [ABSTRACT FROM AUTHOR]