IEEE SIGNALPROCESSING LETTERS, VOL. 12, NO. 1, JANUARY 2005 63 Impulsive Noise Removal Using Threshold Boolean Filtering Based on the Impulse Detecting Functions Igor Aizenberg, Member, IEEE, Constantine Butakoff, and Dmitriy Paliy Abstract—A new filter for impulsive noise removal is presented here. The problem of impulsive noise elimination is closely con- nected with the problem of maximal preservation of image edges. To avoid smoothing of the image during filtering, all noisy pixels must be detected. We consider here an approach, which is based on threshold Boolean filtering, where the binary slices of an image, obtained by the threshold decomposition, are processed by the impulse-detecting Boolean functions proposed in the paper. These functions provide a possibility of single-pass filtering, because they detect and replace impulses at the same time. Index Terms—Impulse detection, impulsive noise, threshold Boolean filter. I. INTRODUCTION I MPULSIVE noise always significantly damages an image. Noise with even a small corruption rate can corrupt most important details. A commonly used filtering approach in this case is median filtering [1]. It usually allows a complete elim- ination of impulsive noise, but its significant disadvantage is image smoothing. Other nonlinear filters that are used for the same purpose (for example, rank-order filters [1]–[3], stack fil- ters [1], weighted median filters [1], [2]), preserve image edges better, but, in general, the results are not good enough. A good way to solve the edge preservation problem is noise detection. According to this approach only the pixels detected as noisy are filtered. Several impulse detectors developed re- cently should be mentioned. In [4] a filter, which is based on global image statistics and local statistics in the filter window, was proposed. This detector marks each pixel as either “no fil- tering”, “edges”, or “noisy”. However, it performs well only for the “salt and pepper” noise model. A detector proposed in [5] is based on an analysis of the so-called “edge flag image” created on the first pass. A differential rank impulse detector [6] com- pares the rank of the pixel of interest in variational series to the rank of the median and additionally it compares the brightness in the pixel of interest to the one closest to it in variational series. Manuscript received March 4, 2004; revised May 26, 2004. This work was supported in part by the Tampere International Center for Signal Processing, Tampere University of Technology, Finland, by the Collaborative Research Center of Computational Intelligence, Department of Computer Science, University of Dortmund, Germany, and by the Computer Vision Lab, Zaragoza Universit, Spain. The associate editor coordinating the review of this manu- script and approving it for publication was Prof. Pamela C. Cosman. I. Aizenberg is at Mapu 18, ap. 3, Tel Aviv 63434, Israel (e-mail: igora@hotbox.ru). C. Butakoff is with Zaragoza University, E-50009 Zaragoza, Spain (e-mail: cbutakoff@yahoo.com). D. Paliy is with Tampere University of Technology, Tampere 33720, Finland (e-mail: dmitriy.paliy@tut.fi). Digital Object Identifier 10.1109/LSP.2004.838198 The mentioned approaches use two-pass filtering, while from the performance point of view it would be very attractive to con- nect noise detection with filtering itself in a single-pass filter. The following recently proposed filters should be mentioned. The first one is the rational median hybrid filter [7], which uses several median filters and a rational decision rule to correct cor- rupted pixels. The second one is the Peak-n-Valley filter [8], which uses local maxima and minima to detect and correct im- pulses. The third one is the switching median filter [9], which uses four one-dimensional Laplacian operators to detect im- pulses and to separate them from edges. We want to propose here a new effective single-pass filter. Our solution is based on threshold Boolean filtering (TBF) [1], [10], where the signal’s binary slices, obtained by threshold decomposition, are processed by a Boolean function. The ef- ficiency of TBF follows from the useful properties of the par- ticular Boolean function, which is the base of this filter. Some ideas for the design of the Boolean functions that are used here were considered in [11] and [12]. One of these functions was used in [11] and [12] in the context of cellular neural Boolean filtering, when the image’s binary planes obtained by direct de- composition are processed separately. However, this approach showed good results only for the “salt and pepper” noise model. We also want to emphasize here the importance of filtering im- pulsive noise with a low corruption rate (below 15%–20% of corrupted pixels), because heavily corrupted images usually get much more attention, while the case of a low corruption rate is important because it requires especially accurate detection of corrupted pixels, since any misdetection leads to smoothing of edges and destruction of details. It should be mentioned that some preliminary ideas developed in this paper were considered in [13]. II. TBF USING IMPULSE DETECTING BOOLEAN FUNCTIONS Any impulse can be identified by a comparison of the brightness values of the analyzed pixel with the ones of the surrounding pixels. Correction of the noisy pixel can be consid- ered as a replacement of its value by the value of some function, whose arguments are values taken from a local window around this corrupted pixel. An attractive way to implement noise elimination is by splitting an image into binary slices, with further processing of these slices as binary images and merging the processing results into the resulting image. We will use here TBF introduced and deeply considered in [10]. A good observation of TBF is also done in [1]. Filtering of binary images itself is reduced to their processing using some Boolean function. We want to propose such Boolean functions that will be able to check whether 1070-9908/$20.00 © 2005 IEEE