Impulse Noise Filtering using MLMVN Olivia Keohane Igor Aizenberg Manhattan College Manhattan College Riverdale, NY, USA Riverdale, NY, USA okeohane01@manhattan.edu igor.aizenberg@manhattan.edu Abstract— In this paper, we consider how a complex-valued neural network, the multilayer neural network with multi-valued neurons (MLMVN), can be efficiently used for impulse noise filtering. It is shown that MLMVN with only a single hidden layer of neurons can restore an image corrupted by random- valued impulse noise while carefully preserving edges and boundaries. MLMVN processes overlapping patches, which to a noisy image should be broken down. A network shall be trained using a robust learning set created from patches randomly picked up from many images. Then, the trained network should be used for actual filtering. Final intensities in pixels of a resulting image are obtained by averaging the intensities over all overlapping patches. This approach becomes highly efficient for images corrupted by random impulse noise with a low corruption rate of 5-10%. It makes it possible to preserve the smallest image details very carefully and avoid the smoothing of edges. MLMVN outperforms sophisticated filters with detectors of impulse noise for a lower corruption rate and shows comparable results for a higher corruption rate. Keywords— Complex-Valued Neural Networks, Multi-Valued Neuron, Multilayer Neural Network with Multi-Valued Neurons, MLMVN, Intelligent Filtering, Impulse noise I. INTRODUCTION Complex-valued neural networks (CVNN) demonstrate their high efficiency when solving various problems of pattern recognition, classification, and prediction. Their flexibility, generalization capability, and their higher functionality in comparison with their real-valued counterparts, are well known and are crucial when it is necessary to deal with highly nonlinear input/output mappings. A comprehensive review of these important features of CVNNs is given, for instance, in [1]-[3]. As it was already pointed out above, CVNNs reveal their high efficiency and superiority in solving real-world problems in a variety of significant areas. For example, forecasting of wind profiles [4] and productivity of oil wells [4], detection of landmines [6], analysis of EEG and signals decoding in brain- computer interfaces [5], and medical imaging [7]. In this paper, we consider how a complex-valued neural network, the multilayer neural network with multi-valued neurons (MLMVN), can be efficiently used for impulse noise filtering. Intelligent image filtering has attracted researches ever since neural networks and fuzzy techniques became commonly and widely used tools in the 1980s. During a long period of time, intelligent filtering was mostly applied by using a feedforward neural network with a single hidden layer and a single output neuron. In such a case, a neural network performs as a low pass filter. Therefore, a feedforward network with a single hidden layer is de-facto a low pass filter. However, this approach was essentially reduced to the intelligent “replication” of classical spatial domain filters. It was based on the processing of a 3x3 or 5x5 local window around a pixel of interest and creation of a single output that is a filtered intensity value in the pixel of interest. This approach was more experimental rather than useful because it was not capable of outperforming traditional spatial domain filters. Impulse noise filtering is a very specific kind of filtering. Unlike additive noise, which distorts image intensities by adding noisy additive components, impulse noise completely substitute original intensities. It is important to note that while any additive or even multiplicative noise corrupts an entire image, impulse noise corrupts only some of its pixels. A level of this corruption is characterized by the corruption rate – a percentage of pixels corrupted by impulses. For a long period of time, a classical median filter was considered the best tool for impulse noise removal. In fact, this filter is as powerful as it is simple. It can efficiently smooth impulses. However, a great disadvantage is while impulse noise does not corrupt an entire image, median filter is applied to all pixels of an image and thereby smoothing not only impulses, but everything else as well. This results in the heavy loss of image sharpness due to the smoothing of edges, boundaries and all small details. Because of this, there became a very high demand for the design of impulse detectors. A possibility to detect impulses prior to the use of median filter (or any other filter), makes it possible to apply filtering only to those specific pixels, which were marked as noisy, and thereby not affecting pixels which were detected clear. Many various detectors were designed. We can address the reader, for example to [9]-[14]. Intelligent tools were also used for impulse noise filtering because of their ability to solve pattern recognition problems and thus recognize, or detect, noisy pixels. We should mention, for instance approaches presented in [15]-[17]. In the 1970s-early 2000s, most efforts of the image processing community in the impulse noise filtering area were focused on the filtering of highly corrupted images. However, it became clear that while it is possible to remove noise even from heavily corrupted images (50-90% corruption rate), the quality of such filtering is low because an image loses its sharpness and all small details become smoothed and mostly indistinguishable. It is important to mention that a special interest was paid to the case of images corrupted by impulse noise with a low corruption rate. On the one hand, this case is of special interest because an accurate detection of impulses in such images makes it possible to remove noise without smoothing an image, its edges and boundaries. On the other hand, modern equipment used in image acquisition does not produce a heavy impulse noise. This makes the case of lower corruption rate a subject of a special attention. With this regard, 978-1-7281-6926-2/20/$31.00 ©2020 IEEE