Impulse noise detection and removal using fuzzy techniques

A new algorithm is presented which can remove impulse noise from corrupted images while preserving details. The algorithm is based on fuzzy impulse detection and fuzzy noise cancellation techniques. Experimental results show that the algorithm is capable of providing significant improvement over many published techniques in terms of both subjective and objective evaluations     

A well-balanced flow equation for noise removal and edge detection

An anisotropic nonlinear diffusion equation for image restoration is presented. The model has two terms: the diffusion term and the forcing term. The balance between these terms is made in a selective way, in which boundary points and interior points of the objects that make up the image are treated differently. The optimal smoothing time concept, which allows for finding the ideal stop time for the evolution of the partial differential equation is also proposed. Numerical results show the proposed model's high performance.     

Impulsive noise detection by second-order differential image and noise removal using adaptive nearest neighbourhood filter

A novel impulsive noise detection method based on the principle that the difference between the noisy pixel and the nearest good pixel will be different from the difference between two nearby good pixels. This is achieved by constructing a second-order differential image. Three new noise removal methods are presented. Simulated results show that the proposed filter gives far better results than many existing filters and is comparable to the results obtained by JM filter based on Jarque-Bera test. Our noise detection method is computationally simpler.     

High performance detection filter for impulse noise removal in images

A high performance detection (HPD) filter is proposed for impulse noise removal in images. In this approach, the noisy pixels are detected iteratively through several phases, based on a set of unique similarity criteria. Simulation results show that the HPD filter outperforms others at medium to high noise rates and suppresses impulse noise effectively while preserving image details, even thin lines.     

Fast detection and removal of impulsive noise using peer groups and fuzzy metrics

A novel approach to impulsive noise detection in color images is introduced. In the paper, the peer group concept is redefined by means of a certain fuzzy metric. This concept is employed for the fast detection of noisy pixels by taking advantage of the fuzzy metric properties. On the basis of the noisy pixel detection a switching filter between the arithmetic mean filter (AMF) and the identity operation is proposed. The proposed switching filter achieves a trade-off between noise suppression and signal-detail preservation and is faster than recently introduced switching filters based on the peer group concept.     

Fast impulsive noise removal

A generic n-dimensional filter with the primary purpose of eliminating impulsive-like noise is presented. This recursive nonlinear filter is composed of two conditional rules, which are applied independently, in any order, one after the other. It identifies noisy items by inspection of their surrounding neighborhood, and afterwards it replaces their values with the most "conservative" ones out of their neighbors' values. In this way, no new values are introduced and the histogram distribution range is conserved. This n-dimensional filter can be decomposed recursively to a lower dimensional space, each time generating two sets of n(n-1)-dimensional filters. This study, which focuses on the case of two-dimensional signals (gray scale images), explores one possible implementation of this new filter and orients the evaluation of its performance toward the median filter, as this filter is the basis of many more sophisticated filters for impulsive noise reduction. Tests were carried out using both real and artificial images. We found this new filter to be much faster than the median filter while performing comparably in terms of both image information conservation and noise reduction, which suggests that it could replace the median filter for the preliminary processing included in state-of-the-art noise removal filters. This new filter should either eliminate or attenuate most noisy pixels in synthetic and natural images not excessively contaminated. It has a slight smoothing effect on nonnoisy image regions. In addition, it is scalable, easily implemented, and adaptable to specific applications.     

Correction of MR kappa-space data corrupted by spike noise

Magnetic resonance images are reconstructed from digitized raw data, which are collected in the spatial-frequency domain (also called kappa-space). Occasionally, single or multiple data points in the k-space data are corrupted by spike noise, causing striation artifacts in images. Thresholding methods for detecting corrupted data points can fail because of small alterations, especially for data points in the low spatial frequency area where the k-space variation is large. Restoration of corrupted data points using interpolations of neighboring pixels can give incorrect results. We propose a Fourier transform method for detecting and restoring corrupted data points using a window filter derived from the striation-artifact structure in an image or an intermediate domain. The method provides an analytical solution for the alteration at each corrupted data point. It can effectively restore corrupted kappa-space data, removing striation artifacts in images, provided that the following three conditions are satisfied. First, a region of known signal distribution (for example, air background) is visible in either the image or the intermediate domain so that it can be selected using a window filter. Second, multiple spikes are separated by the full-width at half-maximum of the point spread function for the window filter. Third, the magnitude of a spike is larger than the minimum detectable value determined by the window filter and the standard deviation of kappa-space random noise.     

Detail preserving impulsive noise removal

Most image processing applications require noise elimination. For example, in applications where derivative operators are applied, any noise in the image can result in serious errors. Impulsive noise appears as a sprinkle of dark and bright spots. Transmission errors, corrupted pixel elements in the camera sensors, or faulty memory locations can cause impulsive noise. Linear filters fail to suppress impulsive noise. Thus, non-linear filters have been proposed. Windyga's peak-and-valley filter, introduced to remove impulsive noise, identifies noisy pixels and then replaces their values with the minimum or maximum value of their neighbors depending on the noise (dark or bright). Its main disadvantage is that it removes fine image details. In this work, a variation of the peak-and-valley filter is proposed to overcome this problem. It is based on a recursive minimum–maximum method, which replaces the noisy pixel with a value based on neighborhood information. This method preserves constant and edge areas even under high impulsive noise probability. Finally, a comparison study of the peak-and-valley filter, the median filter, and the proposed filter is carried-out using different types of images. The proposed filter outperforms other filters in the noise reduction and the image details preservation. However, it operates slightly slower than the peak-and-valley filter.     

Salt-and-Pepper noise removal by median-type noise detectors and detail-preserving regularization.

This paper proposes a two-phase scheme for removing salt-and-pepper impulse noise. In the first phase, an adaptive median filter is used to identify pixels which are likely to be contaminated by noise (noise candidates). In the second phase, the image is restored using a specialized regularization method that applies only to those selected noise candidates. In terms of edge preservation and noise suppression, our restored images show a significant improvement compared to those restored by using just nonlinear filters or regularization methods only. Our scheme can remove salt-and-pepper-noise with a noise level as high as 90%.     

Interictal spike detection using the Walsh transform

The objective of this study was to evaluate the feasibility of using the Walsh transformation to detect interictal spikes in electroencephalogram (EEG) data. Walsh operators were designed to formulate characteristics drawn from experimental observation, as provided by medical experts. The merits of the algorithm are: 1) in decorrelating the data to form an orthogonal basis and 2) simplicity of implementation. EEG recordings were obtained at a sampling frequency of 500 Hz using standard 10-20 electrode placements. Independent sets of EEG data recorded on 18 patients with focal epilepsy were used to train and test the algorithm. Twenty to thirty minutes of recordings were obtained with each subject awake, supine, and at rest. Spikes were annotated independently by two EEG experts. On evaluation, the algorithm identified 110 out of 139 spikes identified by either expert (True Positives = 79%) and missed 29 spikes (False Negatives = 21%). Evaluation of the algorithm revealed a Precision (Positive Predictive Value) of 85% and a Sensitivity of 79%. The encouraging preliminary results support its further development for prolonged EEG recordings in ambulatory subjects. With these results, the false detection (FD) rate is estimated at 7.2 FD per hour of continuous EEG recording.     

Adaptive-threshold neural spike detection by noise-envelope tracking

A new method for adaptive threshold setting is implemented and used in two threshold-based spike detectors: simple threshold and nonlinear energy operator. Detection quality assessment is performed using both a set of artificially generated signals and a real neural recording. Receiver operating curves are obtained and results show that, compared to fix threshold adaptive threshold setting yields performance improvement.     

Robust noise detection for speech detection and enhancement

A simple and robust method of reliably detecting stationary noise periods in a mobile telephony environment is presented. Such noise detection techniques are useful for updating parameters in adaptive voice activity detectors and for speech enhancement techniques, such as spectral subtraction, which require accurate noise models     

Fast algorithm for multiplicative noise removal

In this work, we consider a variational restoration model for multiplicative noise removal problem. By using a maximum a posteriori estimator, we propose a strictly convex objective functional whose minimizer corresponds to the denoised image we want to recover. We incorporate the anisotropic total variation regularization in the objective functional in order to preserve the edges well. A fast alternating minimization algorithm is established to find the minimizer of the objective functional efficiently. We also give the convergence of this minimization algorithm. A broad range of numerical results are given to prove the effectiveness of our proposed model.     

Studies with spike initiators: linearization by noise allowscontinuous signal modulation in neural networks

Engineers and neuroscientists generally believe that noise is something to be avoided in information systems. In this paper we show that noise, in fact, can be an important element in the translation of neuronal generator potentials (summed inputs) to neuronal spike trains (outputs), creating or expanding a range of amplitudes over which the spike rate is proportional to the generator potential amplitude. Noise converts the basically nonlinear operation of a spike initiator into a nearly linear modulation process. This linearization effect of noise is examined in a simple intuitive model of a static threshold and in a more realistic computer simulation of a spike initiator based on the Hodgkin-Huxley (HH) model. The results are qualitatively similar; in each case larger noise amplitude results in a larger range of nearly-linear modulation. The computer simulation of the HH model with noise shows linear and nonlinear features that we earlier had observed in spike data obtained from the VIIIth nerve of the bullfrog. This suggests that these features can be explained in terms of spike initiator properties, and it also suggests that the HH model may be useful for representing basic spike initiator properties in vertebrates.     

HOS-based image sequence noise removal.

In this paper, a new spatiotemporal filtering scheme is described for noise reduction in video sequences. For this purpose, the scheme processes each group of three consecutive sequence frames in two steps: 1) estimate motion between frames and 2) use motion vectors to get the final denoised current frame. A family of adaptive spatiotemporal L-filters is applied. A recursive implementation of these filters is used and compared with its nonrecursive counterpart. The motion trajectories are obtained recursively by a region-recursive estimation method. Both motion parameters and filter weights are computed by minimizing the kurtosis of error instead of mean squared error. Using the kurtosis in the algorithms adaptation is appropriate in the presence of mixed and impulsive noises. The filter performance is evaluated by considering different types of video sequences. Simulations show marked improvement in visual quality and SNRI measures cost as well as compared to those reported in literature.     

Cognition and removal of impulse noise with uncertainty

Uncertainties are the major inherent feature of impulse noise. This fact makes image denoising a difficult task. Understanding the uncertainties can improve the performance of image denoising. This paper presents a novel adaptive detail-preserving filter based on the cloud model (CM) to remove impulse noise. It is called the CM filter. First, an uncertainty-based detector identifies the pixels corrupted by impulse noise. Then, a weighted fuzzy mean filter is applied to remove the noise candidates. The experimental results show that, compared with the traditional switching filters, the CM filter makes a great improvement in image denoising. Even at a noise level as high as 95%, the CM filter still can restore the image with good detail preservation.     

Wavelet-based noise removal for biomechanical signals: a comparative study

The purpose of this paper is to present wavelet-based noise removal (WBNR) techniques to remove noise from biomechanical acceleration signals obtained from numerical differentiation of displacement data. Manual and semiautomatic methods were used to determine thresholds for both orthogonal and biorthogonal filters. This study also compares the performance of WBNR approaches with four automatic conventional noise removal techniques used in biomechanics. The conclusion of this work is that WBNR techniques are very effective in removing noise from differentiated signals with sharp transients while leaving these transients intact. For biomechanical signals with certain characteristics, WBNR techniques perform better than conventional methods, as indicated by quantitative merit measures.     

Removing spike noise from railway geometry measures with a fuzzy filter

This paper describes an algorithm based on fuzzy logic for the real-time detection and removal of impulsive spike noise from measures of track geometry in railway infrastructures. Spike noise is caused by random events, including anomalous reflections of external lights, detection or transmission errors within the measuring systems, and singular parts of tracks (switches, level crossings) hiding the rail profile. Its effects are extremely undesirable because they can generate erroneous alerts about inexistent railway defects. The real-time detection of spike noise is generally difficult, as the inspected tracks have extremely variable characteristics, and the measurement is performed in dynamic and turbulent conditions. By incorporating in a fuzzy system the typical rules used for offline analysis of the measured data, we develop a filtering algorithm that is able to perform spike removal in real time. Moreover, we also propose a variant of the fuzzy filter that improves the reconstruction of the corrupted measures. The proposed algorithm is validated on an extensive set of experimental investigations, which include a comparison with other algorithms selected from recent literature. The results confirm the effectiveness of the filtering algorithm, which has been recently implemented on some measuring vehicles for high-speed lines.     

Constructive action of noise for impulsive noise removal in scalar images

A nonlinear variational approach to remove impulsive noise in scalar images is proposed. Taking benefit from recent studies on the use of stochastic resonance and the constructive role of noise in nonlinear processes, the process is based on the classical restoration process of Perona-Malik in which a Gaussian noise is purposely injected. It is shown that this new process can outperform the original restoration process of Perona-Malik.     

Low-power MicroVrms noise neural spike detector for implantable interface microsystem device

In this paper, an ultra-low-power and low-noise spike detector is proposed for massive integration in the implantable multichannel brain neural recording device. The detector circuit with nonlinear energy operator (NEO) algorithms achieves the spike detecting from action potential including complex noise. The spike detector circuit consists of a differentiator with a fully-differential structure and a multiplier based on CMOS translinear using sub-threshold technique. The differentiator has the steepness of a transmission function with frequency +20 dB/dec, frequency response from 10 Hz to 10.5 kHz. The linear range of multiplier is from −0.9 V to 0.9 V at V_DD = ±1.65 V. The spike detector is implemented in 0.35 μm technology with fully-CMOS process. One detector die size is 0.0187 mm² and its total current consumption of 825 nA. As is demonstrated by measured results, the proposed circuit has detected the instantaneous energy of the input real spike signals well, which the noise of small than 218 μV_rms over a nominal bandwidth of 500–10.5 kHz.