Wavelet Denoising

In this communication we present the first results of a project whose goal is to remove artifacts from electroencephalographic epileptic signals. More precisely the present objective is to remove ocular (blinking) artifacts in simulated and real EEG signal using Independent Component Analysis and wavelet denoising algorithms.

Analysis of evoked potentials (EPs) on a single-trial basis allows the study of the dynamical characteristics of brain activity. However, single-trial responses are buried into the more prominent ongoing electroencephalographic (EEG) activity, and thus advanced procedures are needed to obtain the activity only of the cortical generators that are activated by the experimental task under study. We compare the effectiveness

EEG recordings are usually affected by various artifact types come from non-neural sources and make it difficult for accurate signal classification in the later stage. Thus reliably detecting and removing artifacts from EEG by an automated signal processing algorithm is an active research area. In this paper we have developed a wavelet based artifact removal algorithm from EEG data that selects the best (optimal) threshold parameters, and hence consequently provides the best performance of artifact removal. In the proposed algorithm we choose to sweep both the wavelet filter parameter and threshold parameters until the best accuracy and/or least distortion is achieved by making a decision based on a reference dataset. The criteria for optimized selection are based on the metrics that quantify both amount of artifact removal and amount of distortion in the signal in both time and frequency domain. The algorithm is tested on synthesized EEG data that include different artifact templates and thus quantifies the performance based on several time and frequency domain measures. The achieved results prove that by selecting the optimum mother wavelet and parameter values adaptively would give the best performance both with regard to amount of artifact removal and least signal distortion compared with selecting any predefined mother wavelet and/or constant threshold parameter. This research would help the EEG signal analysis community a platform to work further in future on such problem to be able to properly select the wavelet parameters.

A new method is presented to denoise 1-D experimental signals using wavelet transforms. Although the state-of-the-art wavelet denoising methods perform better than other denoising methods, they are not very effective for experimental signals. Unlike images and other signals, experimental signals in chemical and biophysical applications, for example, are less tolerant to signal distortion and under-denoising caused by the standard wavelet denoising methods. The new method: 1) provides a method to select the number of decomposition levels to denoise; 2) uses a new formula to calculate noise thresholds that does not require noise estimation; 3) uses separate noise thresholds for positive and negative wavelet coefficients; 4) applies denoising to the approximation component; and 5) allows the flexibility to adjust the noise thresholds. The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion. In addition, its computation time is more than six times faster.

According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes de-noising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.

Phonocardiograms (PCGs) have many advantages over traditional auscultation (listening to the heart) because they may be replayed, may be analysed for spectral and frequency content, and frequencies inaudible to the human ear may be recorded. However, various sources of noise may pollute a PCG including lung sounds, environmental noise and noise generated from contact between the recording device and the skin. Because PCG signals are known to be non-linear and it is often not possible to determine their noise content, traditional de-noising methods may not be effectively applied. However, other methods including wavelet de-noising, wavelet packet de-noising and averaging can be employed to de-noise the PCG. This study examines and compares these de-noising methods. This study answers such questions as to which de-noising method gives a better SNR, the magnitude of signal information that is lost as a result of the de-noising process, the appropriate uses of the different methods down to such specifics as to which wavelets and decomposition levels give best results in wavelet and wavelet packet de-noising. In general, the wavelet and wavelet packet de-noising performed roughly equally with optimal de-noising occurring at 3-5 levels of decomposition. Averaging also proved a highly useful de-noising technique; however, in some cases averaging is not appropriate. The Hilbert Transform is used to illustrate the results of the de-noising process and to extract instantaneous features including instantaneous amplitude, frequency, and phase.

This paper compares wavelet and short time Fourier transform based techniques for single channel speech signal noise reduction. Despite success of wavelet denoising of images, it has not yet been widely used for removal of noise in speech signals. We explored how to extend this technique to speech denoising, and discovered some problems in this endeavor. Experimental comparison with large amount test data has been performed. Our results have shown that although the Fourier domain methods still has the superiority, wavelet based alternatives can be very close, and enormous different configurations can still be tried out for possible better solutions.

In this paper we propose several improvements to the original non-local means algorithm introduced by Buades et al. which obtains state-of-the-art denoising results. The strength of this algorithm is to exploit the repetitive character of the image in order to denoise the image unlike conventional denoising algorithms, which typically operate in a local neighbourhood. Due to the enormous amount of weight computations, the original algorithm has a high computational cost.

IJCSNS International Journal of Computer Science and Network Security, VOL.10 No.1, January 2010 58 ... Manuscript received January 5, 2010 Manuscript revised January 20, 2010 ... Comparison of Filters used for Underwater Image Pre-Processing

Digital video cassette (DVC) is a quickly proliferating new standard for real-time digital video recording. DVC is presently used both in consumer and professional applications. In this paper we describe the DVC principles, data organization and video decoding algorithm. Although typically DVC video has very good quality, at low-light levels noise becomes pronounced. We show that noise in the DVC can be reduced by digital postfiltering. For this purpose, a wavelet denoising algorithm is suggested due to its unique properties. Wavelet denoising is described in detail and results of noise reduction are illustrated on examples

Deep neural network as a part of deep learning algorithm is a state-of-the-art approach to find higher level representations of input data which has been introduced to many practical and challenging learning problems successfully. The primary goal of deep learning is to use large data to help solving a given task on machine learning. We propose an methodology for image de-noising project defined by this model and conduct training a large image database to get the experimental output. The result shows the robustness and efficient our our algorithm.