{"title":"An adaptive bayesian wavelet thresholding approach to multifractal signal denoising","authors":"A. Seghouane","doi":"10.1063/1.1835226","DOIUrl":"https://doi.org/10.1063/1.1835226","url":null,"abstract":"Multifractal functions are widely used to model irregular signals, while thresholding of the empirical wavelet coefficients is an effective tool for signal denoising. This paper outlines a Bayesian thresholding approach for multifractal functions observed in a white noise model. To do that, lacunary wavelet series are used to approximate the functions. These random functions are statistically characterized by two parameters. The first parameter governs the intensity of the wavelet coefficients while the second one governs its lacunarity. The estimation is obtained by placing priors on the wavelet coefficients that consists of a mixture of two normal distributions with different standard deviations. These variances are chosen adaptively according to the resolution level of the coefficients and depend on the multifractal function parameters. Estimators of these parameters are constructed and a closed form expressions for the posterior means of the unknown wavelets coefficients are obtained. An example is used to illustrate the method, and a comparison is made with other thresholding methods.","PeriodicalId":206062,"journal":{"name":"Proceedings of the 6th Nordic Signal Processing Symposium, 2004. NORSIG 2004.","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116912310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A novel wavelet based technique for detection and de-noising of ocular artifact in normal and epileptic electroencephalogram","authors":"S. Venkataramanan, N. V. Kalpakam, J. Sahambi","doi":"10.1049/CP:20040520","DOIUrl":"https://doi.org/10.1049/CP:20040520","url":null,"abstract":"The Electroencephalogram (EEG) is a biological signal that represents the electrical activity of the brain. Typical EEG instrumentation settings used are low pass filtering at 75Hz and paper recording at 100 µ V /cm and 30mm/s for 10 to 20 minutes over 8 to 16 simultaneous channels. A commonly encountered problem in clinical practice during EEG recording is the 'blanking' of the EEG signal due to blinking of the user's eyes. Eye-blinks and movements of the eyeballs produce electrical signals that are collectively known as Ocular Artifacts and these are 10 to 100 times stronger than the EEG signal which is being recorded. The effective filtering of these Ocular artifacts is extremely difficult owing to the fact that their frequency spread (1Hz-50Hz) is observed to be overlapping with that of the EEG. Another major drawback of the existing frequency based de- noising techniques is that they require continuous recording of the Electrooculargram (EOG) signals as well. In this paper, we present a novel and simple technique for the detection and subsequent de-noising of these ocular artifacts using Haar wavelets of high orders. A comprehensive error analysis has been carried out, both in the time domain based artifact detection as well as the frequency domain based de-noising of EEG. This procedure has also got the advantage of being highly artifact selective and so we have applied it to detect and de-noise Epileptic EEG signals.","PeriodicalId":206062,"journal":{"name":"Proceedings of the 6th Nordic Signal Processing Symposium, 2004. NORSIG 2004.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126799010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Skewness maximization for impulsive sources in blind deconvolution","authors":"P. Paajarvi, J. LeBlanc","doi":"10.1109/NORSIG.2004.250187","DOIUrl":"https://doi.org/10.1109/NORSIG.2004.250187","url":null,"abstract":"In blind deconvolution problems, a deconvolution filter is often determined in an iterative manner, where the filter taps are adjusted to maximize some objective function of the filter output signal. The kurtosis of the filter output is a popular choice of objective function. In this paper, we investigate some advantages of using skewness, instead of kurtosis, in situations where the source signal is impulsive, i.e. has a sparse and asymmetric distribution. The comparison is based on the error surface characteristics of skewness and kurtosis.","PeriodicalId":206062,"journal":{"name":"Proceedings of the 6th Nordic Signal Processing Symposium, 2004. NORSIG 2004.","volume":" 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113947736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}