Laplacian Signals Research Articles

Identification of atrial fibrillation drivers by means of concentric ring electrodes

Background and objectiveThe prevalence of atrial fibrillation (AF) has tripled in the last 50 years due to population aging. High-frequency (DFdriver) activated atrial regions lead the activation of the rest of the atria, disrupting the propagation wavefront. Fourier based spectral analysis of body surface potential maps have been proposed for DFdriver identification, although these approaches present serious drawbacks due to their limited spectral resolution for short AF epochs and the blurring effect of the volume conductor. Laplacian signals (BC-ECG) from bipolar concentric ring electrodes (CRE) have been shown to outperform the spatial resolution achieved with conventional unipolar recordings. Our aimed was to determine the best DFdriver estimator in endocardial electrograms and to assess the BC-ECG capacity of CRE to quantify AF activity non-invasively. Methods31 AF episodes were simulated using realistic tridimensional models of the atria electrical activity and torso. Periodogram and autoregressive (AR) spectral estimators were computed and the percentile (P90th, P95th and P98th) to impose on the dominant frequencies (DFs) across whole atria to define the best DFdriver estimator evaluated. The identification of DFdriver on DFs from BC-ECG and unipolar surface signals with conventional disc electrodes was compared. ResultsThe best DFdriver estimator was P95th and AR order 100. BC-ECG signals allowed better detection of AF activity than unipolar signals, with a significantly greater percentage of electrode locations in which DFdriver was identified (p-value 0.0095). ConclusionsThe use of BC-ECG signals for body surface Laplacian potential mapping with CRE could be helpful for better AF diagnosis, prognosis and ablation procedures than those with conventional disk electrodes.

Managing electromyogram contamination in scalp recordings: An approach identifying reliable beta and gamma EEG features of psychoses or other disorders.

ObjectiveIn publications on the electroencephalographic (EEG) features of psychoses and other disorders, various methods are utilized to diminish electromyogram (EMG) contamination. The extent of residual EMG contamination using these methods has not been recognized. Here, we seek to emphasize the extent of residual EMG contamination of EEG.MethodsWe compared scalp electrical recordings after applying different EMG‐pruning methods with recordings of EMG‐free data from 6 fully paralyzed healthy subjects. We calculated the ratio of the power of pruned, normal scalp electrical recordings in the six subjects, to the power of unpruned recordings in the same subjects when paralyzed. We produced “contamination graphs” for different pruning methods.ResultsEMG contamination exceeds EEG signals progressively more as frequencies exceed 25 Hz and with distance from the vertex. In contrast, Laplacian signals are spared in central scalp areas, even to 100 Hz.ConclusionGiven probable EMG contamination of EEG in psychiatric and other studies, few findings on beta‐ or gamma‐frequency power can be relied upon. Based on the effectiveness of current methods of EEG de‐contamination, investigators should be able to reanalyze recorded data, reevaluate conclusions from high‐frequency EEG data, and be aware of limitations of the methods.

Sensitivity of the General Linear Model to Assumptions

Non-Gaussian noise often causes in significant performance abatement for systems which are designed using Gaussian assumption. This report challenges the question of General Linear Model with White Gaussian Noise assumption in order to define the sensitivity of the performance of an optimal estimator. Gaussian noise models provide an important role in many signal processing applications. The Laplacian and Uniform signal are two worthy examples of noise that can be compared to the White Gaussian Noise, though the sensitivity which can be compared with any non-Gaussian. White Gaussian Noise has been considered for General Linear Models and deviation from whiteness would affect on our estimates under different circumstances. Moreover, new assumptions have been considered to generate different type of signals in order to evaluate the sensitivity of the General Linear Model.

Independent Component Analysis Using RRAMs

Resistive random-access memories (RRAM)s are considered a promising candidate for neuromorphic circuits and systems. In this letter, we investigate using TiO 2 RRAMs to solve blind source separation problem through independent component analysis (ICA) for the first time. ICA has numerous uses including feature extraction. We deploy a local, unsupervised learning algorithm (error-gated Hebbian rule) to extract the independent components. The online evaluation of the weights during the training is studied taking into consideration the asymmetric nonlinear weight update behavior. The effects of the device variability are considered in the results. Finally, an example of de-mixing two Laplacian signals is given to demonstrate the efficacy of the approach.

Sensitivity analysis of HD-sEMG amplitude descriptors relative to grid parameter variations of a cylindrical multilayered muscle model

The aim of this work is to perform a sensitivity analysis of a high density surface electromyogram (HD-sEMG) amplitude descriptors according to several grid parameters. This study is motivated by the fact that the electrode grid position and layout are crucial to record relevant electromyographic data. For this purpose, an analytical limb model is used, where the upper limb is modeled as a multilayered cylinder with three layers: muscle, fat tissue and skin tissue. Using this model, HD-sEMG signals are computed over the skin as a 2D surface along angular and longitudinal directions. Electrode recording is performed through a surface integration on the 2D surface according to the electrode shape. 16 simulations on 10 anatomies (350 Motor Units) with the same parameters were computed for 3 constant contraction levels: 30%, 50% and 70% of the maximal voluntary contraction. Then, a global sensitivity analysis using the elementary effect method is performed to explore the sensitivity of amplitude descriptors (average rectified value, root mean square value and high order statistics) relative to varying parameters from the electrode grid (inter-electrode distances, electrodes radius, position and rotation). From those grid definitions, monopolar, bipolar and laplacian signals are also computed to see the electrode arrangement sensitivity. The obtained results exposed a huge impact of the grid rotation on the studied criteria. They also showed that parameters specific to the electrode grid layout (inter-electrode distances) have the less impact. Moreover, they exhibited the laplacian arrangement as the most sensitive electrode arrangement to grid modifications.

Design of Forward Adaptive Piecewise Uniform Scalar Quantizer with Optimized Reproduction Level Distribution per Segments

The problem we address in this paper is the design of nearly optimal scalar quantizer in a wide variance range of the Laplacian input signals, using the piecewise uniform quantizers while restricting the class of quantizers to be forward adaptive. Particularly, the design procedure of the piecewise uniform quantizer with an equidistant support region partion and the optimized reproduction level distribution per segments is presented along with the design procedure of its forward adaptive version. Reproduction level optimization is performed by optimizing the granular distortion of the proposed quantizer using the method of the Lagrange multipliers. For the proposed model we study the influence of the segment number on the SQNR, as well as the SQNR robustness in a wide variance range. Since the results obtained for the assumed Laplacian distribution indicate the SQNR improvement over the G.711 standard, one can expect that the proposed quantizer will be effective in the quantization of signals having the same distribution and the time varying characteristics. Ill. 4, bibl. 10 (in English; abstracts in English and Lithuanian).DOI: http://dx.doi.org/10.5755/j01.eee.119.3.1356

Robust audio and speech watermarking using Gaussian and Laplacian modeling

In this paper, a semi-blind multiplicative watermarking approach for audio and speech signals has been presented. At the receiver end, the optimal maximum likelihood (ML) detector aided by the archived information for Gaussian and Laplacian signals in noisy environment is designed and implemented. The performance of the proposed scheme is analytically calculated and verified by simulation. Then, we adapt the proposed scheme to speech and audio signals. To improve robustness, the algorithm is applied to low frequency components of the host signal. Besides, the power of the watermark is controlled elegantly to have inaudibility using perceptual evaluation of audio quality (PEAQ) and perceptual evaluation of speech quality (PESQ) algorithms. Experimental results over several audio and speech signals show the higher robustness of the proposed technique in comparison with other watermarking schemes presented so far.

An Information-Theoretic View of Array Processing

The removal of noise and interference from an array of received signals is a most fundamental problem in signal processing research. To date, many well-known solutions based on second-order statistics (SOS) have been proposed. This paper views the signal enhancement problem as one of maximizing the mutual information between the source signal and array output. It is shown that if the signal and noise are Gaussian, the maximum mutual information estimation (MMIE) solution is not unique but consists of an infinite set of solutions which encompass the SOS-based optimal filters. The application of the MMIE principle to Laplacian signals is then examined by considering the important problem of estimating a speech signal from a set of noisy observations. It is revealed that while speech (well modeled by a Laplacian distribution) possesses higher order statistics (HOS), the well-known SOS-based optimal filters maximize the Laplacian mutual information as well; that is, the Laplacian mutual information differs from the Gaussian mutual information by a single term whose dependence on the beamforming weights is negligible. Simulation results verify these findings.

Sparsity analysis of signals

Abstract In this paper, the signals with generalized Gaussian distribution are considered. A mathematical formula is given to illustrate the sparsity of the signals. According to this formula, the measure of the Laplacian signal is 1, and Gaussian signal is 2. Given a signal, compared with Laplacian signal and Gaussian signal, we can intuitively know how sparse the signal is via its measure. Some examples demonstrate that, if there are no sufficient observed signals (e.g. only three observed signals), one can achieve underdetermined blind source separation (BSS) only for sufficiently sparse source signals (e.g. much sparser than Laplacian signals) by the measure we defined *Supported by National Natural Science Foundation of China (Grant Nos. 60325310, 60505005), Guangdong Province Science Foundation for Program of Research Team (Grant No. 04205783), Guangdong Province Natural Science Foundation (Grant Nos. 05103553, 05006508), and the Specialized Prophasic Basic Research Projects of Ministry of Science a...

Monophasic action potentials and activation recovery intervals as measures of ventricular action potential duration: Experimental evidence to resolve some controversies

Activation recovery intervals (ARIs) and monophasic action potential (MAP) duration are used as measures of action potential duration in beating hearts. However, controversies exist concerning the correct way to record MAPs or calculate ARIs. We have addressed these issues experimentally. To experimentally address the controversies concerning the correct way to record MAPs or calculate ARIs. Left ventricular local electrograms were recorded in isolated pig hearts with an exploring electrode grid, with a KCl reference electrode on the left ventricular myocardium, the aortic root, or the left atrium. Local activation was determined from calculated Laplacian electrograms. With the KCl electrode on the aortic root, local electrograms represented local activation. However, with the KCl electrode on the myocardium remote from the exploring electrode, a combined electrogram emerged consisting of local activation recorded from the grid and remote activation recorded from the reference electrode. The remote, inverted monophasic component did not show propagation and did not correlate with the Laplacian complex. When the KCl electrode was placed on the atrium during AV block, remote atrial monophasic components were completely dissociated from local, ventricular deflections. At left ventricular sites with a positive T wave, the Laplacian signal showed that the end of the T wave was caused by remote repolarization. During cooling-induced regional action potential prolongation, the T wave became negative, whereby the positive flank of the T wave remained correlated with repolarization (recorded with a MAP at the same site). MAPs are recorded from the depolarizing electrode. In both negative and positive T waves, the moment of maximum dV/dt corresponds to local repolarization.

Homomorphic wavelet thresholding technique for denoising medical ultrasound images

A novel homomorphic wavelet thresholding technique for reducing speckle noise in medical ultrasound images is presented. First, we show that the speckle wavelet coefficients in the logarithmically transformed ultrasound images are best described by the Nakagami family of distributions. By exploiting this speckle model and the Laplacian signal prior, a closed form, data-driven, and spatially adaptive threshold is derived in the Bayesian framework. The spatial adaptivity allows the additional information of the image (such as identification of homogeneous or heterogeneous regions) to be incorporated into the algorithm. Further, the threshold has been extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. Experimental results demonstrate the improved performance of the proposed method over other well-known speckle reduction filters. The application of the proposed method to a realistic US test image shows that the new technique, named HomoGenThresh, outperforms the best wavelet-based denoising method reported in [1] by more than 1.6 dB, Lee filter by 3.6 dB, Kaun filter by 3.1 dB and band-adaptive soft thresholding [2] by 2.1 dB at an input signal-to-noise ratio (SNR) of 13.6 dB.

Comments on "Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging".

D.B. Geselowitz and J. Ferrara comment on a paper by R.D. Throne and L.G. Olson which was published in ibid., vol.47, p. 452-62 (2000). Throne and Olson reply to these comments. The discussion concerns the use of a spherical model and a body surface Laplacian in the solution of the electrocardiographic inverse problem and the influence of noise.

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging.

Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, we compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.

Body surface Laplacian electrocardiographic mapping--a review.

It is of great importance and significance to be able to noninvasively map spatially distributed cardiac electrical activity from body surface electrical recordings. The standard electrocardiographic monitoring techniques provide little spatial information regarding cardiac electrical activity. Recently, a new approach-body surface Laplacian electrocardiographic mapping-has been aggressively pursued to provide high-resolution spatial mapping of cardiac electrical activity. The fundamental innovation is the measurement of the Laplacian electrocardiogram distribution over the body surface. The body surface Laplacian electrocardiographic maps have been shown to provide enhanced ability to map multiple spatially separate cardiac bioelectric sources. This article reviews the theoretical and experimental aspects of this emerging mapping technique. First of all, the paper briefly reviews the historical development of body surface mapping and inverse solutions for mapping the distributed cardiac electrical activity. Then the paper reviews the theoretical basis of body surface Laplacian mapping and the biophysical interpretation of body surface Laplacian signals, as well as technical consideration of the Laplacian recording and instrumentation. Investigations of body surface Laplacian maps in computer models and a physical tank model, as well as physiological studies are also reviewed.

Successive refinement of information

The successive refinement of information consists of first approximating data using a few bits of information, then iteratively improving the approximation as more and more information is supplied. The goal is to achieve an optimal description at each stage. In general, an ongoing description which is rate-distortion optimal whenever it is interrupted is sought. It is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a Markov chain. In particular, all finite alphabet signals with Hamming distortion satisfy these requirements. It is also shown that the same is true for Gaussian signals with squared error distortion and for Laplacian signals with absolute error distortion. A simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented. >

A design technique for nonuniform quantizer in PCM generation

This paper is devoted to the use of nonuniform quantizer in order to reduce quantization noise in Communication Systems. The quantizer is designed to minimize the Mean Square quantizing Error (MSE) for a given probability density of the signal distribution. The addition of a suitable nonlinear reference waveform to the constant slope staircase function introduces the desired nonlinearity in quantizer characteristic. In the receiver also, similar process is used to decode the signal. The parameters which characterize the reference waveform are optimized to achieve the minimum MSE. Such a quantizer can profitably be used for Laplacian, Gamma, and Gaussian signals. The improvement of the signal-to-noise ratio (SNR) is shown to be considerably better than that of is law quantizer. The performance for a Laplacian distribution is investigated in detail to highlight the utility of the nonuniform quantizer.

Upper bound on signal/quantising-noise ratio for television d.p.c.m. systems

Consideration is given to an upper bound on signal/quantising-noise ratio for television d.p.c.m. systems. The 7.2 dB gain for entropy coding assumes ε entropy of the bit stream of the quantiser output. The calculations are based on Laplacian signals, because television signals at d.p.c.m. quantiser inputs are approximately Laplacian.