An Algorithm for Wavelet Transform Sub-Band Filter Based ECG signals Detecting

This paper presents a general approach to solving the problem of defining the time of arrival of a signal in the noise, or the similar one of defining the position of a peak in a histogram. In particular, it solves the problem of a signal in white noise, giving the well know result that the optimum filter before a zero crossing discriminator should have an impulse response function equal to the derivative of the waveform to be observed. It then solves the problem of estimating the position of a peak in a histogram in which the number of counts in each bin has a variance equal to the number of counts in that same bin. The resulting optimum filter is the derivative divided by the function itself. Examples of applying the results are given and the un iqueness of the solution to the set of non-linear simultaneous equations resulting from the problem is demonstrated.

The detectability of a pulsed sinusoidal signal in white noise was studied as a function of frequency for three signal durations (1000, 100, and 10 msec). For the two longer signal durations the data are consistent with results obtained in previous experiments; the results obtained with the shortest duration are not. At the higher frequencies the 10 msec signal is easier to hear than either the 100 or 1000 msec signal. At low frequencies the 10 msec signal is easier to hear than the 1000 msec signal but not the 100 msec signal. This interaction of signal frequency and signal duration somewhat complicates the problem of developing a simple model to account for the influence of signal duration on signal detectability. (This research was conducted at the Electronic Defense Group, University of Michigan, under a U. S. Air Force contract monitored by the Operational Applications Laboratory.)

The original q-Markov COVariance Equivalent Realization (q-Markov Cover) method for identification required white noise test signals, which cannot be generated exactly. This paper replaces the unrealizable white-noise signal with a realizable signal (the pseudo-random binary signal, PRBS), and proves that when the period of the PRBS approaches infinity the q-Markov Cover algorithm, operating with PRBS, matches the first q Markov and covariance parameters (as in the original theory with white-noise test signals). The existing q-Markov Cover algorithm will fail to match covariance and Markov parameters exactly due to non-white test signals. The new algorithm will fail to match covariance and Markov parameters exactly due to the finite period of PRBSs. We demonstrate however that the results with PRBSs are far superior to results with ‘white’ noise signals. Apparently, the ‘non-whiteness’ of the test signal degrades the identification performance worse than the ‘non-infinite’ period of the PRBS.

The performance of the maximum likelihood estimator for a 1-D chaotic signal in white Gaussian noise is derived. It is found that the estimator is inconsistent and therefore the usual asymptotic distribution (large data record length) is invalid. However, for high signal-to-noise ratios (SNR's), the maximum likelihood estimator is asymptotically unbiased and attains the Cramér-Rao lower bound (CRLB). © 1995 IEEE

There are numerous studies showing that there is a constant increase in the ocean ambient noise level and the ever-growing demand for developing algorithms for detecting weak signals in ambient noise. In this study, we utilize dynamical and statistical complexity to detect the presence of weak ship noise embedded in ambient noise. The ambient noise and ship noise were recorded in the South China Sea. The multiscale entropy (MSE) method and the complexity-entropy causality plane (C-H plane) were used to quantify the dynamical and statistical complexity of the measured time series, respectively. We generated signals with varying signal-to-noise ratio (SNR) by varying the amplification of a ship signal. The simulation results indicate that the complexity is sensitive to change in the information in the ambient noise and the change in SNR, a finding that enables the detection of weak ship signals in strong background ambient noise. The simulation results also illustrate that complexity is better than the traditional spectrogram method, particularly effective for detecting low SNR signals in ambient noise. In addition, complexity-based MSE and C-H plane methods are simple, robust and do not assume any underlying dynamics in time series. Hence, complexity should be used in practical situations.

Maximum likelihood estimation of a nonparametric signal in white noise by optimal control

Weak signal detection is a significant problem in modern detection such as mechanical fault diagnosis. The uniqueness of chaos and good learning ability of neural networks provide new ideas and framework for weak signal detection field. In this paper, Elman neural network is applied to detect and recover weak pulse signal in chaotic noise. For detection problem of weak pulse signal under chaotic noise, based on short-term predictability of chaotic observations, phase space reconstruction for observed signals is carried out. And Elman deep learning adaptive detection model (EDAD model) is established for weak pulse signal detection, and a hypothesis test is used to detect weak pulse signal from the prediction error. For the recovery of weak pulse signal under chaotic noise, a double-layer Elman deep neural network recovery model (DEDR model) is proposed, which is based on the Elman deep learning network model and single-point jump model for weak pulse signal, and it is optimized with goal of minimizing mean square prediction error of the Elman model. The profile least squares method is applied to estimate parameters of the DEDR model for difficult recovery of weak pulse signal because the DEDR model is essentially a semiparametric model with parametric and nonparametric parts. In the end, simulation experiments show that the model built in this paper can effectively detect and recover weak pulse signal in the background of chaotic noise.

Recent results on joint detection-estimation for discrete data are extended to the continuous data case for Gaussian signals in White Gaussian noise. Stochastic differential equations are obtained describing the temporal evolution of the sufficient statistic for minimum Bayes-risk detection and the optimal mean-square error estimate of the signal state vector. An approximate solution for the estimation equation is suggested.

Conventional mass spectrometry image preprocessing methods used for denoising, such as the Savitzky-Golay smoothing or discrete wavelet transformation, typically do not only remove noise but also weak signals. Recently, memory-efficient principal component analysis (PCA) in conjunction with random projections (RP) has been proposed for reversible compression and analysis of large mass spectrometry imaging datasets. It considers single-pixel spectra in their local context and consequently offers the prospect of using information from the spectra of adjacent pixels for denoising or signal enhancement. However, little systematic analysis of key RP-PCA parameters has been reported so far, and the utility and validity of this method for context-dependent enhancement of known medically or pharmacologically relevant weak analyte signals in linear-mode matrix-assisted laser desorption/ionization (MALDI) mass spectra has not been explored yet. Here, we investigate MALDI imaging datasets from mouse models of Alzheimer's disease and gastric cancer to systematically assess the importance of selecting the right number of random projections k and of principal components (PCs) L for reconstructing reproducibly denoised images after compression. We provide detailed quantitative data for comparison of RP-PCA-denoising with the Savitzky-Golay and wavelet-based denoising in these mouse models as a resource for the mass spectrometry imaging community. Most importantly, we demonstrate that RP-PCA preprocessing can enhance signals of low-intensity amyloid-β peptide isoforms such as Aβ1-26 even in sparsely distributed Alzheimer's β-amyloid plaques and that it enables enhanced imaging of multiply acetylated histone H4 isoforms in response to pharmacological histone deacetylase inhibition in vivo. We conclude that RP-PCA denoising may be a useful preprocessing step in biomarker discovery workflows.

Automatic heart disease detection from human heartbeats is a challenging and intellectual assignment in signal processing because periodically monitoring of the heart beat arrhythmia for patient is an essential task to reduce the death rate due to cardiovascular disease (CVD). In this paper, the focus of research is to design hybrid Convolutional Neural Network (CNN) architecture by making use of Grasshopper Optimization Algorithm (GOA) to classify different types of heart diseases from the ECG signal or human heartbeats. Convolutional Neural Network (CNN) as an artificial intelligence approach is widely used in computer vision-based medical data analysis. However, the traditional CNN cannot be used for classification of heart diseases from the ECG signal because lots of noise or irrelevant data is mixed with signal. So this study utilizes the pre-processing and selection of feature for proper heart diseases classification, where Discrete Wavelet Transform (DWT) is used for the noise reduction as well as segmentation of ECG signal and Grasshopper Optimization Algorithm (GOA) is used for selection of R-peaks features from the extracted feature sets in terms of R-peaks and R-R intervals that help to attain better classification accuracy. For training as well as testing of projected Heartbeats Classification Model (HCM), the Standard MIT-BIH arrhythmia database is utilized with hybrid Convolutional Neural Network (CNN) architecture. The assortment of proper R-peaks and R-R intervals is a major factor and because of the deficiency of apposite pre-processing phases like noise removal, signal decomposition, smoothing and filtering, the uniqueness of extracted feature is less. The experimental outcomes show that the planned HCM is effective for detecting irregular human heartbeats via R-peaks and R-R intervals. When the proposed Heartbeats Classification Model (HCM) was verified on the database, model achieved higher efficiency than other state-of-the-art techniques for 16 heartbeat disease categories and the average classification accuracy is 99.58% with fast and robust responses where the correctly classified heartbeats are 86,005 and misclassified beats is only 108 with 0.42% error rate.

The problem of distributed detection of a deterministic signal with unknown strength using a neural network approach is considered. Since the signal level Is not known there does not exist a uniformly powerful detection scheme for the problem. The neural network architecture used Is a two layer feedforward perceptron model with N Inputs M nodes In the hidden layer and two output nodes that correspond to the signal and noise hypotheses. The back propagation algorithm Is used to train the system with a known noise distribution. For fixed false alarm probabilities the performance of the trained network with regard to a set of test signals is estimated and compared to the performance of some known detection procedures such as Fisher''s method Tlppett''s method and the optimum test. Simulation results are presented for a network with two input nodes and three or four nodes In the hidden layer. When Laplace noise Is assumed the network performs better than the Tlppett method. For the detection of weak and moderate signals in Gaussian noise the network performs reasonably close to the optimum detection scheme. The decision regions for the neural network detection scheme is comparable to those of the Fisher''s and Tlppett''s methods. However unlike the Tippett''s method which has a fixed decision region regardless of the noise distribution the neural network''s decision region changes with the noise distribution. 1. SIGNAL DETECTION

Optimal detection of a known FSK-modulated binary signal in additive white Gaussian noise using a matched filter receiver requires knowledge of second-order noise statistics. The dependence on noise statistics causes the probability of detection to be sensitive to errors in the noise variance value. This makes the optimal scheme of limited use in situations where the noise statistics are unknown and cannot be estimated reliably. We propose an alternative approach, which has a more easily calculated test statistic than the optimal method and yields a constant false detection rate, regardless of noise statistics. While this approach has sub-optimal detection probability, it is significantly advantageous in applications where a primary interest is to limit false detections strictly. In addition, it allows one to determine easily the required detection length (in symbols) to achieve a desired performance level.

This paper introduces the use of chaotic Duffing oscillators to ballistocardiograph system for detection of weak signal. A ballistocardiograph (BCG) is an instrument that records the motions of the body imparted to it by the heart beat. It has been found that digital filters are not suitable for processing the BCG signals in noise. So in this paper, we propose a chaotic oscillators algorithm to detect information from BCG. The principles of using it to detect weak cycle sinusoidal signals are presented firstly. Then, the experimental results have shown that this algorithm is quite effective for detecting BCG signal and improving the ratio of signal to noise.

With the development of Internet of Things, the Healthcare Industrial IoT has become an effective way to curb the high mortality rate of heart disease. The accuracy of such system is mainly rely on the quality of ECG signals, in which noise reduction has been widely used. However, in the IoT environment, many kinds of noise which cannot be predicted in advance exist in signals, and make the signal morphology seriously damaged, which brings great challenge to the existing de-noise methods. By considering the self-adaptation and self-learning of deep neural network, we have proposed a multilayer LSTM model to the noise reduction of dynamic ECGs. Unlike other methods, our model makes both noise and ECG signals as part of time-series data, while other methods always consider them separately. Benefit from the recurrent structure of LSTM model, the most representative features will be extracted in LSTM memory units. By stacking multiple layers per time step, the useful information will be continuously refined and the noise signal will be discarded. Even if the ECG signals comprise many kinds of noise simultaneously, the model can still restore ECG signals with high quality without relying on threshold or signal quality. The experimental results show that the proposed model is insensitive to noise and the improvement of signal-to-noise ratio up to 55dB. This result is much better than the existing methods, which indicates LSTM is a new competitive method for ECG noise reduction.

Automatic identification of digitally modulated signal has to be able to identify the digitally modulated signal correctly and accurately. Importance of automatic identification of digitally modulated signals are rising increasingly. In this paper an advanced technique is presented, that automatically identifies the multi-user chirp modulated signals in Additive White Gaussian Noise (AWGN) channel. The proposed technique is implementing high order moments (fourth, sixth, and eighth) of detail coefficients of discrete wavelet transform (DWT) as a feature extraction set. Adaptive Neural-Fuzzy Inference System (ANFIS) is proposed as a classifier. The proposed identification procedure is capable of identifying multi-user chirp modulated signals with high accuracy at 0dB, 5dB, and 10dB Signal to Noise Ratio (SNR), over AWGN channel.