OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals

A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We propose an approach exploiting the parsimonious time-frequency representation of the signal by applying a new OMP-type algorithm for structured sparsity patterns. An important issue is the scalability of the proposed algorithm since high-dimensional models shall be used for radar signals. Monte-Carlo simulations for modulated signals illustrate the good performance of the method even for low signal-to-noise ratios and a gain of 20 dB for the DOA estimation compared to some elementary method

Feature extraction of vibration signal using OMP-NWE method

Feature extraction is one of the core problems in condition monitoring and fault diagnosis of mechanical equipment. In this study, an OMP-NWE method of feature extraction is proposed, aiming at the problem of low accuracy of existing feature extraction method. The OMP-NWE method integrates the strengths of orthogonal matching pursuit (OMP) algorithm with the benefits of nonparametric waveform estimation (NWE). Signal feature extraction model is constructed by design of filter bank and adaptive template signal. Then the vibration signal is linearly decomposed into a set of best matching waveform, which solves the problem that the basis function must be chosen in advance in OMP algorithm. The OMP-NWE method is applied to the feature extraction of the simulation and experimental vibration signal of rolling bearing, compared with the traditional OMP algorithm. Results show that the SNR of the extracted feature signal using OMP-NWE method increased by 19.22 % compared with that using the OMP method, which illustrates that OMP-NWE method has a higher accuracy in the feature extraction of unknown complex vibration signals. This work provides a new idea and a successful example for the feature extraction of vibration signal in the condition monitoring and fault diagnosis of mechanical equipment

Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification

Objective. The main goal of this work is to develop a model for multi-sensor signals such as MEG or EEG signals, that accounts for the inter-trial variability, suitable for corresponding binary classification problems. An important constraint is that the model be simple enough to handle small size and unbalanced datasets, as often encountered in BCI type experiments. Approach. The method involves linear mixed effects statistical model, wavelet transform and spatial filtering, and aims at the characterization of localized discriminant features in multi-sensor signals. After discrete wavelet transform and spatial filtering, a projection onto the relevant wavelet and spatial channels subspaces is used for dimension reduction. The projected signals are then decomposed as the sum of a signal of interest (i.e. discriminant) and background noise, using a very simple Gaussian linear mixed model. Main results. Thanks to the simplicity of the model, the corresponding parameter estimation problem is simplified. Robust estimates of class-covariance matrices are obtained from small sample sizes and an effective Bayes plug-in classifier is derived. The approach is applied to the detection of error potentials in multichannel EEG data, in a very unbalanced situation (detection of rare events). Classification results prove the relevance of the proposed approach in such a context. Significance. The combination of linear mixed model, wavelet transform and spatial filtering for EEG classification is, to the best of our knowledge, an original approach, which is proven to be effective. This paper improves on earlier results on similar problems, and the three main ingredients all play an important role

Fault Diagnosis of Rotating Equipment Bearing Based on EEMD and Improved Sparse Representation Algorithm

Aiming at the problem that the vibration signals of rolling bearings working in a harsh environment are mixed with many harmonic components and noise signals, while the traditional sparse representation algorithm takes a long time to calculate and has a limited accuracy, a bearing fault feature extraction method based on the ensemble empirical mode decomposition (EEMD) algorithm and improved sparse representation is proposed. Firstly, an improved orthogonal matching pursuit (adapOMP) algorithm is used to separate the harmonic components in the signal to obtain the filtered signal. The processed signal is decomposed by EEMD, and the signal with a kurtosis greater than three is reconstructed. Then, Hankel matrix transformation is carried out to construct the learning dictionary. The K-singular value decomposition (K-SVD) algorithm using the improved termination criterion makes the algorithm have a certain adaptability, and the reconstructed signal is constructed by processing the EEMD results. Through the comparative analysis of the three methods under strong noise, although the K-SVD algorithm can produce good results after being processed by the adapOMP algorithm, the effect of the algorithm is not obvious in the low-frequency range. The method proposed in this paper can effectively extract the impact component from the signal. This will have a positive effect on the extraction of rotating machinery impact features in complex noise environments

Assessing the Convergence of Iterative Parameter Estimation

On September 14th, 2015, the remnants of two massive stars collided, producing gravitational waves that rung out accross the universe. It has been discovered that this is fairly common. Einstein’s Theory of General Relativity, first predicted gravitational waves. After a century of scientific discovery, engineering marvels, and the proliferation of technology, scientists ultimately built an instrument which can detect them. The Laser Interferometer Gravitational-Wave Observatory (LIGO) detected this event, and many more in LIGO’s first and second observational runs. Scientists model the signals that have been detected in order to study the properties of these systems. These parameters, e.g. the mass and spin of each black hole, will in turn yield parts of the recipe for the universe. They may one day grant us insight on the Hubble Constant and the stellar Initial Mass Function. Before these events can be useful in that way, scientists need to apply astrophysical and statistical models to estimate those parameters. This thesis has three goals: (i) To summarize the Bayesian approach adopted by the Rochester Institute of Technology (RIT) parameter estimation group. (ii) To discuss the application of the Kolmogorov-Smirnov test as a goodness of fit test, in order to reduce computational waste and validate parameter estimation results. (iii) To apply parameter estimation techniques, combined with this test, in order to quantify the needs of the algorithm used by the RIT group, as well as justify its methodology. In the pursuit of these goals, I will apply Bayesian statistical theory, test the limits of our techniques, and explore astrophysical models and a real gravitational wave event

Unified selective sorting approach to analyse multi-electrode extracellular data

Extracellular data analysis has become a quintessential method for understanding the neurophysiological responses to stimuli. This demands stringent techniques owing to the complicated nature of the recording environment. In this paper, we highlight the challenges in extracellular multi-electrode recording and data analysis as well as the limitations pertaining to some of the currently employed methodologies. To address some of the challenges, we present a unified algorithm in the form of selective sorting. Selective sorting is modelled around hypothesized generative model, which addresses the natural phenomena of spikes triggered by an intricate neuronal population. The algorithm incorporates Cepstrum of Bispectrum, ad hoc clustering algorithms, wavelet transforms, least square and correlation concepts which strategically tailors a sequence to characterize and form distinctive clusters. Additionally, we demonstrate the influence of noise modelled wavelets to sort overlapping spikes. The algorithm is evaluated using both raw and synthesized data sets with different levels of complexity and the performances are tabulated for comparison using widely accepted qualitative and quantitative indicators