Sparse Signal Representation Research Articles

Sparse learning based classification framework for planetary bearing health diagnostics

Planetary bearings are the most complex and challenging components for health diagnostics among wind turbine and helicopter planetary transmissions. Classical spectrum-based diagnosis strategy for planetary bearings faces great challenges because of complex structures and strong modulation effects. This work develops a novel sparse learning based classification (SLBC) framework with the overlapping segmentation strategy to address planetary bearing health diagnostics. Our SLBC framework learns the reconstructive dictionaries for sparse representations of vibration signals and achieves robust recognitions with the sparse approximation criterion. Firstly, the overlapping segmentation strategy is introduced to fully leverage periodic similarity features and augment training datasets for sparse dictionary learning. Then, the category-specific sub-dictionaries are learned from the augmented training datasets in a data-driven fashion via K-singular value decomposition. Finally, intelligent planetary-bearing fault recognition is achieved via the sparse approximation criterion. Our SLBC framework has been verified effective to classify three and four planetary-bearing health states with diagnostic accuracy of 100% and 99.98%, respectively. Comparisons with several advanced approaches have confirmed the superiority of SLBC in diagnostic accuracy, noise robustness, and computation time for planetary bearing health diagnostics.

Fully learnable deep wavelet transform for unsupervised monitoring of high-frequency time series

High-frequency (HF) signals are ubiquitous in the industrial world and are of great use for monitoring of industrial assets. Most deep-learning tools are designed for inputs of fixed and/or very limited size and many successful applications of deep learning to the industrial context use as inputs extracted features, which are a manually and often arduously obtained compact representation of the original signal. In this paper, we propose a fully unsupervised deep-learning framework that is able to extract a meaningful and sparse representation of raw HF signals. We embed in our architecture important properties of the fast discrete wavelet transform (FDWT) such as 1) the cascade algorithm; 2) the conjugate quadrature filter property that links together the wavelet, the scaling, and transposed filter functions; and 3) the coefficient denoising. Using deep learning, we make this architecture fully learnable: Both the wavelet bases and the wavelet coefficient denoising become learnable. To achieve this objective, we propose an activation function that performs a learnable hard thresholding of the wavelet coefficients. With our framework, the denoising FDWT becomes a fully learnable unsupervised tool that does not require any type of pre- or postprocessing or any prior knowledge on wavelet transform. We demonstrate the benefits of embedding all these properties on three machine-learning tasks performed on open-source sound datasets. We perform an ablation study of the impact of each property on the performance of the architecture, achieve results well above baseline, and outperform other state-of-the-art methods.

Multi-Frequent Band Collaborative EEG Emotion Classification Method Based on Optimal Projection and Shared Dictionary Learning.

Affective computing is concerned with simulating people’s psychological cognitive processes, of which emotion classification is an important part. Electroencephalogram (EEG), as an electrophysiological indicator capable of recording brain activity, is portable and non-invasive. It has emerged as an essential measurement method in the study of emotion classification. EEG signals are typically split into different frequency bands based on rhythmic characteristics. Most of machine learning methods combine multiple frequency band features into a single feature vector. This strategy is incapable of utilizing the complementary and consistent information of each frequency band effectively. It does not always achieve the satisfactory results. To obtain the sparse and consistent representation of the multi-frequency band EEG signals for emotion classification, this paper propose a multi-frequent band collaborative classification method based on optimal projection and shared dictionary learning (called MBCC). The joint learning model of dictionary learning and subspace learning is introduced in this method. MBCC maps multi-frequent band data into the subspaces of the same dimension using projection matrices, which are composed of a common shared component and a band-specific component. This projection method can not only make full use of the relevant information across multiple frequency bands, but it can also maintain consistency across each frequency band. Based on dictionary learning, the subspace learns the correlation between frequency bands using Fisher criterion and principal component analysis (PCA)-like regularization term, resulting in a strong discriminative model. The objective function of MBCC is solved by an iterative optimization algorithm. Experiment results on public datasets SEED and DEAP verify the effectiveness of the proposed method.

Quantum matching pursuit: A quantum algorithm for sparse representations

Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with high-dimensional signals, the computational complexity of the encoder that finds the sparse representation plays an important role. Quantum computing has recently shown promising speed-ups in many representation learning tasks. In this work, we propose a quantum version of the well-known matching pursuit algorithm. Assuming the availability of a fault-tolerant quantum random access memory, our quantum matching pursuit lowers the complexity of its classical counterpart of a polynomial factor, at the cost of some error in the computation of the inner products, enabling the computation of sparse representation of high-dimensional signals. Besides proving the computational complexity of our new algorithm, we provide numerical experiments that show that its error is negligible in practice. This work opens the path to further research on quantum algorithms for finding sparse representations, showing suitable quantum computing applications in signal processing.

Off-Grid DOA Estimation With Mutual Coupling via Block Log-Sum Minimization and Iterative Gradient Descent

Mutual coupling (MC) effect between antennas can deteriorate the direction of arrival (DOA) estimation performance. Block sparse signal representation (BSSR) is an effective solution to mitigate the MC effect. Nevertheless, continuous angle space has to be discretized into a finite set of grid points, which lead to the grid mismatch. In this paper, we present an iterative block sparsity reconstruction algorithm for off-grid DOA estimation with MC. First, by exploiting the banded symmetric Toeplitz structure of MC matrix, a reduced BSSR model is formulated to preferably mitigate the MC effect. Then, an iterative block sparsity reconstruction algorithm with multiple measurement vectors (MMV) is proposed. Due to the NP-hard property of block l0 norm minimization, a block log-sum minimization method is developed to encourage sparsity for such a block sparse recovery problem, and a surrogate objective function is derived via the majorization-minimization approach. Finally, an iterative gradient descent algorithm is explored to refine the DOAs. Simulations verify that the proposed off-grid algorithm has robustness under limited snapshots and coherent sources.

TL-HARDI: Transform learning based accelerated reconstruction of HARDI data

Diffusion magnetic resonance imaging (dMRI) is being extensively used to study the neural architecture of the brain. High angular resolution diffusion imaging (HARDI), a variant of diffusion MRI, measures the diffusion of water molecules along the angular gradient directions in the q-space. It provides better estimates of fiber orientations compared to the traditionally used diffusion tensor imaging (DTI). However, HARDI requires acquisition of relatively large number of samples leading to longer scanning times. Several approaches based on compressive sensing (CS) have been proposed to accelerate HARDI acquisition, leveraging on the sparse representation of the HARDI signal in a pre-specified sparsifying basis. In this paper, we propose to carry out reconstruction of compressively sensed HARDI data using an adaptively learned transform. The transform is learned (i) from the compressive measurements on-the-fly, thereby, eliminating the overhead of choosing fixed sparsifying transforms, and (ii) on overlapping patches of the data, thereby, capturing local image structure effectively. Experiments are conducted on multiple real HARDI data for varying sampling ratios and sampling schemes. The performance of the proposed “TL-HARDI” method is compared with the state-of-the-art methods on various known image quality metrics as well as on dMRI feature maps derived from the reconstructed images. The proposed method is observed to yield better reconstruction than the existing state-of-the-art methods in both quantitative and qualitative comparisons.

Sparse based recurrent neural network long short term memory (rnn-lstm) model for the classification of ecg signals

ABSTRACT In recent years, with the advancement of classical signal processing approaches, numerous works have been performed on the automatic ECG detection schemes for the enhancement of the effectiveness of the identification of the type of ECG heartbeats. One common issue faced by the previous works is the complexity of signal processing. In order to resolve the computational and complexity issues of existing techniques of signal processing, this research work introduces Sparse representation technique for extracting feature. In this study, adaptive thresholding technique combined with Sparse-based Recurrent Neural Network – Long Short Term Memory (RNN-LSTM) model is employed for the classification of ECG signals. P-QRS-T peaks are identified by employing Adaptive thresholding technique. Statistical features are obtained for each signal and are employed in the process of dictionary learning of sparse decomposition. Sparse representations of the incoming ECG signals are used in training the RNN-LSTM network. The trained classifier will give a classified result on giving a test ECG input signal. The performance indices for the process of classification such as accuracy, precision, error rate, sensitivity, and F-score are calculated. The performance of the proposed Sparse based RNN-LSTM classifier is found to be better in comparison with the existing RNN classifier, K-Nearest Neighbor (K-NN) classifier, and Decision Tree (DT) classifier. Furthermore, for validating the performance of the proposed framework, this approach is tested experimentally with real-world raw ECG data acquired using the AD8232 single-lead ECG sensor. The performance of the proposed experimental setup is compared with the existing state-of-the-art approaches.

Dictionary learning for sparse representation of signals with hidden Markov model dependency

The goal of dictionary learning algorithms is factorizing the matrix of training signals Y with K signals, into the dictionary matrix D and the coefficient matrix X which is a sparse matrix. The common approach among the algorithms is minimizing the representation error subject to the sparseness of X using alternation minimization method following 1) the sparsification and 2) the dictionary update steps. In this approach, when D is fixed and X must be estimated (the sparsification step), the minimization problem is divided to K different sparse recovery problems because the training signals are assumed to be independent. However, in some signals this assumption is not correct and the signals are not independent. Therefore, using the current strategy does not lead to the correct estimation of the parameters. The prominence is especially linked to medical signals and images such as electroencephalography (EEG) or diffusion weighted images, where the recordings do not constitute a matrix of independent training signals. In this study, we investigate the dictionary learning problem for sparse representation when there is hidden Markov model (HMM) dependency among the training signals. We propose an approach to improve the performance of the dictionary learning algorithms in the mentioned scenario. The proposed approach is not an independent dictionary learning algorithm. It is a general approach that we can employ for existing dictionary learning algorithms to improve their performance in learning from signals with HMM dependency. We confirm the efficiency of the proposed approach using simulations, and also, present a real application in medical signals for the considered scenario.

Research on Sparse Representation Method of Acoustic Microimaging Signals

Acoustic microimaging (AMI), a technology for high-resolution imaging of materials using a scanning acoustic microscope, has been widely used for non-destructive testing and evaluation of electronic packages. Recently, the internal features and defects of electronic packages have reached the resolution limits of conventional time domain or frequency domain AMI methods with the miniaturization of electronic packages. Various time-frequency domain AMI methods have been developed to achieve super-resolution. In this paper, the sparse representation of AMI signals is studied, and a constraint dictionary-based sparse representation (CD-SR) method is proposed. First, the time-frequency parameters of the atom dictionary are constrained according to the AMI signal to constitute a constraint dictionary. Then, the AMI signal is sparsely decomposed using the matching pursuit algorithm, and echoes selection and echoes reconstruction are performed. The performance of CD-SR was quantitatively evaluated by simulated and experimental ultrasonic A-scan signals. The results demonstrated that CD-SR has superior longitudinal resolution and robustness.

Sparse Signal Representation, Sampling, and Recovery in Compressive Sensing Frameworks

Compressive sensing allows the reconstruction of original signals from a much smaller number of samples as compared to the Nyquist sampling rate. The effectiveness of compressive sensing motivated the researchers for its deployment in a variety of application areas. The use of an efficient sampling matrix for high-performance recovery algorithms improves the performance of the compressive sensing framework significantly. This paper presents the underlying concepts of compressive sensing as well as previous work done in targeted domains in accordance with the various application areas. To develop prospects within the available functional blocks of compressive sensing frameworks, a diverse range of application areas are investigated. The three fundamental elements of a compressive sensing framework (signal sparsity, subsampling, and reconstruction) are thoroughly reviewed in this work by becoming acquainted with the key research gaps previously identified by the research community. Similarly, the basic mathematical formulation is used to outline some primary performance evaluation metrics for 1D and 2D compressive sensing.

Cross-Term Suppression Method for Time-Frequency Spectrum of Engineering Blasting Signals

Abstract Engineering blasting vibration signals are affected by the test environment and contain noise and trend components, which leads to significant cross-term in the time-frequency (TF) distribution. To address these problems, a combined algorithm of matching pursuit (MP) and smooth pseudo-Wigner-Ville distribution (SPWVD) is proposed to suppress the TF spectrum cross-term and extract the signal features. An overcomplete atom library is constructed for signal feature matching according to sparse signal representation theory. Atomic reconstruction of the subsignal is achieved by MP decomposition, and the SPWVD distribution of the reconstructed subsignal is calculated and superimposed, yielding a more accurate TF expression of the blasting signal. The results show that the combined MP-SPWVD method can accurately suppress cross-term and improve the TF identification and feature analysis ability, which verifies the accuracy of its application in signal TF analysis. The combined algorithm is thus suitable for TF feature extraction of engineering blasting signals.

Sparse representations of random signals

Sparse (fast) representations of deterministic signals have been well studied. Among other types, there exists one called adaptive Fourier decomposition (AFD) for functions in analytic Hardy spaces. Through the Hardy space decomposition of the L2‐space, the AFD algorithm also gives rise to sparse representations of signals of finite energy. To deal with multivariate signals, the general Hilbert space context comes into play. The multivariate counterpart of AFD in general Hilbert spaces with a dictionary has been named preorthogonal AFD (POAFD). In the present study, we generalize AFD and POAFD to random analytic signals through formulating stochastic analytic Hardy spaces and stochastic Hilbert spaces. To analyze random analytic signals, we work on two models, both being called stochastic AFD, or SAFD in brief. The two models are respectively made for (i) those expressible as the sum of a deterministic signal and an error term (SAFDI) and for (ii) those from different sources obeying certain distributive law (SAFDII). In the later part of the paper, we drop off the analyticity assumption and generalize the SAFDI and SAFDII to what we call stochastic Hilbert spaces with a dictionary. The generalized methods are named as stochastic POAFDs, SPOAFDI and SPOAFDII. Like AFDs and POAFDs for deterministic signals, the developed stochastic POAFD algorithms offer powerful tools to approximate and thus to analyze random signals.

Neural Network-Guided Sparse Recovery for Interrupted-Sampling Repeater Jamming Suppression

Interrupted-sampling repeater jamming (ISRJ) is a new type of DRFM-based jamming designed for linear frequency modulation (LFM) signals. By intercepting the radar signal slice and retransmitting it many times, ISRJ can obtain radar coherent processing gain so that multiple false target groups can be formed after pulse compression (PC). According to the distribution characteristic of the echo signal and the coherence of ISRJ to radar signal, a new method for ISRJ suppression is proposed in this study. In this method, the position of the real target is determined using a gated recurrent unit neural network (GRU-Net), and the real target can be, therefore, reconstructed by adaptive filtering in the sparse representation of the echo signal based on the target locating result. The reconstruction result contains only the real target, and the false target groups formed by ISRJ are suppressed completely. The target locating accuracy of the proposed GRU-Net can reach 92.75%. Simulations have proved the effectiveness of the proposed method.

Sparse representation and reproduction of speech signals in complex Fourier basis

Sparse representation and reproduction of speech signals in complex Fourier basis

Sparse representation of approximation to identity

The Dirac-[Formula: see text] distribution may be realized through sequences of convolutions, the latter being also regarded as approximation to the identity. This paper proposes the real form of pre-orthogonal adaptive Fourier decomposition (POAFD) method to realize fast approximation to the identity. It belongs to sparse representation of signals having potential applications in signal and image analysis.

Sparse data inpainting for the recovery of Galactic-binary gravitational wave signals from gapped data

ABSTRACT The forthcoming space-based gravitational wave observatory LISA will open a new window for the measurement of Galactic binaries, which will deliver unprecedented information about these systems. However, the detection of Galactic binary gravitational wave signals is challenged by the presence of gaps in the data. Whether being planned or not, gapped data reduce our ability to detect faint signals and increase the risk of misdetection. Inspired by advances in signal processing, we introduce a non-parametric inpainting algorithm based on the sparse representation of the Galactic binary signal in the Fourier domain. In contrast to traditional inpainting approaches, noise statistics are known theoretically on ungapped measurements only. This calls for the joint recovery of both the ungapped noise and the Galactic binary signal. We thoroughly show that sparse inpainting yields an accurate estimation of the gravitational imprint of the Galactic binaries. Additionally, we highlight that the proposed algorithm produces a statistically consistent ungapped noise estimate. We further evaluate the performances of the proposed inpainting methods to recover the gravitational wave signal on a simple example involving verification Galactic binaries recently proposed in LISA data challenges.

Classifying Single Channel Epileptic EEG data based on Sparse Representation using Shallow Autoencoder.

Patient independent epileptic seizure detection algorithm for scalp electroencephalogram (EEG) data is pro- posed in this paper. Principal motivation of this work is to integrate neural and conventional machine learning methods to develop a classification system which can advance the current wearable health systems in terms of computational complexity and accuracy. Being based on processing a single channel EEG processing, the approach is suitable for usage with small wireless sensors. A shallow autoencoder model is utilized for sparse representation of the EEG signal followed by k-nearest neighbor (kNN) classifier to categorize the data as epileptic or non-epileptic. Using a single EEG channel an optimum sparsity level is explored in the encoded sample. Attaining an accuracy, sensitivity and specificity of 98.85%, 99.29% and 98.86% respectively, for CHB-MIT scalp EEG database, proposed classification method outperforms state of- the-art seizure detection methodologies. Experiments has shown that this performance was possible by using a sparsity level of 4 in the auto-encoder. Furthermore, use of shallow learning instead of deep learning approach for generation of sparse but effective representation is computationally lighter than many other feature extraction and preprocessing methods.

Gd-containing scintillators for thermal neutron detection via graph-based particle discrimination.

Neutron-gamma discrimination (NGD) for gadolinium-containing scintillators is a challenging issue which prevents them from being used in highly efficient neutron detectors with high signal-to-noise ratios. Pulse-shape based digital-signal processing has been selected to tackle this issue, with an emphasis on the dimensionality reduction of the raw data and capability to mitigate the influence of noise, unwanted variations, and outliers on the accuracy of classification. We present two graph-embedded non-negative matrix factorization digital classifiers in which an event graph (or a network) is introduced to find a low-dimensional structure hidden in the high-dimensional experimental data. Utilizing energy-independent normalized features of waveforms and a graph composed of mixed-source reference events, the smooth or sparse low-dimensional representation of detector signals from a Ce:Gd3Al2Ga3O12 scintillator leads to a high thermal neutron detection efficiency (77%-80%) and a high NGD ratio (neutron-gamma efficiency ratio, ∼109) simultaneously. Moreover, excellent discrimination between neutron and ambient background events has been achieved. The proposed graph-embedded algorithms may be applied not only for thermal-neutron position-sensitive detectors and single-channel detectors but also for other radiation detectors that need excellent particle (or crystal) discrimination capabilities and high detection efficiencies in many applications, including medical imaging, nondestructive testing, and security scans.

TU85. POLYGENIC RISK SCORE FOR CANNABIS USE DISORDER PREDICTS ACUTE INTOXICATING EFFECTS AND COGNITIVE DEFICITS INDUCED BY DELTA-9-TETRAHYDROCANNABINOL: A PILOT STUDY

Algorithms for learning overcomplete dictionaries for sparse signal representation are mostly iterative minimization methods that alternate between a sparse coding stage and a dictionary update stage. For most however, the notion of consistency of the learned quantities has not been addressed. Based on the observation that the observed signals can be approximated as a sum of rank one matrices, a new adaptive dictionary learning algorithm is proposed in this paper. It is derived via sequential adaptive penalized rank one matrix approximation where the ℓ1-norm is introduced as a penalty promoting sparsity. The proposed algorithm uses a block coordinate descent approach to consistently estimate the unknowns and has the advantage of having simple closed form solutions for both the sparse coding and dictionary update stages. The consistency properties of both the estimated sparse code and dictionary atom are provided. The performance of the proposed algorithm compared to some state of the art algorithms is illustrated on both simulated data and a real functional magnetic resonance imaging (fMRI) data set from a finger tapping experiment.

Blind separation of sparse sources from nonlinear mixtures

Blind source separation (BSS) has been studied well when the sources are sparse signals and their combinations are linear. Sparse component analysis (SCA) or dictionary learning algorithms propose well-known approaches for performing BSS in this model. In this study, we explore BSS when the sources are sparse signals, however, their combinations are nonlinear. The considered scenario can be adapted to several signal processing applications such as machine learning and system identification. To perform BSS, we first approximate the nonlinear mixture functions with the polynomial functions. Then, using an alternating approach, we estimate the sources and the coefficients of polynomial functions. The considered strategy is similar to one employed in dictionary learning algorithms for sparse representation of signals. In fact, in iterations where the sources are estimated, we cluster the signals, and in iterations where the coefficients of polynomial functions are estimated, we assign a polynomial manifold to each cluster. The identifiability issues of the considered nonlinear model are also discussed. Experimental results demonstrate the effectiveness of the proposed method relative to state-of-the-art methods.