Over the last two decades, tensor-based methods have received growing attention in the signal processing community. In this work, the authors proposed a comprehensive overview of tensor-based models and methods for multisensor signal processing. They presented for instance the Tucker decomposition, the canonical polyadic decomposition, the tensor-train decomposition (TTD), the structured TTD, including nested Tucker train, as well as the associated optimisation strategies. More precisely, they gave synthetic descriptions of state-of-the-art estimators as the alternating least square (ALS) algorithm, the high-order singular value decomposition (HOSVD), and of more advanced algorithms as the rectified ALS, the TT-SVD/TT-HSVD and the Joint dImensionally Reduction and Factor retrieval Estimator scheme. They illustrated the efficiency of the introduced methodological and algorithmic concepts in the context of three important and timely signal processing-based applications: the direction-of-arrival estimation based on sensor arrays, multidimensional harmonic retrieval and multiple-input–multiple-output wireless communication systems.

The periodic signals that have predictable and deterministic characteristics are used in the analysis and modelling of dynamical systems in diverse fields. These signals can be detected as the weak signals within the time series obtained from the measurable processes of dynamical systems. The Duffing oscillator is effective in detecting weak periodic signals with a very low signal-to-noise ratio. In this study, the authors present a method to automate the weak periodic signal detection of the Duffing oscillator using a quantitative index for the classification of the periodic and non-periodic signals. In this method, the authors use the wavelet scale index as the quantitative index in the classification of signals. Thus, they are able to plot the wavelet scale index spectrum of the Duffing oscillator where the frequency values of the weak periodic signals correspond to near-zero wavelet scale index parameters. First, the authors perform simulations using the method and detect weak periodic signals embedded in noise. Then, they employ two electroencephalogram signals to demonstrate the feasibility of the proposed method in the empirical data. Lastly, they compare the method to the periodogram power spectral density estimate based on fast Fourier transform.

The reconstruction algorithm is one of the core issues in applying compressed sensing theory to practical applications. Two-dimensional orthogonal matching pursuit (2DOMP) algorithm, as an extension of the traditional orthogonal matching pursuit algorithm, can be used directly for the reconstruction of two-dimensional signals. With 2D separable sampling, the memory requirements and the complexity of 2DOMP are exponentially reduced. However, in 2DOMP algorithm, the requirement of reconstruction matrix is not taken into consideration, merely measurement matrix is used directly. In this study, singular value decomposition is introduced into 2DOMP algorithm, and 2DOMP algorithm based on singular value decomposition (2DOMP-SVD) is proposed. Singular value decomposition of separable measurement matrices is used to obtain optimised separable reconstruction matrices and optimised measurements. Numerical experiments demonstrate that the proposed 2DOMP-SVD algorithm can significantly improve the success rate and robustness of reconstruction. Moreover, the separation design of the matrix can satisfy the requirements for both the measurement matrix and the reconstruction matrix individually, and is suitable for general separable linear system.

Sensor-based human activity classification requires time and frequency domain feature extraction techniques. The set of choice in time and frequency domain features may have a significant impact on the overall classification accuracy. Another problem is to train deep learning models with sufficient dataset. The use of generative models eliminates the requirement of choosing certain features of the signal. As a generative model, restricted Boltzmann machine (RBM) is an energy-based probabilistic graphical model which factorises the probability distribution of a random variable over a binary probability distribution. Conditional restricted Boltzmann machines (CRBMs) is an extension to RBM, which can capture temporal information in time-series signals and can be deployed as a generative model in classification. In this study, the authors show how CRBMs can be trained to learn signal features. They present four generative model training results, RBM, CRBM, generative adversarial network, Wasserstein generative adversarial network – gradient penalty and compare the models' performances with a performance criterion. They show that the CRBM model can generate signals closest to true signals with a significantly higher success rate as compared to other presented generative models. They present a statistical analysis of the findings and show that the findings significantly hold.

Fourier transform infrared (FTIR) spectrometry is commonly used for the identification of reference substances (RSs) in solid, liquid, or gaseous mixtures. An expert is generally required to perform the analysis, which is a bottleneck in emergency situations. This study proposes a support vector machine (SVM)-based algorithm, the peak correlation classifier (PCC), designed to rapidly detect the presence of a specific threat or reference substance in a sample. While SVM has been used in various spectrographic contexts, it has rarely been used on FTIR spectra. The proposed algorithm discovers correlation similarities between the FTIR spectrum of the RS and the test sample and then uses SVM to determine whether or not the RS is present in the sample. The study also shows how the additive nature of FTIR spectra can be used to create ‘synthetic’ substances that significantly improve the detection capability and decision confidence of the SVM classifier.