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.

Surface electromyography (sEMG) signals are stochastic, multicomponent and non-stationary, and therefore their interpretation is challenging. In this study, an attempt has been made to develop an automated muscle fatigue detection system using variational mode decomposition (VMD) features of sEMG signals and random forest classifier. The sEMG signals are acquired from 103 healthy volunteers during isometric (45 subjects) and dynamic (58 subjects) muscle fatiguing contractions and preprocessed. The band-limited intrinsic mode functions (BLIMFs) are extracted from non-fatigue and fatigue segments of the signals using the VMD algorithm. Hjorth features, such as activity, mobility and complexity are extracted from each BLIMF and are given to the random forest classifier. The performance of these features is evaluated using leave-one-subject-out cross-validation. The results show that the complexity feature performs better than others and it has resulted in an accuracy of 83% in dynamic contractions and 80% in isometric contractions. The performance is increased by about 8% in a dynamic condition when the most significant complexity features (p < 0.001) are used and by about 12% for isometric when the authors use all significant features. Therefore, the proposed approach could be used to detect fatigue conditions in various neuromuscular activities and real-time monitoring in the workplace.

In recent years, data mining and algorithm-based methods have been used frequently for the prediction and diagnosis of various diseases. Traumas, being one of the significant health problems in the world, are also one of the most important causes of death. This study aims to predict the presence of traumatic pathology in the lung of the patients admitted to the emergency department due to blunt thorax trauma with no X-ray and computed tomography (CT) history by machine learning methods. The models developed in the study using the 5-fold cross-validation method are most accurately classified by the ensemble (voting) classifier, whether there is a pathology in X-ray (mean accuracy = 0.82) and CT (mean accuracy = 0.83). The K-nearest neighbourhood method classifies patients with pathology in X-ray by 83% accuracy, while the ensemble (voting) method classifies non-pathology patients by 94% accuracy in models. Of CT results, random forest, ensemble (voting), and ensemble (stacking) classifiers are precisely classified by 96%, while those patients with pathology are classified perspicuously by 77%. As a result, a mathematical framework using data mining methods was proposed based on estimating the X-ray and CT results for the thorax graph scan.

The accuracy of cooperative localisation can be severely degraded in non-line-of-sight (NLOS) environments. To mitigate the NLOS errors, the cooperative localisation problem based on time of arrival (TOA) under the mixed line-of-sight (LOS)/NLOS conditions is addressed. By studying the topological relationship between nodes, a TOA NLOS mitigation cooperative localisation algorithm based on the topological unit is proposed. This algorithm is implemented under the classical multidimensional scaling framework. The adjacent topological unit of NLOS measurements are successfully identified by using the LOS matrix, and the NLOS measurements are re-estimated using topological units. The least-square method is used to transform the relative coordinates into absolute coordinates depending on the location of the anchor nodes. Compared to the existing methods, by employing the topological unit, this algorithm only requires the number of LOS anchor nodes to be 2 in the two-dimensional plane, and the better localisation performance can be achieved. Simulation results show that the proposed method works well for both the sparse and dense NLOS environments.

The supervised single-channel speech enhancement presents one mixture recording at the input of the neural network and updates network parameters in order to generate an output as the reconstructed speech signal. However, current neural networks-based single-channel speech enhancement methods are not able to fully utilise pertinence with the specific frequency range of speech signals with limited computational complexity. In this study, the authors studied the power spectral density of mixtures with human speech and noise interferences. Based on the theory that the speech signal distributes at the lower band, they proposed a method to train signal approximation (SA) based neural networks with the lower frequency band of the speech mixture to improve the performance. To realise the lower band approach for single-channel speech enhancement, the method uses a long short-term memory (LSTM) block to exploit short-time Fourier transform of the desired frequency range. Furthermore, in order to improve the speech enhancement performance within reverberant room environments, the dereverberation mask and the enhanced ratio mask are exploited as the training targets of two LSTM blocks, respectively. The detailed evaluations confirm that the proposed method outperforms the state-of-the-art methods.

This work aims to enhance the quality of narrowband (0–4 kHz) voice signal in terms of frequency components, i.e. missing high-frequency components in a range of 4–8 kHz. The proposed artificial bandwidth extension framework uses the optimisation. In this context, a signal model is used to get a better representation of wideband (0–8 kHz) information of a signal. The optimisation is used to obtain the synthesis filter for a given signal model, which is used to synthesise the high-band (4–8 kHz) signal. The discrete Fourier transform addition is performed to add the narrowband signal and estimated high-band signal for removing the leaked information from the synthesis filter and non-ideal low pass filter. Gain adjustment is performed on the estimated high-band signal to make its energy equal to the true high-band signal. Non-stationary characteristics of speech signals generate an assorted variety in synthesis filters and corresponding gain. For this, a deep neural network (DNN) is used to estimate the synthesis filter and gain by using the given narrowband information. The authors analyse the performances of the DNN model on two data sets. Objective and subjective analyses are carried out on these data sets.

This work's contributions include three innovative concepts, an improved model, two-stage Lagrange principle, and minimum-energy scaling optimisation, for quantisation audio watermarking in the wavelet domain. First, discrete wavelet transform (DWT) multi-coefficients quantisation, composed of arbitrary scaling on the lowest DWT coefficients, and the group-based signal-to-noise ratio (SNR) of these coefficients is connected in a model. Then, the two-stage Lagrange principle and minimum-energy approach play two essential roles to obtain the optimal scaling factors. With the proposed scheme, the best fidelity and robustness of embedded audio can be attained and the perceptual evaluation of audio quality (PEAQ) test with an illustration of the relationship between SNR and PEAQ is also performed as well. Simulation results show that each watermarked audio by the proposed method attains a high SNR, good PEAQ, and a low bit error rate (BER). The SNR of most watermarked audios in their method is above 35 or even above 40 and the corresponding subjective difference grade of PEAQ is close to 0. In terms of comparing BER, most of their BER is as low as 2% or less indicating better robustness against many attacks, such as re-sampling, amplitude scaling, and mp3 compression.

In this paper, an adaptive modification rate artificial bee colony (AMR-ABC) algorithm is proposed by incorporating a novel adaptive modification rate to adaptively balance exploration and exploitation to determine which parameters (or the number of parameters) to be updated in a solution during each iteration. The performance of the AMR-ABC algorithm is compared to those the standard ABC algorithm and its two variants, and the Parks–McClellan algorithm for designing Type 3 (orders: 14, 26, and 38) and Type 4 (orders: 13, 25, and 37) linear phase FIR differentiators to evaluate their design capabilities. Design results have shown that the proposed AMR-ABC algorithm (i) outperforms four other design algorithms with the lowest p-norm error in each of the six differentiator designs and (ii) is robust such that the same p-norm error solution with an equiripple amplitude response in each of the six differentiator designs can be obtained by repeating a design with a different population of randomly generated initial solutions. The filter coefficients of six linear phase FIR differentiator designs are given as benchmarks to compare the p-norm error performance of the AMR-ABC algorithm to other algorithms. The AMR-ABC algorithm is attractive to be used for optimisation in this and other design problems.

Based on the theory of phase curvature autofocus (PCA) on stripmap synthetic aperture radar (SAR), an improved algorithm for increasing the accuracy of phase error compensation is presented in this study. PCA method was proposed to extend the phase gradient autofocus method for SAR systems in stripmap mode. The main problems concerned with the traditional PCA algorithm are related to selecting candidates in the image for phase error estimation, windowing, estimation procedure, and range shift due to the phase error. In this study, the modification of traditional PCA algorithm has been performed in different steps including the following: improving range-compressed data, prominent points extraction, adaptive windowing, weighted maximum likelihood for phase error estimation, improving phase error result, range shift compensation, and determining the condition to end the iterations. Real data experiments demonstrate the success of the proposed autofocus method, which is applied to the stretched-based pulsed mode SAR data set in the absence of highly accurate inertial navigation units.

Direction of arrival (DOA) estimation using the improved unfolded coprime array (IUFCA) subject to array motion isdiscussed in this study. Unfolded coprime array (UFCA) consists of two uniform linear subarrays, and the two subarrays are arranged at different sides of theaxis, which leads to a large number of holes in the difference co-array (DCA). With array motion and DCA synthesis,part of the holes can be filled, but there are still holes in the center which lead to the virtual arrays separated.By analyzing the hole positions in the synthetic DCA generated by UFCA motion, the authors improve the originalUFCA by relocating some physical elements, then the two dominantconsecutive DCA segments in the positive and negative sides can be connected. The expression of synthetic DCA is analyzed, and the closed-form expression of theuniform degree of freedom (uDOF) subject to IUFCA motion is studied. Simulation results show that IUFCA motion can obtain a largenumber of uDOFs, which leads to better DOA estimation performance and more identifiable signals compared with existingcoprime array configurations.

The Fourier transform of a N point time series is a N point complex series, while the S-transform (ST) of the same time series is a 2D time–frequency complex matrix. The computation and storage of additional points are a major drag on the usage of ST. In this study the compact S-transform (cST) is presented, with efficiencies brought about through computation of only selected voices (frequencies). The cST spectrum has uncomputed voice gaps that increase in width towards the higher frequencies. Plot of the cST magnitude spectrum is virtually indistinguishable from the ST magnitude plot. Local spectrum at any spot on the cST can be quickly examined in detail through interpolation. The cST requires the computation of approximately voices compared to for the ST. The proportion of computed voices decrease for larger N. For , ∼20% of the voices in the time-frequency spectrum is computed; for only 14% of the voices is computed. For applications, such as audio and speech signal processing where segments of one million samples are not uncommon, <1% of the voices are computed, thereby reducing the computation time by ∼99%.

The authors consider the problem of multi-choice majority voting in a network of n agents where each agent initially selects a choice from a set of K possible choices. The agents try to infer the choice in the majority merely by performing local interactions. Extending the popular ‘Population Protocol’ framework for pairwise interactions between agents, in this study, they propose a new model called ‘Broadcasting Population Protocol’. In the proposed model, each agent broadcasts its messages in such a way that all its neighbours will receive the message simultaneously. They design two distributed algorithms for solving the multi-choice majority voting problem in this new model. They show that these algorithms return the correct output, i.e. the choice in the majority. They also analyse their performances in terms of time and message complexities. They establish via simulations that the proposed algorithms improve both time and message complexities significantly with respect to previous algorithms proposed in conventional population protocols, and they can be utilised in networks where messages can be transmitted to a subset of agents simultaneously, such as wireless networks.

In general, weighted compressive sensing recovery needs to solve optimisation problems with the objective function being the sum of a weighted -norm and a regularised differentiable convex function. Note that the weights in the weight vector are assumed to be positive. In fact, it is possible to achieve outstanding signal recovery performance even if some of the weights are appropriately designed to be negative. However, the negative weights lead to the non-convexity of the optimisation problem, which would place a barrier to attain the optimal solution. To deal with this issue, in this study, the authors propose to solve the problem by applying a well-established algorithm, namely, the alternating direction method of multipliers (ADMM) algorithm. It is shown that the optimal solution can be obtained by taking advantage of this optimisation scheme. The performance of the proposed algorithm is demonstrated by numerical results.