Many practical problems in the real world can be formulated as the non-negative -minimisation problems, which seek the sparsest non-negative signals to underdetermined linear equations. They have been widely applied in signal and image processing, machine learning, pattern recognition and computer vision. Unfortunately, this non-negative -minimisation problem is non-deterministic polynomial hard (NP-hard) because of the discrete and discontinuous nature of the -norm. Inspired by the good performances of the fraction function in the authors’ former work, in this paper, the authors replace the -norm with the non-convex fraction function and study the minimisation problem of the fraction function in recovering the sparse non-negative signal from an underdetermined linear equation. They discuss the equivalence between non-negative -minimisation problem and non-negative fraction function minimisation problem, and the equivalence between non-negative fraction function minimisation problem and regularised non-negative fraction function minimisation problem. It is proved that the optimal solution to the non-negative -minimisation problem could be approximately obtained by solving their regularised non-negative fraction function minimisation problem if some specific conditions are satisfied. Then, they propose a non-negative iterative thresholding algorithm to solve their regularised non-negative fraction function minimisation problem. At last, numerical experiments on some sparse non-negative signal recovery problems are reported.

In this study, the authors study and give a new framework for colour image representation based on colour quaternion wavelet transform (CQWT). The new colour quaternion filter bank is constructed by using radon transform. Starting from link with structure tensors, the authors propose a new multi-scale tool for vector-valued signals which can provide efficient analysis of local features by using the concepts of amplitude, phase, and orientation. To demonstrate the properties of CQWT, new colour image denoising algorithm is proposed by using CQWT and bivariate shrinkage function. The performance of the proposed algorithm is experimentally verified on a variety of noise levels. Experimental results show that the proposed algorithm achieves superior performance both in visual quality and objective peak-signal-to-noise ratio, mean square error, and structure similarity values, compared with other state-of-the-art denoising algorithms.

Electroencephalogram (EEG) is a highly sensitive instrument and is frequently corrupted with eye blinks. Methods based on adaptive noise cancellation (ANC) and discrete wavelet transform (DWT) have been used as a standard technique for removal of eye blink artefacts. However, these methods often require visual inspection and appropriate thresholding for identifying and removing artefactual components from the EEG signal. The proposed work describes an automated windowed method with a window size of 0.45 s that is slid forward and fed to a support vector machine (SVM) classifier for identification of artefacts, after the identification of artefacts, it is fed to an autoencoder for correction of artefacts. The proposed method is evaluated on the data collected from the project entitled ‘Analysis of Brain Waves and Development of Intelligent Model for Silent Speech Recognition’. From the results it is observed that the proposed method performs better in identifying and removing artefactual components from EEG data than existing wavelet and ANC based methods. The proposed method does not require the application of independent component analysis (ICA) before processing and can be applied to multiple channels in parallel.

This study proposes an augmented Lagrange multiplier-based method to perform the singular spectral analysis-based denoising without computing the singular values. In particular, the one-dimensional (1D) signal is first mapped to a trajectory matrix using the window length L. Second, the trajectory matrix is represented as the sum of the signal dominant matrix and the noise-dominant matrix. The determination of these two matrices is formulated as an optimisation problem with the objective function being the sum of the rank of the signal dominant matrix and the norm of the noise-dominant matrix. This study employs the Schatten q-norm operator with and the double nuclear-norm penalty for approximating the rank operator as well as the minimum concave penalty (MCP)-norm operator for approximating the -norm operator. Third, some auxiliary variables are introduced and the augmented Lagrange multiplier algorithm is applied to find the optimal solution. Finally, the 1D denoised signal is obtained by applying the diagonal averaging method to the obtained signal dominant matrix. Computer numerical simulation results show that the authors' proposed method outperforms the existing methods.

Here, a technique for automated detection of epilepsy is proposed, based on a novel set of features derived from the multifractal spectrum of electroencephalogram (EEG) signals. In fractal geometry, multifractal detrended fluctuation analysis (MDFA) is a technique to examine the self-similarity of a non-linear, chaotic and noisy time series. EEG signals which are representatives of complex human brain dynamics can be effectively characterised by MDFA. Here, EEG signals representing healthy, interictal and seizure activities are acquired from an available dataset. The acquired signals are at first analysed using MDFA. Based on the multifractal analysis, 14 novel features are proposed in this study, to distinguish between different types of EEG signals. The statistical significance of the selected features is evaluated using Kruskal–Wallis test and is finally served as input feature vector to a support vector machines classifier for the classification of EEG signals. Four classification problems are presented in this work and it is observed that 100% classification accuracy is obtained for three problems which validate the efficacy of the proposed model for computer-aided diagnosis of epilepsy.

A novel active learning-based electrocardiogram (ECG) signal classification method using eigenvalues and deep learning is proposed. Six statistical features relating to ECG beat intervals are calculated separately for each heartbeat. Both statistical features and eigenvalues of ECG beats are combined into a single feature vector. The eigenvalues of ECG beats are used as an input to denoising autoencoder (DAE). Weighted ECG beat intervals are calculated by using ten-fold cross-validation approach. To learn an efficient feature representation from the hybrid feature vector, DAE is used in an unsupervised way. After completing the feature learning procedure, a softmax regression layer is added on the top of the resulting hidden layer of DAE, and thus a suitable deep neural network (DNN) architecture is built. The learned features obtained from the autoencoder layers are fed to the softmax regression layer for classification. To update weights of the proposed eigenvalues-based DNN model, ECG beats are labelled by the medical expert are used. In order to determine the most informative beats, entropy and Breaking-Ties are also used as selection criteria. The proposed method is evaluated in terms of ECG beats classes. The classification performance of the authors’ proposed model is also compared with the several conventional machine learning classifiers.

In the underdetermined model , where is a K-group sparse matrix (i.e. it has no more than K non-zero rows), the matrix may be also perturbed. Theoretically, a more relaxed condition means that fewer measurements are required to ensure sparse recovery. In this study, a relaxed sufficient condition is proposed for greedy block coordinate descent (GBCD) under total perturbations based on the restricted isometry property in order to guarantee that the support of is recovered. We also show that GBCD fails in a more general case when .

This study presents an efficient no-reference image quality assessment (NR-IQA) technique to assess the quality of images affected by noise. The proposed technique is based on two characteristics of the human eye (retina), namely the presence of centre-surround receptive field and visualisation utilising different spatial frequency channels. In the proposed technique, the authors model centre-surround receptive field using difference of Gaussians (DoG), whereas to mimic multiple frequencies in the centre-surround receptive field, they compute multiple DoG images of different values of standard deviations generated for different frequencies. Furthermore, the singular value decomposition-based features are obtained from the generated DoG images to estimate the image quality. The proposed technique does not require any training, neither based on distorted/original images nor based on subjective human scores, to assess the image quality. The performance of the proposed technique is being analysed on LIVE, TID08, CSIQ and SD-IVL databases and it shows that the proposed technique outperforms recently proposed NR and no-training/training-based IQA techniques. Experimental validation of the proposed technique in the big-data scenario of 10,000 noisy images also shows encouraging results.

Linear-frequency-modulated continuous-wave (LFMCW) radars with deramping technique have several advantages such as compact size, low cost, and easy implementation, compared to traditional pulse radars; however, the non-linear distortions caused by analogue modules, particularly power amplifiers, may deteriorate the radar detection performance. To solve this problem, a digital closed-loop compensation scheme for the LFMCW signal is proposed, which can compensate the LFMCW signal in real time, when the non-linear distortions change with the working environment. The proposed compensation scheme improves the detection performance, noticeably. Considering the speed limitations of field programmable gate arrays (FPGAs), the proposed scheme is implemented in an FPGA at an intermediate-frequency level, using a polyphase processing structure.

Space–frequency modulation (SFM) signal is a potential waveform for multifunction radar with high degrees of freedom of space, time, and frequency. However, the introduction of the additional communication function will modulate the transmitting signal, which will severely deteriorate the autocorrelation function (ACF). Here, a modified CLEAN method is proposed to eliminate the influence of undesired sidelobes in ACF on the air target detection. In the proposed method, undesired sidelobes are treated as extra features of real target to obtain more precise estimation of its complex reflection coefficient. Moreover, by considering about the sparsity of air targets, the authors employ the sparse representation method to estimate the response of the current strongest target. Then the target occlusion is eliminated by iterative cancellation. Simulation results demonstrate that the proposed detector is reliable and effective for the SFM-based integrated system.

Speech recognition is an area that is constantly developing. In this study, the authors present a new system of speech recognition applied to the Arabic language. The system proposed here is based on the harmonic plus noise model (HNM). This model is rather used in speech synthesis tasks and is known for providing excellent speech production quality. Thus, their contribution lies in replacing the conventional mel-frequency cepstrum coefficients (MFCC) parameters with a set of acoustic parameters, extracted through the HNM estimation process. The HNM model allows development of a more adapted processing by distinguishing voiced and unvoiced speech frames and by characterising the harmonic property of speech. As common, their system consists of both training and recognition phases. Deep neural networks and hidden Markov models (DNN–HMM) are used for modelling the voiced frames corresponding to the harmonic part. The DNN model is estimated with static and dynamic parameters. Moreover, the unvoiced frames, which represent the noise part of the HNM, are clustered with an HMM model. The spoken Arabic digits are used to measure the performance of the proposed recognition system and a comparison with the MFCC-based approach is performed.

Inverse problems in imaging such as denoising, deblurring, superresolution have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their indisputable success, CNNs are not mathematically validated as to how and what they learn. In this study, the authors prove that during training, CNN elements solve for inverse problems which are optimum solutions stored as CNN neuron filters. They discuss the necessity of mutual coherence between CNN layer elements in order for a network to converge to the optimum solution. They prove that required mutual coherence can be provided by the usage of residual learning and skip connections. They have set rules over training sets and depth of networks for better convergence, i.e. performance. They have experimentally validated theoretical assertions.

The authors propose a method to recognise facial expressions based on graph signal processing (GSP) techniques. Facial expressions are characterised by local patterns in the facial regions such as eyes, lips etc. and interrelationships among them. A facial expression recognition algorithm needs to capture these variations in the facial regions at the local level and the interrelationships of these regions at the global level. Hence, in the authors’ opinion, GSP seems to be an appropriate tool for the purpose. In this study, a novel method is presented which makes use of graph signals to represent the facial regions. They leverage spectral graph wavelet transform to extract information for creating the feature descriptor. Here, different types of two-channel and three-channel filter banks have been used by setting the weights of their channels for finding the optimum performance of the recognition rate. Through simulation studies, it is observed that the use of Abspline filter bank provides the best result. The experimental investigations on the extended Cohn–Kanade (CK+) and the JAFFE datasets have been carried out and the results confirm the effectiveness of the proposed method in recognition rate improvement.

A new method of extracting acoustic features based on auditory spike code is proposed. An auditory spike code represents the acoustic activities created by the signal, similar to sound encoding of the human auditory system. In the proposed method, an auditory spike code of the signal is computed using a 64-band Gammatone filterbank as the kernel functions. Then, for each spectral band, the sum and non-zero counts of the auditory spike code are determined, and the features corresponding to the population and occurrence rate of the acoustic activities for each band are computed. In addition, the distribution of the acoustic activities on a time axis is analysed based on the histogram of time intervals between the adjacent acoustic activities, and the features for expressing temporal properties of the signal are extracted. The reconstruction accuracy of the auditory spike code is also measured as the features. Different from most conventional features obtained by complex statistical modelling or learning, the features by the proposed method can directly show specific acoustic characteristics contained in the signal. These features are applied to a music genre classification, and it is confirmed that they provide a performance comparable to state-of-the-art features.

Conventionally, near-field scattering effect was considered in antenna measurement, which requires a great amount of measuring efforts and re-measurement if the operational platform has changed. In this study, the authors consider the near-field scattering problem in the framework of adaptive array beamforming theory, which avoids re-measurement and can be adaptive to the arbitrary scenario. Generally, the near-field scattering can result in severe performance degradation in adaptive beamforming applications. They propose a robust adaptive beamforming approach that can maintain the performance in the presence of near-field scatterers with unknown scattering coefficients. In the authors’ approach, the near-field scatterering signal component is incorporated into the presumed steering vector. Thus, it is treated as useful information in this study instead of nuisance interference in the literature. In particular, the properties of the far-field direct-path signal and near-field signal are explored and the large uncertainty set is divided into two small ones describing the far-field and near-field steering vectors, respectively. Simulation examples are provided to show the performance improvement by making use of the near-field scattering signals.

Sleep has great effect on physical health and quality of life. Electroencephalogram (EEG) signal is used in studying sleep process and recently, time–frequency transforms are increasingly utilised in EEG signal analysis. This study proposes an efficient method for sleep stages classification based on a time–frequency transform, namely Stockwell transform. In the introduced method, at first, the Stockwell transform is used to map each 30 s epoch of EEG signal into the time–frequency domains, which results in a complex-valued matrix. Then, the frequency domain is divided into different non-overlapping segments, leading to several matrices. After that, entropy features are extracted from the obtained matrices. In order to determine the sleep stage of each epoch, the computed features are applied to classifier. Support vector machine, weighted K-nearest neighbour, and ensemble bagged tree classifiers are considered. The Pz–Oz and Fpz–Cz channels of EEG signal from Sleep-EDF data set and C3–A2 channel from ISRUC-Sleep data set are used in this research. The results indicate that the proposed method outperforms the recently introduced methods.