Transformation of a random variable is a common need in a design of many algorithms in signal processing, automatic control, and fault detection. Typically, the design is tied to an assumption on a probability density function of the random variable, often in the form of the Gaussian distribution. The assumption may be, however, difficult to be met in algorithms involving non-linear transformation of the random variable. This paper focuses on techniques capable to ensure validity of the Gaussian assumption of the non-linearly transformed Gaussian variable by approximating the to-be-transformed random variable distribution by a Gaussian mixture (GM) distribution. The stress is laid on an analysis and selection of design parameters of the approximate GM distribution to minimise the error imposed by the non-linear transformation such as the location and number of the GM terms. A special attention is devoted to the definition of the novel GM splitting directions based on the measures of non-Gaussianity. The proposed splitting directions are analysed and illustrated in numerical simulations.

Recently, a tight frame, called convolution framelets (CFs) and constructed by convolving local and non-local bases, is proposed to provide valuable insights in understanding the patch-based processing approaches in the viewpoint of sparse representation (SR). However, it is still unclear how to represent signals with energy concentration guarantee in its lifted space and how to optimise the local base for a given non-local base. To address these issues, the equivalence between the signal space and its lifted space is established by the Hankel operator. In the lifted space, the energy concentration property of signals is measured by the sparsity instead of the Euclidean norm and the rank. With the new objective function, an optimisation model is built to train the optimal local base for a given nonlocal base from the training samples, motivating us to propose the optimal matching convolution framelets (OMCFs). In addition, a numerical algorithm is also designed to solve the proposed model using alternating optimisation strategy. The OMCF for SR is tested on the speech signals, and the comparisons with traditional popular SR tools, such as discrete cosine transform (DCT) and Haar wavelets, demonstrate its better performance.

In sparse signal recovery, to overcome the -norm sparse regularisation's disadvantages tendency of uniformly penalise the signal amplitude and underestimate the high-amplitude components, a new algorithm based on a non-convex minimax-concave penalty is proposed, which can approximate the -norm more accurately. Moreover, the authors employ the -norm loss function instead of the -norm for the residual error, as the -loss is less sensitive to the outliers in the measurements. To rise to the challenges introduced by the non-convex non-smooth problem, they first employ a smoothed strategy to approximate the -norm loss function, and then use the difference-of-convex algorithm framework to solve the non-convex problem. They also show that any cluster point of the sequence generated by the proposed algorithm converges to a stationary point. The simulation result demonstrates the authors’ conclusions and indicates that the algorithm proposed in this study can obviously improve the reconstruction quality.

In this study, the authors propose a novel framework for audio source separation based on a cascaded non-negative matrix factorisation (NMF) using homotopy optimisation with perturbation and ensemble (HOPE) and denoising autoencoder. NMF using traditional optimisation has a problem of finding a global solution, and hence could not achieve complete separation of the sources from the mixture. This problem has been addressed using homotopy optimisation in this study. Subsequently, using denoising autoencoder the residual sounds that are usually observed in the separated sources are removed. The enhanced audio signals are filtered using Wiener techniques to obtain the separated signals. The homotopy-based NMF is applied for separating singing voice and drums from song samples using a single-channel mixture. The separated signals are compared with other NMF algorithms by using Blind Source Separation (BSS) Eval objective quality measures. The NMF with HOPE and denoising autoencoder is shown to provide an improvement of up to 6 dB in comparison with other NMF algorithms.

In this study, the authors present a new procedure for the synthesis of the nearly linear-phase infinite impulse response (IIR) filters with two close notch frequencies based on all-pass filter application. The filter is obtained using a parallel connection of the delay line and IIR all-pass filter with a piecewise approximately linear phase. The desired magnitude characteristic is achieved by equiripple approximation of the all-pass filter phase. The magnitude characteristic is equiripple in all passbands. The proposed method is also suitable for the synthesis of complementary filters for extraction of the signal components at prescribed frequencies. The initial solution for the arbitrary order of an all-pass filter is proposed, which attains a sufficient number of phase error extrema. All phase error minima and maxima corresponding to the initial solution have almost identical values, excluding the ones near notch frequencies. As a result, the method exhibits fast and strong convergence. The described method can also be applied for the design of multiple notch filters with two very close notch frequencies.

A method for solving the instantaneous mixtures of the multiple non-stationary wideband signals in the time–frequency (TF) plane is proposed. The blind source separation is performed by calculation of spatial TF distribution matrices, estimation of a separating matrix, estimation of permutation matrices and scaling matrices and TF synthesis. The simulation result shows that the proposed method improves the signal-to-distortion ratio than the preceding methods. Moreover, also the mutual relationship between the source localisation and the source separation is clarified. The source localisation methods using the source separation result and the source separation method using the source localisation result are proposed.

An algorithm is proposed for mixing matrix estimation in underdetermined blind source separation (UBSS) based on homogeneous polynomials representation, in order to blindly identify a mixing matrix in the case where the source signal is insufficiently sparse. First, the observed signal subspaces (hyperplanes) are identified by polynomial fitting, differentiation, and spectral clustering. Then, the intersection lines between clustering planes are estimated by using normal vectors of each subspace, which are finally proved to be column vectors of the mixing matrix up to scaling and ordering. Based on the algebraic-geometric theory, the proposed algorithm can improve the accuracy of mixing matrix estimation, without being influenced by convergence. Simulation results indicate that the proposed algorithm has higher estimation accuracy than traditional algorithms. Additionally, the single-source and multi-source points of the source signal can be detected simultaneously, which increases the robustness of the algorithm.

The study addresses the sensor control problem for multi-target tracking via delta generalised labelled multi-Bernoulli (-GLMB) filter, and proposes two novel single-sensor control schemes. One is that the Rényi divergence is used as the objective function to measure the information gain between the predicted and posterior densities of the -GLMB filter, and it is superior for the overall performance of the system. Since most of the sensor control schemes, including the scheme the authors proposed, are faced the curse of computation, thus the other novel scheme is proposed. This scheme, in which the sum of the statistical distances between the predicted states of targets and sensor is used as the objective function, evades the updated step of the multi-target filter, when computing the objective function for each admissible action. Moreover, these two sensor control schemes are applied to a distributed multi-sensor system, in which the proposed schemes are used for each sensor node and the generalised covariance intersection method is used to compute the fused multi-target posterior density. Finally, they adopt the sequential Monte-Carlo method in bearing and range multi-target tracking scenarios to illustrate the effectiveness of the proposed methods.

The two-dimensional (2D) cubic phase function (CPF) is known as a highly accurate 2D polynomial phase signal estimator, but it has limited applicability due to the requirement for the 3D search for second-order partial phase derivatives. The authors propose an interpolation-based approach simulating non-uniform (NU) signal sampling in order to reduce the 2D CPF calculation complexity. The NU resampling enables the 2D CPF evaluation using the 2D fast Fourier transform and searches over mixed-phase parameter. The computational complexity is reduced from to . The additional stage with dechirping, filtering and phase unwrapping is introduced to refine parameter estimates.

The normalised subband adaptive filter (NSAF) is a useful adaptive filter, which improves the convergence rate compared with the normalised least mean-square algorithm. Most analytical results of the NSAF set the regularisation parameter set to zero or present only steady-state mean-square error performance of the regularised NSAF (-NSAF). This study presents a mean-square performance analysis of -NSAF, which analyses not only convergence behaviour but also steady-state behaviour. Furthermore, a novel adaptive regularisation for NSAF (AR-NSAF) is also developed based on the proposed analysis approach. The proposed AR-NSAF selects the optimal regularisation parameter that leads to improving the performance of the adaptive filter. Simulation results comparing the proposed analytical results with the results achieved from the simulation are presented. In addition, these results verify that the proposed AR-NSAF outperforms the previous algorithms in a system-identification and acoustic echo-cancellation scenarios.

Finger texture (FT) images acquired from different spectral lighting sensors reveal various features. This inspires the idea of establishing a recognition model between FT features collected using two different spectral lighting forms to provide high recognition performance. This can be implemented by establishing an efficient feature extraction and effective classifier, which can be applied to different FT patterns. So, an effective feature extraction method called the surrounded patterns code (SPC) is adopted. This method can collect the surrounded patterns around the main FT features. It is believed that these patterns are robust and valuable. Furthermore, a novel classifier termed the re-enforced probabilistic neural network (RPNN) is proposed. It enhances the capability of the standard PNN and provides better recognition performance. Two types of FT images from the multi-spectral Chinese Academy of Sciences Institute of Automation (CASIA) database were employed as two types of spectral sensors were used in the acquiring device: the white (WHT) light and spectral 460 nm of blue (BLU) light. Supporting comparisons were performed, analysed and discussed. The best results were recorded for the SPC by enhancing the equal error rates at 4% for spectral BLU and 2% for spectral WHT. These percentages have been reduced to 0% after utilising the RPNN.

Separating signal from unwanted noise is a major problem when analysing biomedical data, such as electrocardiography. Electrocardiogram (ECG) data are typically a mixture of real signal and various sources of noise, including baseline wander, power line interference, and electromagnetic interference. Since ECG signals are non-stationary physiological signals, the wavelet transform has been proposed to be an effective tool for eliminating unwanted noise from the ECG data. Here, the authors proposed a new noise reduction method for ECG data based on the discrete wavelet transform and hidden Markov model. They performed Monte Carlo simulations to compare the performance of this new method with seven other well-known denoising techniques.

This study proposes a heuristic approach for designing highly efficient, infinite impulse response (IIR) type Digital First-Order Differentiator (DFOD) by employing a nature-inspired evolutionary algorithm called Moth-Flame Optimisation (MFO) for the detection of the QRS complexes in the electrocardiogram (ECG) signal. The designed DFOD is used in the pre-processing stage of the proposed QRS complex detector, to generate feature signals corresponding to each R-peak by efficiently differentiating the ECG signal. The generated feature signal is employed to detect the precise instants of the R-peaks by using a Hilbert transform-based R-peak detection logic. The performance efficiency of the proposed QRS complex detector is evaluated by using all the first channel records of the MIT/BIH arrhythmia database (MBDB), regarding the standard performance evaluation metrics. The proposed approach has resulted in Sensitivity (Se) of 99.93%, Positive Predictivity (PP) of 99.92%, Detection Error Rate (DER) of 0.15%, and QRS Detection Rate (QDR) of 99.92%. Performance comparison with the recent works justifies the superiority of the proposed approach.

This work analyses the discrete solution of Hughes-Hartogs (HH) for the transmission rate maximisation problem with power constraint in the orthogonal frequency division multiplexing access (OFDMA) systems and explores mechanisms to reduce the computational complexity of greedy algorithms. In addition to the solution characterisation, a computational complexity analysis is developed, considering the number of executed operations for running time purpose. Moreover, the authors have compared the system capacity via the throughput obtained with the HH solution, and its variants combined with three complexity reduction mechanisms. These tools consist of an initial allocation bit vector calculated by rounding the results of the water-filling (WF) solution, the multiple subchannels per iteration updating and the adoption of a subchannel grouping procedure. Their findings indicate that the update of multiple subchannels and the subcarriers grouping techniques reduce the number of iterations required for convergence of the original HH, with some throughput degradation. Also, the bit-allocation mechanism based on the WF is deployed as an alternative to overcome the HH solution, increasing the computational complexity.

The mainlobe interference is a noticeable issue in the passive bistatic radar (PBR). Because the direction of arrival of interference is close to the target echo, the mainlobe interference can hardly be suppressed effectively by the conventional method. The mainlobe interference will mask the low-level targets of interest, and the blind area of detection will be formed in the direction of the interference source. The mainlobe interference signals, which come from the unrelated transmitters can be assumed to be mutually independent on the statistics. In this study, the method based on the independent component analysis (ICA) is proposed to suppress the mainlobe interference. The method exploits the principal components analysis to extract the mainlobe interference components which are whitened and compressed. Then, the ICA based on the negentropy is applied to separate the mainlobe interference components for the samples in the time domain. The mainlobe interference can be suppressed by the extensive cancellation algorithm with the separated interference sample as the reference. The proposed method based on the ICA is able to suppress the multiple mainlobe interferences and improve the performance of detection in the PBR. The simulation results prove the feasibility of the method proposed in this study.