Parameter retrieval of ocean internal waves from synthetic aperture radar (SAR) images is an important issue of oceanography; however, the extraction precision is usually limited by the complex waveforms and the noise. To improve the performance of parameter extraction, traditional methods usually focus on removing the noise on SAR images by exploiting its statistical character, but the structure character of ocean internal waves does not draw enough attentions to improve the image quality for parameter extraction. This study presents a local low-rank approach to extract the parameters robustly by associating the noise removing and parameter extraction together. An optimisation model is first developed by associating the speckle suppression and the exploration of the structural prior of internal wave, where the local low-rank prior is utilised. Also then, a numerical algorithm based on alternating optimisation scheme is designed to solve the proposed model. The proposed approach not only improves the extraction precision, but is also robust to the non-ideal cases such as the deformed waveforms. In experiments, both simulations and real data are used to demonstrate the efficiency and robustness of the proposed method.

This study proposes a computer cryptographic system through performing the chaotic modulation on the intrinsic mode functions with a non-dyadic number of the encrypted signals. First, the empirical mode decomposition is applied to an input signal to generate a set of intrinsic mode functions. Then, these intrinsic mode functions are categorised into two groups of signals. Next, a type 1 polyphase is employed to represent each group of signals. These polyphase components are combined to generate a non-dyadic number of polyphase components. Second, the chaotic modulation is applied to these combined polyphase components for performing the encryption in the time frequency domain. To reconstruct the original signal, first, the chaotic demodulation is applied to the encrypt components to reconstruct the combined polyphase components. Then, the original groups of intrinsic mode functions are reconstructed through the type 2 polyphase representation and the original signal is reconstructed. Compared with the chaotic filter bank system, the proposed approach enjoys the nonlinear and adaptive property of the empirical mode decomposition. Therefore, a better security performance can be achieved particularly for the non-stationary signals. Compared with the conventional chaotic modulation approach, the proposed system allows performing the cryptography in the time frequency domain.

Herein, inspired by the unscented particle filter (UPF), an improved particle filter (PF) using an unscented information filter based on M-estimate (UIF-BM) to approximate the importance density function (IDF) is designed. The filtering method is proposed to obtain an accurate state estimation for a non-linear discrete time dynamical system with non-Gaussian system noises and observation noises contaminated by some Gaussian impulsive noises. The PF framework is used as a common method to handle non-Gaussian system noises. In order to obtain a precise IDF, UIF based on M-estimate is used for heavy-tailed observation noises. Meanwhile, instead of the robust Gaussian filter, the robust IF can avoid the numerical problem that zero weight functions cannot be incorporated into the framework. The simulation results indicate the estimation accuracy and efficiency of the proposed filter. Compared with the UIF-BM, PF, and UPF, the superiority of the proposed filter against the non-ideal system and observation noises is obvious.

Classification is presented as a pre-processing step in this study. The state of the subject is classified as the unmoving state with normal breathing (normal breathing class), unmoving state with no breathing (stop breathing class) or the state when the subject is moving (erratic signal class) before breathing estimation algorithms are applied. Estimation algorithms may be applied to obtain breathing rate if normal breathing class is detected or alarms may be generated if stop breathing is detected, and fine-grained classification of activities may be pursued if the erratic signal is detected. Experiments were performed using a single-channel pulse-modulated continuous wave radar with three subjects for a total of 135 min. In each experiment, the subject was continuously monitored for 15 min and the subject performed activities that resulted in a signal that belonged to one of the three classes. Besides extracting a feature that assessed the distribution of energy of the signal in the frequency domain, a novel nonlinear time series feature extraction method based on the higher-dimensional embedding technique was applied to ascertain periodicity of the reflected signal. Bayes classifier was used to classify each 5-s segment of radar returns. A 30-fold cross validation resulted in 97% of overall classification accuracy.

The authors investigate the issue of direction of arrival (DOA) estimation in the presence of phase noise for multiple sources with a synthetic linear array, which is synthesised by a short moving array. The extended towed array measurements (ETAM) method can extend the array aperture greatly, but can only be applied to multiple coherent sources and requires the array to move with constant velocity. To tackle the problems, the authors generalise the ETAM method to multiple incoherent sources and array non-uniform motion case. The authors first formulate the manifold of the extended synthetic array (SA) moving with known velocity in a straight line. Then the initial DOA estimates and phase correction factors are estimated successively by two-dimensional multiple signal classification (2D-MUSIC) spectrum search using adjacent measurements sampled by the moving array. Moreover, to reduce the complexity, the authors also propose a reduced dimensional MUSIC (RD-MUSIC) method to turn the two-dimensional peak search to one-dimensional. As the array aperture is extended by proper compensation, the DOA estimation performance of the proposed SA method improves. Besides, the proposed method can resolve more number of sources than sensors since every two measurements are used for estimation in each process. Simulation results validate the effectiveness of the proposed method.

This study deals with the detection of unknown signals in white noise. The authors present a new detector, based on the difference of a deterministic function of the energy of the signal and the energy of the same signal, which has been filtered. Unlike usual energy detector (ED), the proposed detector consists in exploiting the behaviour of the energy of filtered white noise, which can be a priori determined since the used filter is known. Thus, if the measured energy differs from an expected value, the detector decides that a signal is present in the band. In order to have the same asymptotic complexity as ED, a simple two-tap filter is used. The theoretical expressions of the probabilities of detection and false alarm are developed, and the optimal threshold is deduced. Simulations show that the proposed detector achieves better performance than ED, in both additive white Gaussian noise and Rayleigh channels. Furthermore, the relevance of the analytical results is proved through simulations.

Multi-lead ECG compression (M-lEC) has attracted tremendous attention in long-term monitoring of the patient's heart behaviour. This study proposes a method denoted by block sparse M-lEC (BlS M-lEC) in order to exploit between-lead correlations to compress the signals in a more efficient way. This is due to the fact that multi-lead electrocardiography signals are multiple observations of the same source (heart) from different locations. Consequently, they have a high correlation in terms of the support set of their sparse models which leads them to share dominant common structure. In order to obtain the block sparse model, the collaborative version of lasso estimator is applied. In addition, it is shown that raised cosine kernel has advantages over conventional Gaussian and wavelet (Daubechies family) due to its specific properties. It is demonstrated that using raised cosine kernel in constructing the sparsifying basis matrix gives a sparser model which results in higher compression ratio and lower reconstruction error. The simulation results show the average improvement of 37, 88 and 90–97% for BlS M-lEC compared to the non-collaborative case with raised cosine kernel, Gaussian kernel and collaborative case with Daubechies wavelet kernels, respectively, in terms of reconstruction error while the compression ratio is considered fixed.

Very large scale integration architecture for the blocks in the novel algorithm with parallel processing is proposed. It increases the performance of the proposed coder. Since the mean is removed from electrocardiogram (ECG) signal it is represented by less number of bits. The lifting scheme-based Haar wavelet transform with five levels decomposition is used to decompose the mean removed ECG signal. One sub-band of approximation coefficient (A ₅) and five sub-bands of detailed coefficients (D ₅, D ₄, D ₃, D ₂ and D ₁) are obtained. Each sub-band is represented by the corresponding number of bits by using adaptive encoder. The converted bits are transmitted through the channel using a compact format. The coding efficiency shows that the proposed coder outperforms than other coders such as novel algorithm, Djohn, Alshamali, EZW, Benzid, Chan, Khaldi, Gurkan, Wang and Set Partitioning In Hierarchical Trees (SPIHT). The proposed coder is tested on the MIT-BIH arrhythmia database (48 records) and the MIT-BIH ECG compression test database (two records) and its performance is evaluated by using evaluation metrics such as compression ratio (CR) and per cent root mean square difference (PRD). For MIT-BIH arrhythmia database record 117, a CR of 9.132:1 is achieved by the proposed coder with PRD 1.2274%.

The authors construct the piecewise vibrational resonance (VR) method by introducing the piecewise idea and combine the re-scaled and twice sampling methods for the linear frequency modulated (LFM) signal. Importantly, they put forward a new spectral amplification factor to quantify the VR. The new spectral amplification factor has some advantages as compared with the cross-correlated coefficient, which can also be used to quantify the aperiodic VR. The top value of the spectrum amplification factor is the necessary and sufficient condition for the occurrence of the optimal VR phenomenon. Here, they discuss the effects of different parameters on VR by using some numerical examples. The method described in this study provides an effective way to improve the LFM signal, and even other kinds of frequency modulated signals.

This study proposes a direction-based similarity measure for trajectory clustering. The proposed description of the trajectory was based on extracting the direction changes in the segmented trajectories (sub-trajectories). The authors applied spectral clustering to segment a trajectory to several sub-trajectories. Then, trajectory descriptions were computed based on the direction change in different levels of resolution in terms of trajectory instances. To measure the similarity of trajectories, these segments were used as the input of Time Warp Matching method. Finally, the hierarchical clustering was applied to cluster similar trajectories. The direction-based description helps to achieve rotation and location invariance characteristics. Some experiments were performed to compare the proposed trajectory descriptor with similar approaches in the application of trajectory clustering. The empirical quality of the proposed similarity measure is evaluated on a clustering task. Compared to well-known similarity measures, the proposed method proved to be effective in the considered experiment.

Signal processing on graphs using adjacency matrix (as opposed to more traditional graph Laplacian) results in an algebraic framework for graph signals and shift invariant filters. This can be seen as an example of the algebraic signal processing theory. In this study, the authors examine the concepts of homomorphism and isomorphism between two graphs from a signal processing point of view and refer to them as GSP isomorphism and GSP homomorphism, respectively. Collectively, they refer to these concepts as structure preserving maps (SPMs). The fact that linear combination of signals and linear transforms on signals are meaningful operations has implications on the GSP isomorphism and GSP homomorphism, which diverges from the topological interpretations of the same concepts (i.e. graph isomorphism and graph homomorphism). When SPMs exist between two graphs, signals and filters can be mapped between them while preserving spectral properties. They examine conditions on adjacency matrices for such maps to exist. They also show that isospectral graphs form a special case of GSP isomorphism and that GSP isomorphism and GSP homomorphism is intrinsic to resampling and downsampling process.

Blind reconstruction of channel coding parameters plays a significant role in non-cooperative military and spectrum surveillance applications. Further, it also gives additional advantages in applications such as cognitive radio, adaptive modulation and coding, and so on. In this study, blind estimation algorithms are proposed to identify code dimension and codeword length parameters of low-density parity-check (LDPC) codes at the receiver over noisy or erroneous channel conditions assuming a non-cooperative scenario. The proposed algorithms are validated using different test cases. Moreover, the accuracy of estimation of code dimension and codeword length parameters of LDPC codes using the proposed algorithms is also given for different M-ary phase-shift keying schemes. From the simulation results, it is observed that the accuracy of estimation improves with decrease in code rate, codeword length, and modulation order.

This study proposes a block-sparse non-uniform norm constraint normalised subband adaptive filter (BS-NNCNSAF) for the block-sparse system identification problem, which is obtained by minimising a novel cost function involving the non-uniform mixed l _{2, p} norm like a constraint. It can achieve better performance compared with the existing algorithms in the block-sparse system identification. To further enhance the performance of the algorithm, the shrinkage BS-NNCNSAF (SH-BS-NNCNSAF) algorithm is proposed. The proposed SH-BS-NNCNSAF algorithm is derived by taking the priori and the posteriori subband errors to achieve the time-varying subband step sizes. Finally, simulations have been carried out to verify the performance of proposed algorithms. The simulation results verify that the proposed algorithms improve the performance of the filter, in terms of system identification in sparse systems.

In this study, a modification to the affine projection adaptive filtering algorithm is proposed which is based on a three-level clipping of the input signal as applied to the weight update process. This clipping operation causes the input signal to be quantised into three levels, namely, 0, 1, and −1. By doing so, the proposed scheme, in addition to reducing the computational complexity, achieves an error convergence performance that is comparable to, or even at times better than that of the conventional affine projection algorithm (APA) for a certain range of the clipping threshold. The proposed adaptive algorithm is compared with some low complexity variants of APA with respect to the convergence rate and computational complexity, and its superiority to its counterparts of the same order of complexity in terms of the convergence rate is demonstrated. The mean square error analysis based on the energy conservation relation and the stability analysis is also presented for the proposed clipped APA.

Optimal integer-order transfer function approximations to model the single fractance element-based fractional-order low-pass filter (FLF) for any arbitrary order α, where, 0 < α < 1, is proposed here. First of all, the integer-order filter coefficients for FLFs, with α varying from 0.01 to 0.99 in steps of 0.01, are directly obtained by using a metaheuristic algorithm called colliding bodies optimisation. For practical usability, the approximated FLF coefficients are explicitly provided in the form of analytical equations by employing a curve fitting on the optimised coefficients in the second step. The proposed approach provides a simpler design procedure in comparison to the reported literature which approximates the FLF by substituting an integer-order rational approximation of the s^α operator in the transfer function of the ideal FLF. Simulations confirm the superior modelling accuracy of the proposed design over the recent literature.