Over-complete Dictionary Matrix Research Articles

Complex sparse Bayesian learning for guided wave dispersion curve estimation in plate-like structures

This paper proposes a new dispersion curve estimation method that employs the complex sparse Bayesian learning (CSBL). It is well accepted that guided wave packets are distorted because of the differences in propagation velocities at different frequencies; thus, the preceding velocity–frequency curve estimation is beneficial for wave packet recovery, feature recognition and defect localization. Conventional dispersion curve estimation methods, such as two-dimensional Fourier transform and multiple signal classification, are suitable for array signal and are restricted by the transducer aperture, leading to a small application scope. According to the frequency–response model of the guided wave, for each frequency, the responses obtained by the transducers can be sparsely represented based on an overcomplete dictionary matrix constructed using multiple discretized wavenumbers and known distances. A CSBL algorithm was developed to infer the posterior probability density function of the weight vector in the sparse representation. The non-zero elements in the sparse weight vector mean that the corresponding dictionary atoms indicated wavenumbers are contained in the frequency response, and the velocity–frequency curve can be finally derived from the wavenumber–frequency curve. The proposed CSBL method has a satisfactory capability to solve this sparse representation of the complex frequency response because a hierarchical form of the Laplace prior is employed to achieve a high degree of sparsity of the weight vector. This method effectively incorporates the real and imaginary parts of the complex frequency response by employing the same hyperparameter to integrate the known information. This method requires only a few randomly placed transducers; thus, it has a wide range of applications. The effectiveness of the proposed approach was validated using multiple guided-wave signals obtained through numerical simulations and an experimental study on a plate structure.

Smart meter data transmission based on compressed sensing

To achieve high-precision load recognition for residential electricity consumption and to solve the transmission problem of collecting large amounts of current data from household appliances by smart meters, a data transmission method based on compressed sensing is proposed to reduce data transmission costs. Firstly, a dictionary learning algorithm is used to sparsely represent the current data of household appliances, and the over-complete dictionary matrix is used as the sparse matrix; then a random Gaussian matrix is used as the measurement matrix for data transmission, and finally, regular orthogonal matching pursuit algorithm is used to complete the data reconstruction. The experimental results show that the reconstruction effect of this method is better than the traditional reconstruction method under the same compression ratio.

Time-Delay Estimation by Enhanced Orthogonal Matching Pursuit Method for Thin Asphalt Pavement With Similar Permittivity

Time-delay estimation (TDE) for thin top layers of asphalt pavement is a challenging task due to the limited resolution of ground penetrating radar (GPR) as well as small permittivity difference between top layers. Echoes backscattered from the interfaces of top layers with similar permittivity have usually much smaller amplitudes compared with other echoes, which can be called weak signals. The weak backscattered echoes are usually too sensitive to the noise and other strong echoes that current signal processing approaches (subspace-based methods and compressed sensing based methods) might have false estimation results even failures without proper processing of them. Therefore, in this paper, an enhanced orthogonal matching pursuit (OMP) method is proposed to deal with weak signals resulting from similar permittivity of adjacent asphalt layers. Based on the orthogonality between signal and noise subspaces, we firstly apply the truncated singular value decomposition (SVD) on the received signals, in order to reduce the noise impact. Secondly, we build an orthogonal matrix to the mode matrix of the pre-estimated strong backscattered echoes, and map it to the overcomplete dictionary matrix, such that the influence of the residual of the strong backscattered echoes can be reduced. Finally, the time-delays of backscattered echoes and layer thicknesses are estimated. Compared with conventional approaches, the proposed method is more suitable for TDE in thin asphalt pavement detection. The accuracy of the proposed method is validated by both numerical and experimental data.

Super‐resolution forward‐looking imaging method for manoeuvering platform with optimised dictionary and extended sparsity adaptive matching pursuit

In forward-looking imaging, left-right Doppler is ambiguous and cross-range resolution is limited by real aperture, which result in traditional synthetic aperture radar imaging methods no longer applicable. Besides, the impact of three-dimensional acceleration on an over-complete dictionary matrix and sparse reconstruction kernel is not considered in conventional super-resolution forward-looking imaging methods. To solve these problems, a super-resolution forward-looking imaging method for manoeuvering platforms is proposed. First, the range walk caused by forward-looking geometry and higher-order phase introduced by three-dimensional acceleration are eliminated by compensating a pre-processing function. Subsequently, according to beam steering-based geometry and linear regression model, the over-complete dictionary matrix is optimised to more accurately describe the complicated forward-looking geometry with curved trajectory. Finally, sparsity adaptive matching pursuit kernel with an improved halting condition is adopted to reconstruct the forward-looking scene. The proposed method is supported by point target simulation and surface target simulation.

AFP-SRC: identification of antifreeze proteins using sparse representation classifier

Species living in the extreme cold environment fight against the harsh conditions using antifreeze proteins (AFPs), which manipulate the freezing mechanism of water in more than one way. This amazing nature of AFPs turns out to be extremely useful in several industrial and medical applications. The lack of similarity in their structure and sequence makes their prediction an arduous task, and identifying them experimentally in the wet laboratory is time-consuming and expensive. In this research, we propose a computational framework for the prediction of AFPs, which is essentially based on a sample-specific classification method using sparse reconstruction. A linear model and an over-complete dictionary matrix (ODM) of known AFPs are used to predict a sparse class-label vector that provides a sample-association score. Delta rule is applied for the reconstruction of two pseudo-samples using lower and upper parts of the sample-association vector and based on the minimum recovery score, class labels are assigned. We compare our approach with contemporary methods on a standard dataset. The proposed method outperforms the contemporary methods in terms of balanced accuracy and Youden’s index. The MATLAB implementation of the proposed method is available at the author’s GitHub page ( https://github.com/Shujaat123/AFP-SRC ).

A Dictionary Optimization Method for Reconstruction of ECG Signals after Compressed Sensing.

This paper presents a new approach for the optimization of a dictionary used in ECG signal compression and reconstruction systems, based on Compressed Sensing (CS). Alternatively to fully data driven methods, which learn the dictionary from the training data, the proposed approach uses an over complete wavelet dictionary, which is then reduced by means of a training phase. Moreover, the alignment of the frames according to the position of the R-peak is proposed, such that the dictionary optimization can exploit the different scaling features of the ECG waves. Therefore, at first, a training phase is performed in order to optimize the overcomplete dictionary matrix by reducing its number of columns. Then, the optimized matrix is used in combination with a dynamic sensing matrix to compress and reconstruct the ECG waveform. In this paper, the mathematical formulation of the patient-specific optimization is presented and three optimization algorithms have been evaluated. For each of them, an experimental tuning of the convergence parameter is carried out, in order to ensure that the algorithm can work in its most suitable conditions. The performance of each considered algorithm is evaluated by assessing the Percentage of Root-mean-squared Difference (PRD) and compared with the state of the art techniques. The obtained experimental results demonstrate that: (i) the utilization of an optimized dictionary matrix allows a better performance to be reached in the reconstruction quality of the ECG signals when compared with other methods, (ii) the regularization parameters of the optimization algorithms should be properly tuned to achieve the best reconstruction results, and (iii) the Multiple Orthogonal Matching Pursuit (M-OMP) algorithm is the better suited algorithm among those examined.

Data-Driven Human Modeling by Sparse Representation

Data-driven methods for modeling the realistic shapeof 3D human bodies need to access datasets that contain a large amount of 3D human models. We develop a method based on sparse representation in this paper to represent 3D human models as signals of patches. Unlike the general mesh compression approaches, all mesh models used in a data-driven human modeling framework have the same mesh connectivity. By using this property, we segment a human model into patches containing the same number of vertices. L0-learning algorithm is selected to train an overcomplete dictionary matrix, which in turn introduces sparse representation of the dataset. Patch signals of individual human models can then be extracted by using the dictionary matrix. With the ease of balance control between sparsity and accuracy that is featured by the chosen learning algorithm, a representation with high compression ratio and low shape-approximation error can be determined. The results have been compared with the widely used statistic representation based on principal component analysis (PCA) to verify the effectiveness of our approach. Moreover, the method for using sparse representation in the regression-based statistical modeling of 3D human models has been presented at the end of the paper.

Analysis of brain functional connectivity network in MS patients constructed by modular structure of sparse weights from cognitive task-related fMRI.

Cognitive dysfunction in multiple sclerosis (MS) seems to be the result of neural disconnections, leading to a wide range of brain functional network alterations. It is assumed that the analysis of the topological structure of brain connectivity network can be used to assess cognitive impairments in MS disease. We aimed to identify these brain connectivity pattern alterations and detect the significant features for the distinction of MS patients from healthy controls (HC). In this regard, the importance of functional brain networks construction for better exhibition of changes, inducing the improved reflection of functional organization structure should be precisely considered. In this paper, we strove to introduce a framework for modeling the functional connectivity network by considering the two most important intrinsic sparse and modular structures of brain. For the proposed approach, we first derived group-wise sparse representation via learning a common over-complete dictionary matrix from the aggregated cognitive task-based functional magnetic resonance imaging (fMRI) data of all subjects of the two groups to be able to investigate between-group differences. We then applied the modularity concept on achieved sparse coefficients to compute the connectivity strength between the two brain regions. We examined the changes in network topological properties between relapsing-remitting MS (RRMS) and matched HC groups by considering the pairwise connections of regions of the resulted weighted networks and extracting graph-based measures. We found that the informative brain regions were related to their important connectivity weights, which could distinguish MS patients from the healthy controls. The experimental findings also proved the discrimination ability of the modularity measure among all the global features. In addition, we identified such local feature subsets as eigenvector centrality, eccentricity, node strength, and within-module degree, which significantly differed between the two groups. Moreover, these nodal graph measures have been served as the detectors of brain regions, affected by different cognitive deficits. In general, our findings illustrated that integration of sparse representation, modular structure, and pairwise connectivity strength in combination with the graph properties could help us with the early diagnosis of cognitive alterations in the case of MS.

A blind image deblurring algorithm based on relative gradient and sparse representation

A blind image deblurring algorithm based on relative gradient and sparse representation is proposed in this paper. The layered method restores the image by three steps: edge extraction, blur kernel estimation and image reconstruction. The positive and negative gradients in texture part have reversal changes, and the edge part that reflects the image structure has only one gradient change. According to the characteristic, the edge of the image is extracted by using the relative gradient of image, so as to estimate the blur kernel of the image. In the stage of image reconstruction, in order to overcome the problem of oversize of the image and the overcomplete dictionary matrix, the image is divided into small blocks. An overcomplete dictionary is used for sparse representation, and the image is reconstructed by the iterative threshold shrinkage method to improve the quality of image restoration. Experimental results show that the proposed method can effectively improve the quality of image restoration.

Compressed sensing method for human activity recognition using tri-axis accelerometer on mobile phone

The diversity in the phone placements of different mobile users' dailylife increases the difficulty of recognizing human activities by using mobile phone accelerometer data. To solve this problem, a compressed sensing method to recognize human activities that is based on compressed sensing theory and utilizes both raw mobile phone accelerometer data and phone placement information is proposed. First, an over-complete dictionary matrix is constructed using sufficient raw tri-axis acceleration data labeled with phone placement information. Then, the sparse coefficient is evaluated for the samples that need to be tested by resolving L1 minimization. Finally, residual values are calculated and the minimum value is selected as the indicator to obtain the recognition results. Experimental results show that this method can achieve a recognition accuracy reaching 89.86%, which is higher than that of a recognition method that does not adopt the phone placement information for the recognition process. The recognition accuracy of the proposed method is effective and satisfactory.

Antenna placement optimisation for compressed sensing‐based distributed MIMO radar

Since a better localisation performance is achieved by exploiting the spatial diversity in the distributed multiple-input and multiple-output (MIMO) radar systems, the authors consider the problem of further improving this performance by optimising the antenna placement in this study. In the localisation processes, a novel compressed sensing-based method is proposed to exploit the target sparsity, where an over-complete dictionary matrix containing all the possible echo waveforms from the discretised area is first established. In addition, to further improve the localisation performance, a novel iterative method is proposed to minimise the mutual coherence of the dictionary matrix by optimising the antenna placement of both transmitters and receivers. Moreover, the theoretical distribution of the mutual coherence is derived, and an asymptotic performance with increasing the number of antennas is also provided. Simulation results demonstrate the localisation performance improvement for multiple targets by optimising the antenna placement in the distributed MIMO radar.