Sparse Basis Research Articles

Multi-lead ECG Compression Based on Compressive Sensing

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.

Mixed Compressive Sensing Back-Projection for SAR Focusing on Geocoded Grid

This article presents a new scheme called 2-D mixed compressive sensing back-projection (CS-BP-2D), for synthetic aperture radar (SAR) imaging on a geocoded grid, in a single measurement vector frame. The back-projection linear operator is derived in matrix form and a patched-based approach is proposed for reducing the dimensions of the dictionary. Spatial compressibility of the radar image is exploited by constructing the sparsity basis using the back-projection focusing framework and fast solving the reconstruction problem through the orthogonal matching pursuit algorithm. An artifact reduction filter inspired by the synthetic point spread function is used in postprocessing. The results are validated for simulated and real-world SAR data. Sentinel-1 C-band raw data in both monostatic and space-borne transmitter/stationary receiver bistatic configurations are tested. We show that CS-BP-2D can focus both monostatic and bistatic SAR images, using fewer measurements than the classical approach, while preserving the amplitude, the phase, and the position of the targets. Furthermore, the SAR image quality is enhanced and also the storage burden is reduced by storing only the recovered complex-valued points and their corresponding locations.

Research on compressive sensing of strong earthquake signals for earthquake early warning

Earthquake early warning is an effective method to reduce casualties and losses. Based on the theory of compressive sensing, this paper proposes a strong earthquake signal processing architecture based on compressive sensing for difficulties of the acquisition, transmission and storage of massive strong earthquake data that the large-scale earthquake warning systems faced. Based on this, the observation vector of strong earthquake signal can be obtained with a predetermined compression ratio and used for transmission and storage. When necessary, the observation value is reconstructed to restore the original strong earthquake signal with a high probability. The paper analyzes the selection of sparse basis and observation matrix, discusses the reconstruction algorithms, base pursuit (BP) and orthogonal matching pursuit (OMP), and verifies the feasibility of the whole framework from compressed sampling to data reconstruction through experiments. The proposed framework has brought great convenience to the sampling, transmission, storage, and processing of the earthquake early warning system. It is foreseeable that replacing the traditional Nyquist sampling value with the observation values in the compressive sensing theory will cause a fundamental change in the signal characteristics, which will further affect the theory and technical system of the entire earthquake early warning system.

Non-Negative Sparse PCA: An Intelligible Exact Approach

An iterative method for the computation of a non-negative sparse principal component basis is presented. The iterative nature of the proposed method enables online learning, useful for time-evolving data, such as stock price time series. This way, the computation of the covariance matrix is avoided whenever new data become available. Due to the non-negative constraints explicitly enforced, the extracted eigenvectors turn to be sparse without employing any sparsity controlling parameter. Accordingly, only one parameter has to be tuned, i.e., the learning rate. Also, the complexity of the method under study is approximately linear under plausible assumptions. To assess the method’s performance, comprehensive experimental evaluation is conducted on both image and financial data. The proposed method is thoroughly compared to state-of-the-art and yields promising experimental findings.

High Dimensional Channel Estimation Using Deep Generative Networks

This paper presents a novel compressed sensing (CS) approach to high dimensional wireless channel estimation by optimizing the input to a deep generative network. Channel estimation using generative networks relies on the assumption that the reconstructed channel lies in the range of a generative model. Channel reconstruction using generative priors outperforms conventional CS techniques and requires fewer pilots. It also eliminates the need of a priori knowledge of the sparsifying basis, instead using the structure captured by the deep generative model as a prior. Using this prior, we also perform channel estimation from one-bit quantized pilot measurements, and propose a novel optimization objective function that attempts to maximize the correlation between the received signal and the generator's channel estimate while minimizing the rank of the channel estimate. Our approach significantly outperforms sparse signal recovery methods such as Orthogonal Matching Pursuit (OMP) and Approximate Message Passing (AMP) algorithms such as EM-GM-AMP for narrowband mmWave channel reconstruction, and its execution time is not noticeably affected by the increase in the number of received pilot symbols.

Wireless Transmission Method for Large Data Based on Hierarchical Compressed Sensing and Sparse Decomposition.

With the widespread application of wireless sensor networks, large-scale systems with high sampling rates are becoming more and more common. The amount of original data generated by the wireless sensor network is very large, and transmitting all the original data back to the host wastes network bandwidth and energy. This paper proposes a wireless transmission method for large data based on hierarchical compressed sensing and sparse decomposition. This method includes a hierarchical signal decomposition method based on the same sparse basis and different sparse basis hierarchical compressed sensing method with a mask. Compared with the traditional compressed sensing method, this method reduces the error of signal reconstruction, reduces the amount of calculation during signal reconstruction, and reduces the occupation of hardware resources. We designed comparison experiments between the traditional compressed sensing algorithm and the method proposed in this article. In addition, the experiments’ results prove that our proposed method reduces the execution time, as well as the reconstruction error, compared with the traditional compressed sensing algorithm, and it can achieve better reconstruction at a relatively low compression ratio.

A New Approach for Transformation-Based Fuzzy Rule Interpolation

Fuzzy rule interpolation (FRI) is of particular significance for reasoning in the presence of insufficient knowledge or sparse rule bases. As one of the most popular FRI methods, transformation-based fuzzy rule interpolation (TFRI) works by constructing an intermediate fuzzy rule, followed by running scale and move transformations. The process of intermediate rule construction selects a user-defined number of rules closest to an observation that does not match any existing rule, using a distance metric. It relies upon heuristically computed weights to assess the contribution of individual selected rules. This process requires a move operation in an effort to force the intermediate rule to overlap with an unmatched observation, regardless of what rules are selected and how much contribution they may each make. It is, therefore, desirable to avoid this problem and also to improve the automation of rule interpolation without resorting to the user's intervention for fixing the number of closest rules. This article proposes such a novel approach to selecting a subset of rules from the sparse rule base with an embedded rule weighting scheme for the automatic assembling of the intermediate rule. Systematic comparative experimental results are provided on a range of benchmark datasets to demonstrate statistically significant improvement in the performance achieved by the proposed approach over that obtainable using conventional TFRI.

Spectrum sensing of wideband signals based on cyclostationary and compressive sensing

Compressive sensing is a powerful technique used to overcome the problem of high sampling rate when dealing with wideband signal spectrum sensing which leads to high speed analogue to digital convertor (ADC) accompanied with large hardware complexity, high processing time, long duration of signal spectrum acquisition and high consumption power. Cyclostationary based detection with compressive technique will be studied and discussed in this paper. To perform the compressive sensing technique, Discrete Cosine Transform (DCT) is used as sparse representation basis of received signal and Gaussian random matrix as a sensing matrix, and then 𝓁1- norm recovery algorithm is used to recover the original signal. This signal is used with cyclostationary detector. The probability of detection as a function of SNR with several compression ratio and processing time versus compression ratio are used as performance parameters. The effect of the recovery error of reconstruction algorithm is presented as a function of probability of detection.

Sparsity Learning-Based CSI Feedback for FDD Massive MIMO Systems

In frequency-division duplexing mode, accurate channel state information (CSI) needs to be acquired at the base station by feedback from the terminals. However, the costly feedback overhead generated by large-scale arrays poses an arduous challenge to the traditional feedback scheme. In this letter, we propose a sparse learning-based CSI feedback method in a compressive sensing framework for massive MIMO systems. The key insights are to learn the sparse structure of CSI through the recursive least squares algorithm and process a continuous update of the sparse basis. Accordingly, a CSI sparse characteristic adaptive dictionary is constructed. The simulation results reveal that the proposed scheme achieves excellent performance in terms of both compression efficacy and recovery accuracy.

Posterior Information-Based Image Measurement Matrix Optimization

In order to enhance the robustness of image compression sensing system and reduce the mutual coherence between measurement matrix and sparse basis, this paper proposes an image measurement matrix optimization algorithm based on posterior information. Based on the traditional measurement matrix optimization model, the proposed algorithm considers the image reconstruction error from the OMP algorithm and uses it as a regular term. Matrix F-norm expansion and singular value decomposition are used to reduce the computational complexity and ensure the convergence of algorithm. Besides, the gradient matrix method is used to iteratively solve the measurement matrix. The proposed measurement matrix optimization model makes full use of the reconstruction error information of the image itself, not only improves the robustness of image compression sensing system, but also reduces the mutual coherence between the measurement matrix and the sparse basis. Experiments results show that compared with the state-of-the-art measurement matrix optimization algorithms, the proposed algorithm can reduce the average correlation coefficient more effectively, and the peak signal-to-noise ratio of the image can be increased by up to 1.2 dB.

Enhanced Tensor Completion Based Approaches for State Estimation in Distribution Systems

Grid state estimation is essential for effective control and management of distribution systems. While weighted least squares has been the conventional method for state estimation, sparsity-aware methods have become popular due to their superior performance with limited data. Matrix completion and compressed sensing-based state estimation approaches exploit the underlying smoothness in the state variables. However, classic matrix completion methods do not take into account the temporal correlation of system states. Compressed sensing methods, on the other hand, require an appropriate choice of sparsifying basis that may not be easy to identify. This article proposes a block tensor completion based framework which uses an alternative approach to estimate voltage phasor, power injections, and branch currents. This approach utilizes the temporal correlation of the system states in a tensor trace-norm minimization formulation with power flow equations as constraints. Feature scaling is introduced in the problem formulation to benefit from the improved sensitivity of the tensor trace norm to the matrix columns in the scaled unfoldings of the tensor. Weighted tensor norm is utilized to exploit the structures of the different unfoldings of the state measurement tensor to improve the voltage estimation. The estimation accuracy is further improved by alternatively estimating the tensor columns and increasing the available data at each stage in the tensor completion process. The proposed methods are evaluated on the IEEE-33, 37 test systems, and a 100-node test system. The proposed methods are shown to provide significant performance gains relative to the classic matrix and tensor completion based approaches.

SPECTRUM SENSING OF WIDE BAND SIGNALS BASED ON ENERGY DETECTION WITH COMPRESSIVE SENSING

Compressive sensing (CS) technique is used to solve the problem of high sampling rate with wide band signal spectrum sensing where high speed analogue to digital converter is needed to do that. This leads to difficult hardware implementation, large time of sensing and detection with high consumptions power. The proposed approach combines energy-based detection, with CS compressive sensing and investigates the probability of detection, and the probability of false alarm as a function of the SNR, showing the effect of compression to spectrum sensing performance of cognitive radio system. The Discrete Cosine Transform (DCT) is used as a sparse representation basis of the received signal, and random matrix as a compressive matrix.

Image Compressive Sensing via Hybrid Nonlocal Sparsity Regularization.

This paper focuses on image compressive sensing (CS). As the intrinsic properties of natural images, nonlocal self-similarity and sparse representation have been widely used in various image processing tasks. Most existing image CS methods apply either self-adaptive dictionary (e.g., principle component analysis (PCA) dictionary and singular value decomposition (SVD) dictionary) or fixed dictionary (e.g., discrete cosine transform (DCT), discrete wavelet transform (DWT), and Curvelet) as the sparse basis, while single dictionary could not fully explore the sparsity of images. In this paper, a Hybrid NonLocal Sparsity Regularization (HNLSR) is developed and applied to image compressive sensing. The proposed HNLSR measures nonlocal sparsity in 2D and 3D transform domain simultaneously, and both self-adaptive singular value decomposition (SVD) dictionary and fixed 3D transform are utilized. We use an efficient alternating minimization method to solve the optimization problem. Experimental results demonstrate that the proposed method outperforms existing methods in both objective evaluation and visual quality.

A Multi-Scale Compressed Sensing Algorithm Based on Variational Mode

The compressed sensing algorithm based on the hybrid sparse base (TFWBST+wave atom) usually uses two kinds of image sparse transformations to realize the sparse representation of structure and texture respectively. However, due to the lack of constraints on image texture and structure and the lack of orthogonality of the two sparse bases, the sparse coefficient of structure and the sparse coefficient of texture after transformation are often not good enough to reflect their respective components, that is, the texture coefficient often loses the detail information of texture. To overcome this phenomenon, this paper combines the compressed sensing algorithm based on hybrid base with the layered variational image decomposition method to form the variational multi-scale compressed sensing, which is to establish the CS image reconstruction model with minimal energy functional. The layered variational image decomposition decomposes image into different feature components by minimizing energy functional. The reconstruction of each layer by compressed sensing algorithm is very suitable for texture and detail reconstruction. In this model, TFWBST transform and wave atom are combined as a joint sparse dictionary, and the image decomposition is carried out under the (BV, G, E) variational framework, which is introduced into multi-scale compressed sensing technology to reconstruct the original image. In this new functional, TFWBST transform and wave atom are used to represent structure and texture respectively, and multiscale (BV, G, E) decomposition which can decompose an image into a sequence of image structure, texture and noise is added for restricting image parts. Experiments show that the new model is very robust for noise, and that can keep edges and textures stably than other multi-scale restoration and reconstruction of images.

Hyperspectral polarization-compressed imaging and reconstruction with sparse basis optimized by particle swarm optimization

Hyperspectral polarized images are widely used in target detection, and compressive sensing has been developed to shorten the acquisition time and reduce the memory usage. However, the current systems have defects in measuring the polarization information, and current sparse bases meet problems in reconstructing process. This paper combines compressive sensing and machine learning to obtain polarized images. Both the simpler system and the sparse basis optimizing method are developed. Liquid crystal tunable filter (LCTF) serves as both hyperspectral filter and linear polarizer. The LCTF compresses the first three Stokes parameters by changing the transmission axis angle of its incident surface. The LCTF and quarter-wave plate (QWP) compress all four Stokes parameters by changing the fast axis angle of QWP. Then, the Stokes parameters can be reconstructed based on the sparse basis optimized by particle swarm optimization (PSO) algorithm. The sparse basis optimized through the spatially local images of a target in one spectral band also works for both global images of this target in many other spectral bands and images of other targets.

Sparse aperture bistatic ISAR imaging under low signal-to-noise ratio condition

A sparse representation-based bistatic inverse synthetic aperture radar (ISAR) imaging method can achieve a high-resolution image of a target with sparse aperture data. However, the bistatic ISAR system is more sensitive to noise than the monostatic one because of its nonmirror reflection geometry. To overcome this drawback, we propose the sparse aperture bistatic ISAR imaging method based on joint sparse model. Considering the joint sparse information of bistatic ISAR echo, a joint sparse imaging model is constructed. Then, the dechirped sparse aperture bistatic ISAR echo after translational compensation is transformed into range fast time and azimuth slow time domains by the joint sparse imaging model, and a corresponding azimuth sparse basis is constructed. Then a joint sparse complex approximate message passing algorithm is proposed to joint sparse imaging model. The joint sparse imaging problem is converted to a block sparse imaging problem by vectorization. Using the relationship between the vectorization of the matrix and the Kronecker product, a matrix iteration structure is proposed to solve the joint sparse model efficiently and accurately. The experimental results based on both scattering point model and electromagnetic calculation model data verify the effectiveness of the proposed imaging method.

Simultaneous coded aperture and dictionary optimization in compressive spectral imaging via coherence minimization.

Coded aperture snapshot spectral imaging (CASSI) reconstructs a hyperspectral image from several two-dimensional (2D) projections via compressive sensing. The reconstruction quality and the sampling efficiency of CASSI can be effectively improved by decreasing the coherence of the underlying sensing matrix. Efforts have been made to minimize the coherence with individual optimization on coded aperture or sparse basis. In this paper, a simultaneous optimization on the system projection and the over-complete dictionary is introduced to minimize the Frobenius norm coherence. The dual-disperser structure and the RGB image sensor are adopted for the lowest coherence in terms of system configuration. The coded aperture and the dictionary are optimized with genetic algorithm and gradient descent respectively, and simultaneous optimization is conducted iteratively. Low coherence of sensing matrix is acquired after the simultaneous optimization, with both reconstruction quality and sampling efficiency significantly improved. Compared to the non-optimized system and state-of-the-art systems with individually optimized coded aperture or dictionary, the simultaneous optimization promotes the peak signal-to-noise ratio by more than 5dB. The coherence minimization via simultaneous optimization on the system matrix and the sparse representation basis may open opportunities for further development of other compressive-sensing-based computational imaging systems.

Single-pixel compressive imaging based on random DoG filtering

As its name implies, compressive sensing aims to bring compression during sampling. However, the deployment of this technique depends on recovering a high fidelity image through a low number of measurements with a simple hardware and fast software. To this end, we introduce an encoding scheme that by filtering the scene acquires information about the image structure. To prepare a set of proposed encoding patterns, at the first step, a filter bank containing a number of Difference of Gaussian (DoG) kernels with different scales is prepared. Then, by randomly selecting the filters from the bank and under-sampling the scene with them at random points, each encoding pattern is constructed. The idea is inspired by the Human Visual System (HVS) that uses a set of size-tuned DoG kernels at each point in the field-of-view. These encoding patterns, which make a set of linearly independent vectors, form the rows of a structured measurement matrix. This matrix allows making relatively well-conditioned dictionaries by different sparsifying bases. The effectiveness of this method is confirmed by simulations and analyses.

Nested Sparse Successive Galerkin Approximation for Nonlinear Optimal Control Problems

Solving the Hamilton-Jacobi-Bellman (HJB) equation for nonlinear optimal control problems usually suffers from the so-called curse of dimensionality. In this letter, a nested sparse successive Galerkin method is presented for HJB equations, and the computational cost only grows polynomially with the dimension. Based on successive approximation techniques, the nonlinear HJB partial differential equation (PDE) is transformed into a sequence of linear PDEs. Then the nested sparse grid methods are employed to solve the resultant linear PDEs. The designed method is sparse in two aspects. Firstly, the solution of the linear PDE is constructed based on sparse combinations of nested basis functions. Secondly, the multi-dimensional integrals in the Galerkin method are efficiently calculated using nested sparse grid quadrature rules. Once the successive approximation process is finished, the optimal controller can be analytically given based on the sparse basis functions and coefficients. Numerical results also demonstrate the accuracy and efficiency of the designed nested sparse successive Galerkin method.

Trends in Compressive Sensing for EEG Signal Processing Applications.

The tremendous progress of big data acquisition and processing in the field of neural engineering has enabled a better understanding of the patient’s brain disorders with their neural rehabilitation, restoration, detection, and diagnosis. An integration of compressive sensing (CS) and neural engineering emerges as a new research area, aiming to deal with a large volume of neurological data for fast speed, long-term, and energy-saving purposes. Furthermore, electroencephalography (EEG) signals for brain–computer interfaces (BCIs) have shown to be very promising, with diverse neuroscience applications. In this review, we focused on EEG-based approaches which have benefited from CS in achieving fast and energy-saving solutions. In particular, we examine the current practices, scientific opportunities, and challenges of CS in the growing field of BCIs. We emphasized on summarizing major CS reconstruction algorithms, the sparse basis, and the measurement matrix used in CS to process the EEG signal. This literature review suggests that the selection of a suitable reconstruction algorithm, sparse basis, and measurement matrix can help to improve the performance of current CS-based EEG studies. In this paper, we also aim at providing an overview of the reconstruction free CS approach and the related literature in the field. Finally, we discuss the opportunities and challenges that arise from pushing the integration of the CS framework for BCI applications.