Multiple Measurement Vector Model Research Articles

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Wideband DOA Estimation Utilizing a Hierarchical Prior Based on Variational Bayesian Inference

The direction-of-arrival (DOA) estimation of wideband signals, based on sparse signal reconstruction, has recently been proposed, owing to its unique high-resolution performance. As a typical tool of sparse signal reconstruction, sparse Bayesian learning (SBL) enhances little sparsity in most works, leading to a non-robust local fitting. To significantly enhance sparsity, we proposed a novel hierarchical Bayesian prior framework, and deduced a novel iterative approach. It was discovered that the iterative approach had a lower computational complexity than the majority of current state-of-the-art algorithms. Besides, the proposed approach achieves a high angular estimation accuracy and sparsity performance, by utilizing the joint sparsity of the multiple measurement vector (MMV) models. Moreover, the approach stabilizes the estimated values between different frequencies or snapshots, so as to obtain a flat spatial spectrum. Extensive simulation results are presented, to demonstrate the superior performance of our method.

Mainlobe Interference Suppression for Radar Network via RPCA-Based Covariance Matrix Reconstruction

Radar networks can provide spatial diversity by observing targets from different perspectives with adequately separated receiving stations. This article proposes a mainlobe interference suppression approach for radar networks based on covariance matrix reconstruction. First, we formulate the mainlobe interference suppression under multiradar configuration as a multichannel signal enhancement problem and perform range and Doppler equalization to improve interferences’ spatial correlation. Then, we estimate the signal and interference covariance matrix from the sampling covariance matrix by solving a robust principal component analysis (RPCA) model. After that, we devise a time-domain-constrained (TDC) linear estimator dependent on the reconstructed covariance matrices to enhance target echo. To remove those duplicate false targets caused by signal enhancement and estimate the state of the physical targets, we establish and solve a generalized multiple measurement vector (GMMV) model based on the fact that targets have unique locations in the state space. Finally, we confirm the effectiveness of the proposed approach with numerical experiments and demonstrate better performance in comparison with the subspace projection method.

Channel estimation for underwater acoustic OFDM communications via temporal sparse Bayesian learning

Channel estimation is a challenging task for underwater acoustic (UWA) communications. In this paper, we investigate the channel estimation for OFDM based UWA communications by utilizing the channel characteristics as auxiliary information. Firstly, the channel estimation problem is formulated as a sparse signal recovery problem using block-wise single measurement vector (SMV) model and multiple measurement vector (MMV) model. Then we develop a novel channel estimators under the temporal sparse Bayesian learning (TSBL) framework by jointly exploiting the temporal correlation and sparsity based on the block-wise SMV model. For the MMV model, a variational Bayesian inference based TSBL (VBI-TSBL) method is introduced that considers the inter-block correlations and exploits the row-sparsity by a linear temporal correlation model. The two Bayesian inference methods realize the posterior and parameter estimation of channel via expectation maximization (EM) and variational EM algorithm, respectively. Simulation and sea-trial experiments show the proposed channel estimators outperform the benchmarks in terms of bit error rate, mean square error of channel estimation and the robustness.

Parallel Greedy Search for Random Access in Wireless Networks

We consider the random access problem in wireless networks such as cellular networks and massive machine type communication networks, where a large number of devices/users are connected to a base station. In order to establish communication with the base station, as a part of the random access procedure, active users select and transmit codes (pilot sequences) randomly from a codebook. Since the active users are typically a small fraction of the total users, sparse signal recovery algorithms are employed to detect the transmitted codes. In this paper, we use multiple measurement vector model for the received signal and develop a parallel greedy search algorithm and it’s stopping criteria to detect the active users. We show through simulations that the proposed scheme, compared with the existing greedy algorithms, gives better detection performance at lower false alarms levels. We study how the code length and the code word size need to be chosen in order to detect a given number of active users. We also address the scenario when there are different timing offsets for signals received from different users.

Super-resolution fluorescence blinking imaging using compressive sensing

Super-resolution optical fluctuation imaging (SOFI) is an extensively used super-resolution (SR) imaging technique. The sample condition and imaging system are simpler than most SR systems, and the cusp-artifacts limit the resolution of high-order SOFI. To improve the resolution of SOFI, an alternative method is to improve the reconstruction algorithm. Here, compressive sensing (CS) is used in SOFI to improve its resolution. The detailed CS reconstruction algorithm is chosen as multiple measurement vector model sparse Bayesian learning (MSBL). We demonstrate that MSBL can achieve higher than threefold resolution improvement in simulation under certain conditions. The SOFI experiment analysis demonstrates that MSBL can improve the resolution about 2.5-fold compared with the diffraction limit. All results prove that MSBL has a higher resolving ability compared with other algorithms. Our results prove that CS is a broad applicability tool for most of the existing SR microscopy techniques and can be applied in 3D and live-cell SR fluorescence microscopy imaging in the future.

Bayesian Learning-Based Multiuser Detection for Grant-Free NOMA Systems

Grant-Free Non-Orthogonal Multiple Access (GF-NOMA) is considered as a promising technology to support the massive connectivity of Machine-Type Communications (MTC). The design of efficient and high-performance multi-user detection (MUD) scheme is a challenging issue of GF-NOMA, especially when the number of active users is unknown and relatively high. This paper adopts Sparse Bayesian Learning (SBL) approaches to solve the MUD problem of GF-NOMA in MTC. The MUD problem within a certain access slot is formulated as a Single Measurement Vector (SMV) model and efficiently solved via SBL-based methods. To further improve the MUD performance, we set up a Multiple Measurement Vector (MMV) model and develop block SBL-based MUD methods, by exploiting the temporal correlation of user activity over successive access slots. Then to extend the usage of the aforementioned algorithms to the scenarios with relatively high, or quasi-sparse, user activity, we propose novel SBL-based MUD algorithms via post sparse error recovery methodology, for both the SMV and MMV problem models. Simulation results show that the proposed SBL-based MUD algorithms achieve substantial performance gain over traditional ones, especially when the number of active users is unknown and relatively high.

Multi-band inverse synthetic aperture radar fusion imaging based on multiple measurement vector model

The range resolution of inverse synthetic aperture radar (ISAR) imaging can be improved by directly increasing the bandwidth of the transmitted signal. However, it complicates the design of radar system hardware and increases the manufacturing cost. Aiming at solving the abovementioned problems, a multi-band ISAR fusion imaging method based on the multiple measurement vectors (MMV) model is proposed to improve the range resolution. First, a multi-band ISAR fusion imaging model based on the compressed sensing theory is established. Second, to improve the computational efficiency, a MMV accelerated improved linearized Bregman algorithm is proposed to solve the model. Nesterov’s acceleration gradient method and the condition number optimization of the sensing matrix are combined to further improve the iterative convergence speed. Finally, experimental results based on the simulation data and measured data verify the effectiveness and superiority of the proposed algorithm, which can achieve multi-band ISAR fusion imaging with higher imaging efficiency and better image quality.

Flat-field multiplexed multifocal structured illumination super-resolution microscopy

Multifocal structured illumination microscopy (MSIM) can achieve optically sectioned images with twice the diffraction limited resolution at an imaging speed of 1 Hz and an imaging depth of up to 50 μm. Compared with the traditional wide-field SIM, the MSIM has greater imaging depth and optical sectionning ability, and it is more suitable for long-term three-dimensional (3D) super-resolution imaging of living thick samples. However, the MSIM has some problems, such as slow imaging speed and complex image post-processing process. In this work, a fast super-resolution imaging method and system based on the flat-field multiplexed MSIM (FM-MSIM) is proposed. By inserting a beam shaping device into the illumination light path, the Gaussian beam is reshaped into a uniform flat-top profile, thereby improving the intensity uniformity of excitation multi-spot focal array and expanding the field of view. By elongating each diffraction limited excitation focal point four times along the <i>Y</i> direction to form a new multiplexed multifocal array pattern, the number of scanning steps is reduced, the energy utilization is improved, and then the imaging speed and signal-to-noise ratio are improved. Combined with the sparse Bayesian learning image reconstruction algorithm based on multiple measurement vector model, the image reconstruction steps are simplified, the imaging speed can be improved at least 4 times while ensuring the spatial resolution of MSIM. On this basis, the established FM-MSIM system is used to carry out the super-resolution imaging experiments on the BSC cell microtubule samples and mouse kidney slices. The experimental results prove the fast three-dimensional super-resolution imaging ability of the system, which is of great significance in developing the fast MSIM.

Approaching Sub-Nyquist Boundary: Optimized Compressed Spectrum Sensing Based on Multicoset Sampler for Multiband Signal

Compressed spectrum sensing naturally pursues the use of fewer sampling resources to achieve spectrum support reconstruction and signal recovery. The theoretical lower boundary of averaging sampling rate to recover the multiband signal has been proved to be twice the Landau rate. However, it is still unreachable in practice. Based on the multicoset sampling architecture, this paper analyzes the influencing factors on perfect spectrum reconstruction from three aspects: data model, sampling pattern and greedy reconstruction algorithms, for which practical and feasible optimization schemes are proposed. To reduce redundant reconstruction for the multiple measurement vectors (MMV) signal model, a block MMV model is proposed to improve the accuracy in the spectrum support set reconstruction process. A sampling pattern selection algorithm is proposed to ensure a higher success rate of the spectrum support reconstruction to optimize the sensing matrix. We also deduced the representation of the signal and noise energy in the reconstructed spectrum based on the mathematical model of compressed sensing. We thus proposed a non-orthogonal double-threshold matching pursuit algorithm to avoid a high false-alarm rate due to the manually set converging conditions for matching pursuit algorithms. Numerical experiments on real-world wideband signals are carried out to demonstrate the feasibility and advantages of the proposed approaches. With integrated optimization, the required sampling density to ensure perfect reconstruction is approaching the sub-Nyquist sampling boundary.

The MMV tail null space property and DOA estimations by tail-[formula omitted] minimization

The tail-minimization approach is applied to the joint sparse multiple measurement vector (MMV) model and direction of arrival (DOA) estimations. The mechanism is to estimate the support T of the jointly sparse matrix and minimize the energy in the complement Tc of T during each iteration. An MMV tail-null-space property (MMV-tail-NSP) is derived, which is shown to be necessary and sufficient for the unique solution of the MMV tail minimization problem. The MMV-tail-NSP condition is also shown to be more likely to hold than that of the conventional MMV-NSP for any given MMV basis pursuit problem. Two recovery guarantees and error bound analyses are also derived based on the MMV-robust-tail-NSP condition and merely the MMV-tail-NSP assumption, respectively. Study shows that the MMV tail-minimization approach is among the most effective techniques for the MMV DOA model. In particular, the MMV tail-minimization approach is able to recover signals of rank-enriched sparsity level K0≡[spark(A)−1+rank(X)]/2. In fact, this approach can handle signal recovery of greater sparsity levels than that by others. The advantages of the MMV tail-minimization approach are also reflected in numerous aspects such as handling low signal-to-noise ratio (SNR), limited number of snapshots, and correlated source signals. Results are more accurate with higher resolution as well. It is also capable of detecting the number of sources and estimating DOAs simultaneously. All these characteristics and advantages are fully evidenced by extensive simulation studies.

A Novel Downward-Looking Linear Array SAR Imaging Method Based on Multiple Measurement Vector Model with L 2 , 1 -Norm

Downward-looking linear array synthetic aperture radar (DLLA SAR) is a kind of three-dimensional (3-D) radar imaging system. To obtain the superresolution along the crosstrack direction of DLLA SAR, the sparse regularization models with single measurement vector (SMV) have been widely applied. However, the robustness of the sparse regularization models with SMV is unsatisfactory, especially in the low signal-to-noise rate (SNR) environment. To solve this problem, we proposed a novel imaging method for DLLA SAR based on the multiple measurement vector (MMV) model with L 2 , 1 -norm. At first, we exchange the processing order between the along-track (AT) domain and the crosstrack (CT) domain to keep the same sparse structure of the signal in the crosstrack domain so that we can establish the imaging problem as a sparse regularization model based on the MMV model. Moreover, the mixed L 2 , 1 -norm is introduced into the regularization term of the MMV model. Finally, the modified orthogonal matching pursuit (OMP) algorithm is designed for the MMV model with the L 2 , 1 -norm. The simulations verify that the proposed method has better performance in the lower SNR environment and requires lower computation compared with the conventional methods.

Clustering structure based multiple measurement vectors model and its algorithm

Most multi-measurement vector models are based on the ideal assumption of shared sparse structure. However, due to time varying and multiple focuses of complex data, it is often difficult to meet the assumption in reality. Therefore, people have been working hard to utilise various sparse structures to make up for the problem. In this paper, we take the clustering structure of signals into account and propose the Clustering Structure based Multiple Measurement Vectors (CS-MMV) model, which not only utilises clustering characteristic between coefficients but also considers clustering structure within coefficients. Furthermore, we extend a classic algorithm to implement the new model. Experiments on simulation data and two face benchmarks show that the new model is more suitable for complex data with clustered structure, and the extended algorithm can effectively improve the performance of sparse recovery.

Clustering structure based multiple measurement vectors model and its algorithm

Clustering structure based multiple measurement vectors model and its algorithm

Multiple Measurement Vector-Based Complex-Valued Multifrequency ECT

Complex-valued, multifrequency electrical capacitance tomography (CVMF-ECT) is a recently developed tomographic concept which is capable of simultaneously reconstructing spectral permittivity and conductivity properties of target objects within the region of interest. To date, this concept has been limited to simulation and another key issue restricting its wide adoption lies in its poor image quality. This letter reports a CVMF-ECT system to verify its practical feasibility and further proposes a novel image reconstruction framework to effectively and efficiently reconstruct multifrequency images using complex-valued capacitance data. The image reconstruction framework utilizes the inherent spatial correlations of the multifrequency images as a priori information and encodes it by using multiple measurement vector (MMV) model. Alternating direction method of multipliers was introduced to solve the MMV problem. Real-world experiments validate the feasibility of CVMF-ECT, and MMV-based CVMF-ECT method demonstrates superior performance compared with conventional ECT approaches.

Jointly Sparse Signal Recovery and Support Recovery via Deep Learning With Applications in MIMO-Based Grant-Free Random Access

In this article, we investigate jointly sparse signal recovery and jointly sparse support recovery in Multiple Measurement Vector (MMV) models for complex signals, which arise in many applications in communications and signal processing. Recent key applications include channel estimation and device activity detection in MIMO-based grant-free random access which is proposed to support massive machine-type communications (mMTC) for Internet of Things (IoT). Utilizing techniques in compressive sensing, optimization and deep learning, we propose two model-driven approaches, based on the standard auto-encoder structure for real numbers. One is to jointly design the common measurement matrix and jointly sparse signal recovery method, and the other aims to jointly design the common measurement matrix and jointly sparse support recovery method. The proposed model-driven approaches can effectively utilize features of sparsity patterns in designing common measurement matrices and adjusting model-driven decoders, and can greatly benefit from the underlying state-of-the-art recovery methods with theoretical guarantee. Hence, the obtained common measurement matrices and recovery methods can significantly outperform the underlying advanced recovery methods. We conduct extensive numerical results on channel estimation and device activity detection in MIMO-based grant-free random access. The numerical results show that the proposed approaches provide pilot sequences and channel estimation or device activity detection methods which can achieve higher estimation or detection accuracy with shorter computation time than existing ones. Furthermore, the numerical results explain how such gains are achieved via the proposed approaches.

Sparse Doubly-Selective Channel Estimation Techniques for OSTBC MIMO-OFDM Systems: A Hierarchical Bayesian Kalman Filter Based Approach

Hierarchical Bayesian Kalman filter (HBKF) based schemes are conceived for doubly-selective sparse channel estimation in orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) wireless systems. Initially, a pilot based multiple measurement vector (MMV) model is formulated for estimating the OSTBC MIMO-OFDM channel. This is followed by the development of a low-complexity, online pilot-based HBKF (P-HBKF) scheme for tracking the sparse time-varying frequency-selective channel. The salient advantages of the proposed P-HBKF technique are that it requires significantly lower number of pilot subcarriers, while also exploiting the inherent sparsity of the wireless channel. Subsequently, data detection is also incorporated in the proposed framework, leading to the development of a procedure for joint sparse doubly-selective channel estimation and symbol detection. Recursive Bayesian Cramér-Rao bounds and closed form expressions are also obtained for the asymptotic mean square error (MSE) based on the solution of the Riccati equation for the KF for benchmarking the performance. Simulation results are presented for validating the theoretical bounds and for comparing the performance of the proposed and existing techniques.

ISAR Imaging Based on Multiple Measurement Vector Model Sparse Signal Recovery Algorithm

A multiple measurement vector (MMV) model blocks sparse signal recovery. ISAR imaging algorithm is proposed to improve ISAR imaging quality. Firstly, the sparse imaging model is built, and block sparse signal recovery algorithm-based MMV model is applied to ISAR imaging. Then, a negative exponential function is proposed to approximately block L0 norm. The optimization solution of smoothed function is obtained by constructing a decreasing sequence. Finally, the correction steps are added to ensure the optimal solution of the block sparse signal along the fastest descent direction. Several simulations and real data simulation experiments verify the proposed algorithm has advantages in imaging time and quality.

Sparse Aperture ISAR Imaging Method Based on Joint Constraints of Sparsity and Low Rank

A new inverse synthetic aperture radar (ISAR) imaging framework is proposed to obtain high cross-range resolution under sparse aperture conditions, which is a challenge when the signal-to-noise ratio is low. Motivated by the sparsity and low rank of target’s 2-D distribution, the imaging problem is converted to the simultaneously sparse and low-rank signal matrix reconstruction problem under multiple measurement vector (MMV) model, and a novel reconstruction method based on joint constraints of sparsity and low rank is proposed. Due to the over-relax problem, the traditional convex optimization method cannot achieve a better performance using joint structures than exploiting just one of the constraints. As such, a nonconvex penalty function is introduced. To avoid the local minima, the convexity of the cost function should be ensured when constructing the nonconvex penalty function. The adaptive filtering framework, which is a powerful way to recovery the sparse low-rank matrix accurately from its noisy observation, is adopted as a reconstruction algorithm. Furthermore, the optimal step size formula and the idea of smoothed zero norm are used to enhance the convergence and the ability to suppress noise. The newly proposed method is verified by the simulation experiment, which has a better performance in image quality, robustness to noise, and imaging speed.

MMV-based OMP for DOA estimation with 1-bit measurement

This paper shows a novel scheme for direction-of-arrival (DOA) estimation of narrowband signals. In the scheme, the 1-bit measurement is used to reduce the system cost. A recovery compressed sensing (CS)-based algorithm with multiple measurement vector (MMV) is proposed to make up the information loss. The purposed MMV-OMP algorithm provides a new idea which make the compress sensing framework applicable directly to an MMV model. The effectiveness of the proposed approach is assessed through numerical simulations under different environment configurations. Comparisons with other methods are reported as well.