Sparse Reconstruction Problem Research Articles

Compressed Sensing-Based DOA Estimation with Antenna Phase Errors

In array signal processing, the direction of arrivals (DOAs) of the received signals are estimated by measuring the relative phases among antennas; hence, the estimation performance is reduced by the inconsistency among antennas. In this paper, the DOA estimation problem of the uniform linear array (ULA) is investigated in the scenario with phase errors among the antennas, and a diagonal matrix composed of phase errors is used to formulate the system model. Then, by using the compressed sensing (CS) theory, we convert the DOA estimation problem into a sparse reconstruction problem. A novel reconstruction method is proposed to estimate both the DOA and the unknown phase errors, iteratively. The phase errors are calculated by a gradient descent method with the theoretical expressions. Simulation results show that the proposed method is cost-efficient and outperforms state-of-the-art methods regarding the DOA estimation with unknown phase errors.

Block-sparse compressive localization for incipient tip vortex cavitation noise

Marine propeller cavitation is a dominant noise source of ships. Thus, localizing the cavitation noise source is essential for subsequent remedy. Given that incipient tip vortex cavitation (TVC) noise radiates in all directions as a monopole source and a few noise sources exist in the vicinity of the propeller, the localization problem can be considered as a sparse signal reconstruction problem. Compressive sensing (CS) based localization technique utilizes a sparsity promoting constraint and solves the localization problem efficiently with high resolution. Block-sparse CS, based on block-sparsity, is adopted to process multiple frequency components of the sources coherently. Block-sparse CS localization of TVC shows superior performance with high resolution compared to the conventional CS based incoherent multiple frequency processing. To demonstrate the performance of the block-sparse CS localization, both synthetic and real cavitation tunnel experiment data are used.

Sparse aperture ISAR imaging algorithm based on adaptive filtering framework

Under sparse aperture conditions, some problems arise with inverse synthetic aperture radar (ISAR) imaging such as low-azimuth resolution and susceptibility to noise. To solve them, the sparseness of scattering points is used to transform the imaging problem into the sparse signal reconstruction problem, and a sparse aperture ISAR imaging algorithm based on adaptive filtering framework is proposed, which is named smoothed L0 norm-Newton's method least mean square (LMS) algorithm. Firstly, the L0 norm LMS algorithm is taken as the reconstruction method for its advantages of simple structure and high-reconstruction accuracy. Then, the smoothed L0-norm method is extended to the complex domain of radar signal processing to increase the accuracy and maintain a good robustness. Finally, in order to speed up the convergence, Newton's method is introduced to the LMS algorithm. Simulation results show that the reconstruction image of the proposed method has higher resolution and better anti-noise performance than those of other reconstruction algorithms.

Common-Innovation Subspace Pursuit for Distributed Compressed Sensing in Wireless Sensor Networks

We study the sparse signal reconstruction problem in a wireless sensor network (WSN) using distributed compressed sensing. The sparse signals from multiple sensors are modeled by the mixed-support set model that characterizes the inter-correlation of the signals by the common support set and represents the individual features by the innovation support sets. A novel algorithm, namely common-innovation subspace pursuit (CISP), is proposed to estimate the common and innovation support sets separately, to reduce the reconstruction error and computing time. The proposed algorithm consists of two stages, the eigen-value decomposition-based common subspace pursuit and projection-based innovation subspace pursuit. We analyze the convergence performance of the CISP algorithm, where a bound of reconstruction error is provided. Furthermore, a range of simulations and experiments are conducted to evaluate the performance of the proposed algorithm. The results of simulations on a hierarchical clustering-based WSN show that the proposed CISP algorithm is superior over the orthogonal matching pursuit and distributed parallel pursuit algorithms in terms of both reconstruction error and runtime, in the scenario of a large-scale sensor network. Moreover, the experiments on the real data from the temperature and humidity sensors deployed in the Intel Berkeley Lab verify that, the proposed CISP algorithm is capable of reconstructing the multiple sparse signals accurately and efficiently, in the real-life application.

SBL-Based Direction Finding Method with Imperfect Array

The imperfect array degrades the direction finding performance. In this paper, we investigate the direction finding problem in uniform linear array (ULA) system with unknown mutual coupling effect between antennas. By exploiting the target sparsity in the spatial domain, the sparse Bayesian learning (SBL)-based model is proposed and converts the direction finding problem into a sparse reconstruction problem. In the sparse-based model, the off-grid errors are introduced by discretizing the direction area into grids. Therefore, an off-grid SBL model with mutual coupling vector is proposed to overcome both the mutual coupling and the off-grid effect. With the distribution assumptions of unknown parameters including the noise variance, the off-grid vector, the received signals and the mutual coupling vector, a novel direction finding method based on SBL with unknown mutual coupling effect named DFSMC is proposed, where an expectation-maximum (EM)-based step is adopted by deriving the estimation expressions for all the unknown parameters theoretically. Simulation results show that the proposed DFSMC method can outperform state-of-the-art direction finding methods significantly in the array system with unknown mutual coupling effect.

A weighted sparse reconstruction-based ultrasonic guided wave anomaly imaging method for composite laminates

Ultrasonic guided wave is a promising tool for structural health monitoring and nondestructive testing. Numerous signal processing methods have been proposed to detect and localize anomalies based on ultrasonic guided waves for plate-like structures. However, imaging performance is limited in these methods, such as large spot size and significant artifacts. To achieve a better imaging performance of Lamb waves, a weighted sparse reconstruction-based anomaly imaging method is proposed for plate-like structures. Scattering signals are sparsely decomposed in a dictionary pre-constructed from Lamb wave propagation and scattering models. The pixel value at each location of the imaging region can be obtained by solving a weighted sparse reconstruction problem. To verify the accuracy and effectiveness of the proposed method, experiments on a carbon fiber reinforced plastic with and without additional mass are conducted. The experimental results show that the proposed method can achieve anomaly imaging with smaller spot size and fewer artifacts.

A linearly convergent algorithm for sparse signal reconstruction

For the sparse signal reconstruction problem in compressive sensing, we propose a projection-type algorithm without any backtracking line search based on a new formulation of the problem. Under suitable conditions, global convergence and its linear convergence of the designed algorithm are established. The efficiency of the algorithm is illustrated through some numerical experiments on some sparse signal reconstruction problem.

Compressive Sensing Inspired Multivariate Median

A new form of the multivariate median is introduced. It is defined as a point in the multidimensional space whose sum of distances from a set of multidimensional hyperplanes is minimal. This median can be used to formulate and solve the problem of sparse signal reconstruction. Application of the proposed multivariate median is illustrated on examples.

Enhanced Channel Estimation and Codebook Design for Millimeter-Wave Communication

The existing channel estimation methods for millimeter-wave communications, e.g., hierarchical search and compressed sensing, either acquire only one single multipath component (MPC) or require considerably high training overhead. To realize fast yet accurate channel estimation, we propose a multipath decomposition and recovery approach in this paper. The proposed approach has two stages. In the first stage, instead of directly searching the real MPCs, we decompose each real MPC into several virtual MPCs and acquire the virtual MPCs by using the hierarchical search based on a normal-resolution codebook. Then, in the second stage, the real MPCs are recovered from the acquired virtual MPCs in the first stage, which turns out to be a sparse reconstruction problem, where the size of the dictionary matrix is greatly reduced by exploiting the results of the virtual multipath acquisition. Moreover, to make the proposed approach applicable for both analog and hybrid beamforming/combining devices with strict constant-modulus constraint, we particularly design a codebook for the hierarchical search by using an enhanced subarray technique, and the codebook is also applicable in other hierarchical search methods. Performance comparisons show that the proposed approach achieves a superior tradeoff between estimation performance and training penalty over the state-of-the-art alternatives.

A Reversed Visible Light Multitarget Localization System via Sparse Matrix Reconstruction

A reversed indoor multitarget localization system employing compressive sensing (CS) theory is proposed for the first time in terms of visible light positioning (VLP). Unlike conventional VLP systems, where targets process the received light signals to localize themselves, our system works reversely by using multiple photodiodes (PDs) mounted on the ceiling to localize mobile targets that carry light emitting diodes. By utilizing its nature of sparsity, the problem of multitarget localization is formulated as a problem of sparse matrix reconstruction, and a 3-step workflow is developed to solve the problem. In this workflow, first, a sensing matrix is redesigned by using QR decomposition to enable CS theory. Next, the conventional l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization (l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> M) algorithm which is highly vulnerable to noise in solving a localization problem is theoretically analyzed and subsequently improved by adopting a reweighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> M approach. Finally, a subgrid localization algorithm is proposed to overcome a common unpractical assumption of on-grid locations, tackle the false peak problem in sparse matrix reconstruction, and ultimately improve the localization precision. The feasibility of our system and supporting algorithms is verified through extensive simulations. Our system demonstrates a good positioning accuracy of 7.4 cm by using 25 PDs when SNR = 20 dB. We also investigate the impact of various factors on the positioning performance, and the obtained results provide an insightful reference paving the way to a practical system design.

An algebraic perspective on integer sparse recovery

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this technology are ubiquitous, ranging from wireless communications to medical imaging, and there is now a solid foundation of mathematical theory and algorithms to robustly and efficiently reconstruct such signals. However, in many of these applications, the signals of interest do not only have a sparse representation, but have other structure such as lattice-valued coefficients. While there has been a small amount of work in this setting, it is still not very well understood how such extra information can be utilized during sampling and reconstruction. Here, we explore the problem of integer sparse reconstruction, lending insight into when this knowledge can be useful, and what types of sampling designs lead to robust reconstruction guarantees. We use a combination of combinatorial, probabilistic and number-theoretic methods to discuss existence and some constructions of such sensing matrices with concrete examples. We also prove sparse versions of Minkowski’s Convex Body and Linear Forms theorems that exhibit some limitations of this framework.

Compressive normal mode estimation in shallow water

Estimation of normal modes in an ocean waveguide from acoustic data on a vertical line array involves estimation of mode shapes and their wavenumbers. Since these horizontal mode wavenumbers are sparse, compressive sensing (CS) can solve the sparse signal reconstruction problem with high accuracy. Here, grid-free CS technique, atomic norm minimization (ANM) is used to estimate the horizontal mode wavenumbers and their mode shapes. These mode shapes and wavenumbers can be estimated using the grid-free CS without a priori knowledge of the environment. The grid-free CS successfully extracts mode shapes and wavenumbers even with a partial water column spanning array and even in the case when the mode shape functions are not orthogonal.

Adaptive decomposition-based evolutionary approach for multiobjective sparse reconstruction

This paper aims at solving the sparse reconstruction (SR) problem via a multiobjective evolutionary algorithm. Existing multiobjective evolutionary algorithms for the SR problem have high computational complexity, especially in high-dimensional reconstruction scenarios. Furthermore, these algorithms focus on estimating the whole Pareto front rather than the knee region, thus leading to limited diversity of solutions in knee region and waste of computational effort. To tackle these issues, this paper proposes an adaptive decomposition-based evolutionary approach (ADEA) for the SR problem. Firstly, we employ the decomposition-based evolutionary paradigm to guarantee a high computational efficiency and diversity of solutions in the whole objective space. Then, we propose a two-stage iterative soft-thresholding (IST)-based local search operator to improve the convergence. Finally, we develop an adaptive decomposition-based environmental selection strategy, by which the decomposition in the knee region can be adjusted dynamically. This strategy enables to focus the selection effort on the knee region and achieves low computational complexity. Experimental results on simulated signals, benchmark signals and images demonstrate the superiority of ADEA in terms of reconstruction accuracy and computational efficiency, compared to five state-of-the-art algorithms.

Sound source localization and speech enhancement with sparse Bayesian learning beamforming.

Speech localization and enhancement involves sound source mapping and reconstruction from noisy recordings of speech mixtures with microphone arrays. Conventional beamforming methods suffer from low resolution, especially with a limited number of microphones. In practice, there are only a few sources compared to the possible directions-of-arrival (DOA). Hence, DOA estimation is formulated as a sparse signal reconstruction problem and solved with sparse Bayesian learning (SBL). SBL uses a hierarchical two-level Bayesian inference to reconstruct sparse estimates from a small set of observations. The first level derives the posterior probability of the complex source amplitudes from the data likelihood and the prior. The second level tunes the prior towards sparse solutions with hyperparameters which maximize the evidence, i.e., the data probability. The adaptive learning of the hyperparameters from the data auto-regularizes the inference problem towards sparse robust estimates. Simulations and experimental data demonstrate that SBL beamforming provides high-resolution DOA maps outperforming traditional methods especially for correlated or non-stationary signals. Specifically for speech signals, the high-resolution SBL reconstruction offers not only speech enhancement but effectively speech separation.

Variational Bayesian Inference-Based Counting and Localization for Off-Grid Targets With Faulty Prior Information in Wireless Sensor Networks

The benefits of compressive sensing (CS) on counting and localization in wireless sensor networks have already been demonstrated in previous works. However, most existing solutions usually become infeasible in the presence of off-grid targets, which is inevitable for the traditional CS-based localization methods. To mitigate the error caused by off-grid targets, in this paper, a more accurate sparse approximation model is applied where the true and unknown sparsifying dictionary is approximated with its first-order Taylor expansion around a known dictionary. Based on the model, the counting and localization problem is formulated as a sparse reconstruction problem that recovers two sparse signals with related supports. To solve the problem, we develop an iterative algorithm under a variational Bayesian inference framework. Moreover, in practice, some faulty prior information (e.g., coarse positions) is usually available. To incorporate the information, a three-level hierarchical prior model is introduced and imposed on the sparse signals to be recovered, where the supports of sparse signals are learned in the third level. Additionally, a grid pruning mechanism and matrix inversion lemma are leveraged to accelerate the inference process. Extensive simulation results demonstrate that, compared with state-of-the-art algorithms, the proposed algorithm can achieve counting and localization with higher accuracy as well as lower cost.

A Fast and Accurate Basis Pursuit Denoising Algorithm With Application to Super-Resolving Tomographic SAR

$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many remote sensing problems, such as image fusion, target detection, image super-resolution, and others and have led to promising results. However, solving such sparse reconstruction problems is computationally expensive and has limitations in its practical use. In this paper, we proposed a novel efficient algorithm for solving the complex-valued $L_1$ regularized least squares problem. Taking the high-dimensional tomographic synthetic aperture radar (TomoSAR) as a practical example, we carried out extensive experiments, both with simulation data and real data, to demonstrate that the proposed approach can retain the accuracy of second order methods while dramatically speeding up the processing by one or two orders. Although we have chosen TomoSAR as the example, the proposed method can be generally applied to any spectral estimation problems.

Jointly Iterative Adaptive Approach Based Space Time Adaptive Processing Using MIMO Radar

To solve the problem of large training samples requirement of space time adaptive processing (STAP), a jointly sparse matrices recovery-based method is proposed for clutter plus noise covariance matrix estimation by exploiting the transmitting waveform orthogonality of multiple-in multiple-out (MIMO) radar. The clutter spatio-temporal spectrum estimation problem is modeled as a sparse matrix reconstruction problem. Multiple training samples are generated based on the received signal of MIMO radar from a single training range cell. In order to recover the spatio-temporal spectrum matrices corresponding to different training samples, a jointly 2-D iterative adaptive approach is formulated to provide high accuracy and efficiency. Compared with the existing sparse recovery (SR)-based STAP method with single training range cell, due to the application of matricization process and MIMO radar, the proposed method can not only improve the clutter covariance matrix estimation accuracy but also reduce the computational complexity. In the heterogeneous and non-stationary environment, the proposed method can achieve better clutter suppression performance than conventional SR-based STAP methods using multiple training range cells. Simulation results are given to demonstrate the advantages of the proposed method over existing methods.

Split Bregman Algorithm for Structured Sparse Reconstruction

Sparse reconstruction has attracted considerable attention in recent years and shown powerful capabilities in many applications. In standard sparse reconstruction, the sparse nonzero elements appear anywhere in a vector. However, in many applications, the nonzero elements usually exhibit additional structure. Structured sparsity can be reconstructed from asymptotically less measurement than standard sparsity. In this paper, a unified framework is given to express the existing sparsity structures. Then efficient algorithm based on split Bregman iteration is proposed to solve the structured sparse reconstruction problem. The convergence of the proposed algorithm is also discussed. Numerical results show the effectiveness of the proposed algorithm for both synthetic and real-world data.

Learning Large-Scale Fuzzy Cognitive Maps Based on Compressed Sensing and Application in Reconstructing Gene Regulatory Networks

Learning large-scale sparse fuzzy cognitive maps (FCMs) from observed data automatically without any prior knowledge remains an outstanding problem. Most existing methods are slow and have difficulty in dealing with large-scale FCMs, because of the large searching space. We develop a framework based on compressed sensing (CS), a convex optimization method, to learn large-scale sparse FCMs, called CS-FCM. Combining with the sparsity of FCMs, the task of learning FCMs is first decomposed into sparse signal reconstruction problems. The ability of CS to exactly recover the sparse signals provides CS-FCM the probability to exactly learn FCMs. In the experiments, CS-FCM is applied to learn both synthetic data with varying sizes and densities and real-life data. The results show that CS-FCM obtains good performance by just learning from a small amount of data. CS-FCM can effectively learn sparse FCMs with 1000 nodes and even more, which have one million weights to be determined. CS-FCM is also applied to reconstruct gene regulatory networks (GRNs), and the well-known benchmark datasets DREAM3 and DREAM4 are tested. The results show that CS-FCM also obtains high accuracy in reconstructing GRNs. CS-FCM establishes a paradigm for learning large-scale sparse FCMs with high accuracy.

Fast super-resolution estimation of DOA and DOD in bistatic MIMO Radar with off-grid targets

ABSTRACTIn this paper, we focus on the problem of joint DOA and DOD estimation in Bistatic MIMO Radar using sparse reconstruction method. In traditional ways, we usually convert the 2D parameter estimation problem into 1D parameter estimation problem by Kronecker product which will enlarge the scale of the parameter estimation problem and bring more computational burden. Furthermore, it requires that the targets must fall on the predefined grids. In this paper, a 2D-off-grid model is built which can solve the grid mismatch problem of 2D parameters estimation. Then in order to solve the joint 2D sparse reconstruction problem directly and efficiently, three kinds of fast joint sparse matrix reconstruction methods are proposed which are Joint-2D-OMP algorithm, Joint-2D-SL0 algorithm and Joint-2D-SOONE algorithm. Simulation results demonstrate that our methods not only can improve the 2D parameter estimation accuracy but also reduce the computational complexity compared with the traditional Kronecker Compressed Sensing method.