Simultaneous Orthogonal Matching Pursuit Research Articles

Compressive Downlink Channel Estimation for FDD Massive MIMO Using Weighted $l_{p}$ Minimization

We propose a weighted $l_{p}$ minimization method for downlink channel estimation in frequency division duplexing massive multiple-input multiple-output (MIMO) systems. The proposed algorithm involves two stages, in which it first diagnoses the downlink supports by utilizing the channel sparsity in angular domain and angular reciprocity for uplink and downlink channels. In stage two, a weighted $l_{p}$ minimization algorithm based on the diagnosed supports is used for downlink channel estimation. The diagnosed supports are used for generating the weighting matrix in the weighted $l_{p}$ minimization. The restricted isometry property (RIP)-based guarantees and upper bound of the recovery error are derived. Our analytical results have the universal forms for the $l_{p} (0 minimization and the weighted $l_{p} (0 minimization, and can reduce to the RIP-based analysis results for the $l_{1}$ minimization and the weighted $l_{1}$ minimization which have been discussed in the previous literature. The discussion on the weight selection is also presented which is based on the derived upper bound. Simulations show that the weighted $l_{p}$ minimization is preferred when the correct percentage of the estimated support is more than 0.5. For the channel estimation, the proposed method with support diagnosis and the weighted $l_{p}$ minimization can achieve higher estimation accuracy compared with the $l_{p}$ minimization, weighted subspace pursuit, weighted $l_{1}$ minimization, general $l_{1}$ minimization, joint orthogonal matching pursuit, and simultaneous orthogonal matching pursuit in the medium and high signal-to-noise-rate regions.

A novel training sequence applied to DCS-based channel estimation

Studies have indicated that the distributed compressed sensing based (DCS-based) channel estimation can decrease the length of the reference signals effectively. In block transmission, a unique word (UW) can be used as a cyclic prefix and reference signal. However, the DCS-based channel estimation requires diversity sequences instead of UW. In this paper, we proposed a novel method that employs a training sequence (TS) whose duration time is slightly longer than the maximum delay spread time. Based on proposed TS, the DCS approach perform perfectly in multipath channel estimation. Meanwhile, a cyclic prefix construct could be formed, which reduces the complexity of the frequency domain equalization (FDE) directly. Simulation results demonstrate that, by using the method of simultaneous orthogonal matching pursuit (SOMP), the required channel overhead has been reduced thanks to the proposed TS.

Iterative Method for Simultaneous Sparse Approximation

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method with Adaptive Thresholding (SIMAT). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIMAT outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIMAT is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.

A Hybrid Orthogonal Forward-Backward Pursuit Algorithm for Partial Fourier Multiple Measurement Vectors Problem

In solving the partial Fourier Multiple Measurement Vectors (FMMV) problem, existing greedy pursuit algorithms such as Simultaneous Orthogonal Matching Pursuit (SOMP), Simultaneous Subspace Pursuit (SSP), Hybrid Matching Pursuit (HMP), and Forward-Backward Pursuit (FBP) suffer from low recovery ability or need sparsity as a prior information. This paper combines SOMP and FBP to propose a Hybrid Orthogonal Forward-Backward Pursuit (HOFBP) algorithm. As an iterative algorithm, each iteration of HOFBP consists of two stages. In the first stage, α indices selected by SOMP are added to the support set. In the second stage, the support set is shrank by removing β indices. The choice of α and β is critical to the performance of this algorithm. The simulation results showed that, by using proper parameters, HOFBP has better performance than other greedy pursuit algorithms at the expense of more computing time in some cases. HOFBP does not need sparsity as a prior knowledge.

Improved Joint Sparse Models for Hyperspectral Image Classification Based on a Novel Neighbour Selection Strategy

Joint sparse representation has been widely used for hyperspectral image classification in recent years, however, the equal weight assigned to each neighbouring pixel is less realistic, especially for the edge areas, and one fixed scale is not appropriate for the entire image extent. To overcome these problems, we propose an adaptive local neighbour selection strategy suitable for hyperspectral image classification. We also introduce a multi-level joint sparse model based on the proposed adaptive local neighbour selection strategy. This method can generate multiple joint sparse matrices on different levels based on the selected parameters, and the multi-level joint sparse optimization can be performed efficiently by a simultaneous orthogonal matching pursuit algorithm. Tests on three benchmark datasets show that the proposed method is superior to the conventional sparsity representation methods and the popular support vector machines.

Distributed compressed sensing based channel estimation for underwater acoustic multiband transmissions.

Distributed compressed sensing techniques are applied to enhance sparse channel estimation performance in underwater acoustic multiband systems. The core idea is to use receptions from multiple sub-bands to enhance the detection of channel tap positions. A known variant of the orthogonal matching pursuit (OMP) algorithm based on the distributed compressed sensing principle is simultaneous orthogonal matching pursuit (SOMP). However, the impulse responses across multiple sub-bands may have different arrival structures, although they often show a certain level of similarity. To address such differences at the sub-bands, a multiple selection strategy is applied to select multiple candidates at individual sub-bands at each iteration. This is different from the conventional OMP and SOMP algorithms that select only one candidate at each iteration. When the multiple selection strategy is combined with the SOMP algorithm, the proposed algorithm is referred to as JB-MSSOMP algorithm. To take advantage of channel coherence between adjacent data blocks from different sub-bands, the multiple selection strategy is further used over time. This leads to JBT-MSSOMP algorithm. Computer simulations show improved channel estimation performance of the proposed JB-MSSOMP and JBT-MSSOMP algorithms over the OMP or SOMP algorithms. Communication data from a recent acoustic experiment demonstrates improved receiver performance with the proposed channel estimators.

3-D Shearlet Transform Based Feature Extraction for Improved Joint Sparse Representation HSI Classification

In this paper, a feature extraction approach based on a three-dimensional shearlet transform (shearlet 3D) is proposed. We aim at exploiting shearlet 3D to highlight the intrinsic properties of hyperspectral images (HSIs), well known by their correlated information and high dimensionality. First, we decompose the HSI to yield coefficients arranged in cubes that help the computing of statistical parameters. Afterward, using a simultaneous orthogonal matching pursuit (SOMP) algorithm, a classification process is carried out. SOMP relies on the powerful sparse representation paradigm, which helps representing data in a low-dimensional space. It is also built over the assumption that the contextual information incorporation into the sparse recovery problem improves the classification performance. To this algorithm, we propose to add an adapted decision rule where a similarity measurement is calculated to well assign the appropriate labels to pixels of interest. Experimental results proved that our proposed method outperformed state-of-the-art classifiers. Thanks to our proposed approach, we succeeded to build discriminative descriptors reaching high overall accuracies for two different HSI datasets, without taking into account all the shearlet 3D coefficients.

A Sliding Window-Based Joint Sparse Representation (SWJSR) Method for Hyperspectral Anomaly Detection

In this paper, a new sliding window-based joint sparse representation (SWJSR) anomaly detector for hyperspectral data is proposed. The main contribution of this paper is to improve the judgments about the probability of anomaly presence in signals using the integration of information gathered during transition of sliding window for each pixel. In this method, each pixel experiences different spatial positions with respect to the spatial neighbors through the transition of this sliding window. In each position, an optimized local background dictionary is formed using a K-Singular Value Decomposition (K-SVD) algorithm and the recovery error of sparse estimation for each pixel is calculated using a simultaneous orthogonal matching pursuit algorithm (SOMP). Thus, the votes of each signal in terms of the anomaly presence in each spatial neighborhood are calculated and the variance of these recovery errors is considered as the detection criterion. The experimental results of the proposed SWJSR method on both synthetic and real datasets proved its higher performance compared to the Global RX (GRX), Local RX (LRX), Collaborative Representation Detector (CRD), Background Joint Sparse Representation (BJSR), Causal RX Detector (CR-RXD, CK-RXD), and Sliding Local RX(SLRX) detectors with an average efficiency improvement of about 7.5%, 14.25%, 8.2%, 8.25%, 6.45%, 6.5%, and 3.6%, respectively, in comparison to the mentioned algorithms.

Joint sparse representation based classification of rub-impact in rotating machinery with multiple acoustic emission sensors

Acoustic emission (AE) technique has been widely used for the classification of rub-impact in rotating machinery due to its high sensitivity, wide frequency response range and dynamic detection property. However, it is still unsatisfied to effectively classify the rub-impact in rotating machinery under complicated environment using traditional classification method tailored to a single AE sensor. Recently, motivated by the theory of compressed sensing, a sparse representation based classification (SRC) method has been successfully used in many classification applications. Moreover, when dealing with multiple measurements the joint sparse representation based classification (JSRC) method could improve the classification accuracy with the aid of employing structural complementary information from each measurement. This paper investigates the use of multiple AE sensors for the classification of rub-impact in rotating machinery based on the JSRC method. First, the cepstral coefficients of each AE sensor are extracted as the features for the rub-impact classification. Then, the extracted cepstral features of all AE sensors are concatenated as the input matrix for the JSRC based classifier. Last, the backtracking simultaneous orthogonal matching pursuit (BSOMP) algorithm is proposed to solve the JSRC problem aiming to get the rub-impact classification results. The BSOMP has the advantages of not requiring the sparsity to be known as well as deleting unreliable atoms. Experiments are carried out on real-world data sets collected from in our laboratory. The results indicate that the JSRC method with multiple AE sensors has higher rub-impact classification accuracies when compared to the SRC method with a single AE sensor and the proposed BSOMP algorithm is more flexible and it performs better than the traditional SOMP algorithm for solving the JSRC method.

Underdetermined Wideband DOA Estimation for Off-Grid Sources with Coprime Array Using Sparse Bayesian Learning.

Sparse Bayesian learning (SBL) is applied to the coprime array for underdetermined wideband direction of arrival (DOA) estimation. Using the augmented covariance matrix, the coprime array can achieve a higher number of degrees of freedom (DOFs) to resolve more sources than the number of physical sensors. The sparse-based DOA estimation can deteriorate the detection and estimation performance because the sources may be off the search grid no matter how fine the grid is. This dictionary mismatch problem can be well resolved by the SBL using fixed point updates. The SBL can automatically choose sparsity and approximately resolve the non-convex optimizaton problem. Numerical simulations are conducted to validate the effectiveness of the underdetermined wideband DOA estimation via SBL based on coprime array. It is clear that SBL can obtain good performance in detection and estimation compared to least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS) , simultaneous orthogonal matching pursuit total least squares (SOMP-TLS) and off-grid sparse Bayesian inference (OGSBI).

Sparse Bayesian Learning for Channel Estimation in Time-Varying Underwater Acoustic OFDM Communication

In this paper, we study the sparse Bayesian learning (SBL) framework for channel estimation in underwater acoustic (UWA) orthogonal frequency-division multiplexing (OFDM) communication systems, which provides a desirable property of preventing structural error with fewer convergence errors for sparse signal reconstruction compared with the compress sensing (CS)-based methods. First, we design a SBL-based channel estimator for block-by-block processing using the channel sparse structure independently in each block. Then, we propose a joint channel model after Doppler compensation for multi-block joint processing, where the delays of the channels for several consecutive blocks are similar and the path gains exhibit temporal correlation, and we denote a temporal correlation coefficient for path gains to evaluate the strength of the correlation. Furthermore, we propose the temporal multiple SBL (TMSBL)-based channel estimator to jointly estimate the channels by taking advantage of the channel coherence between consecutive OFDM blocks. Results of numerical simulation and sea trial demonstrate the effectiveness of the SBL and TMSBL channel estimator algorithms in time-varying UWA channel, which achieve better channel estimation performance and lower bit error rate compared with the existing CS-based methods, such as orthogonal matching pursuit (OMP) and simultaneous OMP, especially the TMSBL estimator achieves the best performance in strong temporal correlated channels and maintains robustness in weak temporal correlated channels.

Sparse Channel Estimation for Massive MIMO-OFDM Systems Over Time-Varying Channels

For downlink orthogonal frequency division multiplexing-based massive multiple-input-multiple-output transmission over the time-varying channel, channel estimation is very challenging due to numerous channel coefficients to be estimated. To track this problem, this paper proposes a novel sparse channel estimation scheme, exploiting the sparsity in the delay domain and the high correlation in the spatial domain. By utilizing the basis expansion model (BEM) to model the time variation and the generalized-spatial BEM to model the spatial correlation, we are able to significantly reduce the number of the coefficients to be estimated. Then, the channel estimation is formulated into a compressive sensing problem with a quasi-block-sparse matrix to be recovered. Motivated by the quasi-block sparsity, a novel quasi-block simultaneous orthogonal matching pursuit (QBSO) algorithm is developed to recover the channel, which seeks nonzero channel tap positions at the first stage and calculates the channel coefficients at the second stage. Moreover, an adaptive-QBSO algorithm is further designed to improve the recovery accuracy, where the measurement matrix is adaptively designed based on the estimated virtual angle of departure, and thus, the sparsity representation can be strengthened. We also discuss the design of pilot pattern including pilot values and positions. Simulation results are provided to validate the effectiveness of our proposed channel estimation scheme.

Near-Optimum Sparse Channel Estimation Based on Least Squares and Approximate Message Passing

Accurately estimating the sparse channel with sequential under-sampled received signal is a challenging problem in broadband wireless communication systems, especially when prior knowledge of the sparsity level and the probability distribution of the sparse channel is unavailable. A joint least-squares (LS) and approximate-message-passing (AMP) algorithm based on sparse Bayesian learning (SBL) model, named LS-AMP-SBL, is proposed to approach the optimal performance given by Oracle-LS, where Oracle-LS requires exact knowledge of the support of the sparse channel. The proposed algorithm has three steps. First, AMP-SBL estimates the sparse channel iteratively until convergence. Then, based on the coarse estimated channel of the first step and an adaptable threshold derived from the effective noise level, the support of the sparse channel can be detected with a high probability. The third step is to estimate the sparse channel using LS with the estimated support from the second step. By introducing a proper and adaptable threshold based on AMP-SBL operation, the proposed scheme is capable of accurately detecting the support of the spare channel, and thus achieves a near-optimal performance but with a much lower complexity than both simultaneous orthogonal matching pursuit and basic pursuit. Simulation results demonstrate that the proposed LS-AMP-SBL can approach the performance bound given by Oracle-LS.

Cone-based joint sparse modelling for hyperspectral image classification

Joint sparse model (JSM) is being extensively investigated on hyperspectral images (HSIs) and has achieved promising performance for classification. In JSM, it is assumed that neighbouring hyperspectral pixels can share sparse representations. However, the coefficients of the endmembers used to reconstruct a test HSI pixel is desirable to be non-negative for the sake of physical interpretation. Hence in this paper, we introduce the non-negativity constraint into JSM. The non-negativity constraint implies a cone-shaped space instead of the infinite sample space for pixel representation. This leads us to propose a new model called cone-based joint sparse model (C-JSM), to install the non-negativity on top of the sparse and joint modelling. To solve the C-JSM problem, we also propose a new algorithm through introducing the non-negativity constraint into the simultaneous orthogonal matching pursuit (SOMP) algorithm. The new algorithm is called non-negative simultaneous orthogonal matching pursuit (NN-SOMP). Experiments and investigations show that the proposed C-JSM can produce a more stable, sparse representation and a superior classification than other methods which only ensure the sparsity, non-negativity or spatial coherence.

Greedy algorithms for diffuse optical tomography reconstruction

Diffuse optical tomography (DOT) is a noninvasive imaging modality that reconstructs the optical parameters of a highly scattering medium. However, the inverse problem of DOT is ill-posed and highly nonlinear due to the zig-zag propagation of photons that diffuses through the cross section of tissue. The conventional DOT imaging methods iteratively compute the solution of forward diffusion equation solver which makes the problem computationally expensive. Also, these methods fail when the geometry is complex. Recently, the theory of compressive sensing (CS) has received considerable attention because of its efficient use in biomedical imaging applications. The objective of this paper is to solve a given DOT inverse problem by using compressive sensing framework and various Greedy algorithms such as orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP), and stagewise orthogonal matching pursuit (StOMP), regularized orthogonal matching pursuit (ROMP) and simultaneous orthogonal matching pursuit (S-OMP) have been studied to reconstruct the change in the absorption parameter i.e, Δα from the boundary data. Also, the Greedy algorithms have been validated experimentally on a paraffin wax rectangular phantom through a well designed experimental set up. We also have studied the conventional DOT methods like least square method and truncated singular value decomposition (TSVD) for comparison. One of the main features of this work is the usage of less number of source–detector pairs, which can facilitate the use of DOT in routine applications of screening. The performance metrics such as mean square error (MSE), normalized mean square error (NMSE), structural similarity index (SSIM), and peak signal to noise ratio (PSNR) have been used to evaluate the performance of the algorithms mentioned in this paper. Extensive simulation results confirm that CS based DOT reconstruction outperforms the conventional DOT imaging methods in terms of computational efficiency. The main advantage of this study is that the forward diffusion equation solver need not be repeatedly solved.

A General Framework for Hardware Trojan Detection in Digital Circuits by Statistical Learning Algorithms

The continuous globalization of the semiconductor industry has significantly raised the vulnerability of chips under hardware Trojan (HT) attacks. It is extremely challenging to detect HTs in fabricated chips due to the existence of process variations (PVs), since PVs may cause larger impacts than HTs. In this paper, we propose a novel framework for HT detection in digital integrated circuits. The goal of this paper is to detect HTs inserted during fabrication. The HT detection problem is formulated as an under-determined linear system by a sparse gate profiling technique, and the existence of HTs is mapped to the sparse solution of the linear system. A Bayesian inference-based calibration technique is proposed to recover PVs for each chip for the sparse gate profiling technique. A batch of under-determined linear systems are solved together by the well-studied simultaneous orthogonal matching pursuit algorithm to get their common sparse solution. Experimental results show that even under big measurement errors, the proposed framework gets quite high HT detection rates with low measurement cost.

An improved RIP-based performance guarantee for sparse signal recovery via simultaneous orthogonal matching pursuit

Recently, based on restricted isometry property (RIP), some sufficient conditions for exact support recovery with simultaneous orthogonal matching pursuit (SOMP) algorithm have been proposed when measurement matrices are different. In this paper, in the noiseless case, one sufficient condition for exact support recovery with SOMP is presented to improve the existing results. By using a counter example, in the noiseless case, an open problem presented in (Xu et. al, 2015) is solved.

FUSION OF MULTI-SCALE DEMS FROM DESCENT AND NAVCM IMAGES OF CHANG’E-3 USING COMPRESSED SENSING METHOD

Abstract. The multi-source DEMs generated using the images acquired in the descent and landing phase and after landing contain supplementary information, and this makes it possible and beneficial to produce a higher-quality DEM through fusing the multi-scale DEMs. The proposed fusion method consists of three steps. First, source DEMs are split into small DEM patches, then the DEM patches are classified into a few groups by local density peaks clustering. Next, the grouped DEM patches are used for sub-dictionary learning by stochastic coordinate coding. The trained sub-dictionaries are combined into a dictionary for sparse representation. Finally, the simultaneous orthogonal matching pursuit (SOMP) algorithm is used to achieve sparse representation. We use the real DEMs generated from Chang’e-3 descent images and navigation camera (Navcam) stereo images to validate the proposed method. Through the experiments, we have reconstructed a seamless DEM with the highest resolution and the largest spatial coverage among the input data. The experimental results demonstrated the feasibility of the proposed method.

A Novel Geometric Dictionary Construction Approach for Sparse Representation Based Image Fusion

Sparse-representation based approaches have been integrated into image fusion methods in the past few years and show great performance in image fusion. Training an informative and compact dictionary is a key step for a sparsity-based image fusion method. However, it is difficult to balance “informative” and “compact”. In order to obtain sufficient information for sparse representation in dictionary construction, this paper classifies image patches from source images into different groups based on morphological similarities. Stochastic coordinate coding (SCC) is used to extract corresponding image-patch information for dictionary construction. According to the constructed dictionary, image patches of source images are converted to sparse coefficients by the simultaneous orthogonal matching pursuit (SOMP) algorithm. At last, the sparse coefficients are fused by the Max-L1 fusion rule and inverted to a fused image. The comparison experimentations are simulated to evaluate the fused image in image features, information, structure similarity, and visual perception. The results confirm the feasibility and effectiveness of the proposed image fusion solution.

DOA estimation using multiple measurement vector model with sparse solutions in linear array scenarios

A novel algorithm is presented based on sparse multiple measurement vector (MMV) model for direction of arrival (DOA) estimation of far-field narrowband sources. The algorithm exploits singular value decomposition denoising to enhance the reconstruction process. The proposed multiple nature of MMV model enables the simultaneous processing of several data snapshots to obtain greater accuracy in the DOA estimation. The DOA problem is addressed in both uniform linear array (ULA) and nonuniform linear array (NLA) scenarios. Superior performance is demonstrated in terms of root mean square error and running time of the proposed method when compared with conventional compressed sensing methods such as simultaneous orthogonal matching pursuit (S-OMP), l2,1 minimization, and root-MUISC.