Group Sparse Reconstruction Research Articles

Enhanced DOA Estimation Exploiting Multi-Frequency Sparse Array

In this paper, we develop a general framework of multi-frequency sparse array to estimate the direction-of-arrival (DOA) of a significantly higher number of targets than the number of physical sensors. The multi-frequency sparse arrays are designed to offer zero lag redundancy in the rendered difference coarray so that the available degrees of freedom are fully utilized to enable high-resolution DOA estimation. A modified sensor interpolation technique is developed to accurately estimate the signal correlation matrix so that the effect of holes in the difference coarray is mitigated. The proposed technique accounts for both self-lags between signals corresponding to the same frequencies and the cross-lags between signals corresponding to different frequencies. As such, it enhances the DOA estimation performance compared to existing methods that either perform array interpolation utilizing only the self-lags or carry out group sparse reconstruction without exploiting array interpolation. Simulation results verify the offerings of the multi-frequency sparse arrays.

Improved two-dimensional DOA estimation using parallel coprime arrays

The conventional coprime array consists of two uniform linear subarrays to construct an effective difference coarray with desirable characteristics. Such linear coprime arrays only provide one-dimensional (1-D) direction-of-arrival (DOA) estimation. In this paper, we propose a novel coprime array configuration with parallel subarrays, along with an effective method for two-dimensional (2-D) DOA estimation. The 2-D DOA estimation problem is cast as two separate 1-D problems for reduced complexity and is solved using one of the two mechanisms based on the number of sensors and that of sources. When there are less sources than the number of sensors, subspace-based and rank-reduction estimation (RARE) techniques are sequentially applied to the physical array output. On the other hand, when the number of sources is equal to or larger than that of sensors, a virtual difference coarray is formed and group sparse reconstruction and least squares operations are then applied. In both scenarios, the proposed methods automatically pair the corresponding azimuth and elevation angles. The proposed methods resolve up to MN sources using 2M+N−1 sensors, which are the same as in the 1-D DOA estimation using conventional coprime arrays. Simulations results are presented delineating both the accuracy and resolution capability of the proposed method.

Performance Evaluation of Group Sparse Reconstruction and Total Variation Minimization for Target Imaging in Stratified Subsurface Media

Sparse reconstruction methods have been successfully applied for efficient radar imaging of targets embedded in stratified dielectric subsurface media. Recently, a total variation minimization (TVM) based approach was shown to provide superior image reconstruction performance over standard L1-norm minimization-based method, especially in case of non-point-like targets. Alternatively, group sparse reconstruction (GSR) schemes can also be employed to account for embedded target extent. In this paper, we provide qualitative and quantitative performance evaluations of TVM and GSR schemes for efficient and reliable target imaging in stratified subsurface media. Using numerical electromagnetic data of targets buried in the ground, we demonstrate that GSR and TVM provide comparable reconstruction performance qualitatively, with GSR exhibiting a slight superiority over TVM quantitatively, albeit at the expense of less flexibility in regularization parameters.

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.

Image annotation refinement via 2P-KNN based group sparse reconstruction

Image annotation aims at predicting labels that can accurately describe the semantic information of images. In the past few years, many methods have been proposed to solve the image annotation problem. However, the predicted labels of the images by these methods are usually incomplete, insufficient and noisy, which is unsatisfactory. In this paper, we propose a new method denoted as 2PKNN-GSR (Group Sparse Reconstruction) for image annotation and label refinement. First, we get the predicted labels of the testing images using the traditional method, i.e., a two-step variant of the classical K-nearest neighbor algorithm, called 2PKNN. Then, according to the obtained labels, we divide the K nearest neighbors of an image in the training images into several groups. Finally, we utilize the group sparse reconstruction algorithm to refine the annotated label results which are obtained in the first step. Experimental results on three standard datasets, i.e., Corel 5K, IAPR TC12 and ESP Game, show the superior performance of the proposed method compared with the state-of-the-art methods.

Multi-Helical Path Exploitation in Sparsity-Based Guided-Wave Imaging of Defects in Pipes

In this paper, a defect localization scheme for cylindrical pipes is presented which relies on guided-wave scattering by defects. The proposed scheme is predicated on the use of a sparse array of ultrasonic transducers and the sparse nature of defects on the pipe surface. Two circular rings of transducers, functioning as transmitters and receivers, are used to encompass the region to be inspected. Multiple helical paths exist for waves to travel from the transmitters to the receivers, after being scattered by the defects. Model based dictionary matrices are constructed for each path, relating the signals arriving at the receivers to the locations of potential defects. The resulting linear signal model is inverted by group sparse reconstruction to localize defects present in the pipe. Experimental validations of the proposed multi-helical path exploitation approach are provided for defects on an aluminum pipe.

Cramer–Rao type bounds for sparsity-aware multi-sensor multi-target tracking

Conventionally, sparsity-aware multi-sensor multi-target tracking (MTT) algorithms comprise a two-step architecture that cascades group sparse reconstruction and MTT algorithms. The group sparse reconstruction algorithm exploits the apriori information that the measurements across multiple sensors share a common sparse support in a discretized target state space and provides a computationally efficient technique for centralized multi-sensor information fusion. In the succeeding step, the MTT filter performs the data association, compensates for the missed detections, removes the clutter components, and improves the accuracy of multi-target state estimates according to the pre-defined target dynamic model. In a recent work, a novel technique was proposed for sparsity-aware multi-sensor MTT that deploys a recursive feedback mechanism such that the group sparse reconstruction algorithm also benefits from the apriori knowledge about the target dynamics. As such, it is of significant interest to compare the tracking performance of these methods to the optimal multi-sensor MTT solution, with and without considering the missing samples. In this paper, we analytically evaluate the Cramer-Rao type performance bounds for these two schemes for sparsity-aware MTT algorithms and show that the recursive learning structure outperforms the conventional approach, when the measurement vectors are corrupted by missing samples and additive noise.

Multipath exploitation for enhanced defect imaging using Lamb waves

This paper presents a multipath exploitation approach for defect imaging in thin-walled structures using Lamb waves under the sparse reconstruction framework. An image of the defects in the region of interest is obtained by inverting a multipath propagation model via group sparse reconstruction. This permits accurate imaging of regions close to the structure boundary without the introduction of ‘false’ defects or ghosts. Real-data measurements of defects close to the edge of an aluminum plate are used to demonstrate the effectiveness of the multipath exploitation scheme.

Robust group compressive sensing for DOA estimation with partially distorted observations

In this paper, we propose a robust direction-of-arrival (DOA) estimation algorithm based on group sparse reconstruction algorithm utilizing signals observed at multiple frequencies. The group sparse reconstruction scheme for DOA estimation is solved through the complex multitask Bayesian compressive sensing algorithm by exploiting the group sparse property of the received multi-frequency signals. Then, we propose a robust reconstruction algorithm in the presence of distorted signals. In particular, we consider a problem where the observed data in some frequencies are distorted due to, e.g., interference contamination. In this case, the residual error will follow the impulsive Gaussian mixture distribution instead of the Gaussian distribution due to the fact that some of the estimation errors significantly depart from the mean value of the estimation error distribution. Thus, the minimum least square restriction used in the conventional sparse reconstruction algorithm may lead to a failed reconstruction result. By exploiting the maximum correntropy criterion which is inherently insensitive to the impulsive noise, a weighting vector is derived to automatically mitigate the effect of the distorted narrowband signals, and a robust group compressive sensing approach is developed to achieve reliable DOA estimation. The robustness and effectiveness of the proposed algorithm are verified using simulation results.

DOA estimation exploiting a uniform linear array with multiple co-prime frequencies

The co-prime array, which utilizes a co-prime pair of uniform linear sub-arrays, provides a systematical means for sparse array construction. By choosing two co-prime integers M and N, O(MN) co-array elements can be formed from only O(M+N) physical sensors. As such, a higher number of degrees-of-freedom (DOFs) is achieved, enabling direction-of-arrival (DOA) estimation of more targets than the number of physical sensors. In this paper, we propose an alternative structure to implement co-prime arrays. A single sparse uniform linear array is used to exploit two or more continuous-wave signals whose frequencies satisfy a co-prime relationship. This extends the co-prime array and filtering to a joint spatio-spectral domain, thereby achieving high flexibility in array structure design to meet system complexity constraints. The DOA estimation is obtained using group sparsity-based compressive sensing techniques. In particular, we use the recently developed complex multitask Bayesian compressive sensing for group sparse signal reconstruction. The achievable number of DOFs is derived for the two-frequency case, and an upper bound of the available DOFs is provided for multi-frequency scenarios. Simulation results demonstrate the effectiveness of the proposed technique and verify the analysis results.

Correlated spectroscopic imaging of calf muscle in three spatial dimensions using group sparse reconstruction of undersampled single and multichannel data.

To implement a 5D (three spatial + two spectral) correlated spectroscopic imaging sequence for application to human calf. Nonuniform sampling was applied across the two phase encoded dimensions and the indirect spectral dimension of an echo planar-correlated spectroscopic imaging sequence. Reconstruction was applied that minimized the group sparse mixed ℓ2,1-norm of the data. Multichannel data were compressed using a sensitivity map-based approach with a spatially dependent transform matrix and utilized the self-sparsity of the individual coil images to simplify the reconstruction. Single channel data with 8× and 16× undersampling are shown in the calf of a diabetic patient. A 15-channel scan with 12× undersampling of a healthy volunteer was reconstructed using 5 virtual channels and compared to a fully sampled single slice scan. Group sparse reconstruction faithfully reconstructs the lipid cross peaks much better than ℓ1 minimization. COSY spectra can be acquired over a 3D spatial volume with scan time under 15 min using echo planar readout with highly undersampled data and group sparse reconstruction.

Group Sparse Reconstruction of Multi-Dimensional Spectroscopic Imaging in Human Brain in vivo

Four-dimensional (4D) Magnetic Resonance Spectroscopic Imaging (MRSI) data combining 2 spatial and 2 spectral dimensions provides valuable biochemical information in vivo; however, its 20–40 min acquisition time is too long to be used for a clinical protocol. Data acquisition can be accelerated by non-uniformly under-sampling (NUS) the ky− t1 plane, but this causes artifacts in the spatial-spectral domain that must be removed by non-linear, iterative reconstruction. Previous work has demonstrated the feasibility of accelerating 4D MRSI data acquisition through NUS and iterative reconstruction using Compressed Sensing (CS), Total Variation (TV), and Maximum Entropy (MaxEnt) reconstruction. Group Sparse (GS) reconstruction is a variant of CS that exploits the structural sparsity of transform coefficients to achieve higher acceleration factors than traditional CS. In this article, we derive a solution to the GS reconstruction problem within the Split Bregman iterative framework that uses arbitrary transform grouping patterns of overlapping or non-overlapping groups. The 4D Echo-Planar Correlated Spectroscopic Imaging (EP-COSI) gray matter brain phantom and in vivo brain data are retrospectively under-sampled 2×, 4×, 6×, 8×, and 10___ and reconstructed using CS, TV, MaxEnt, and GS with overlapping or non-overlapping groups. Results show that GS reconstruction with overlapping groups outperformed the other reconstruction methods at each NUS rate for both phantom and in vivo data. These results can potentially reduce the scan time of a 4D EP-COSI brain scan from 40 min to under 5 min in vivo.

SU‐E‐I‐32: Improving Vessel Delineation in Brain Using Susceptibility Weighted MRI and Group Sparse Reconstruction

Purpose:To optimize small vessel delineation on non‐contrast enhanced susceptibility weighted MRI protocol for MRI guided intervention in the brain.Methods:Multiple 5mm slices of the brain in a healthy volunteer were acquired with a 16‐echo gradient echo sequence and a 32 channel head coil on a 3T scanner. K‐space was under‐sampled by a factor of 2. Images were reconstructed using 1) the vendor ASSET algorithm, 2) sparsity enforcing TV regularization applied to each slice and echo individually, and 3) group sparse reconstruction on each slice individually but all echoes simultaneously. The group sparse reconstruction increases the signal‐tonoise ratio SNR of later echoes by utilizing the shared edges of brain structure between the echoes, which include the blood vessels. Quantitative PPM maps are computed from the complex images and are post processed by a method that removes background off‐resonance effects. Magnitude images and corrected PPM maps are compared.Results:PPM maps show blood vessels with high contrast. The magnitude images and ppm maps using method 1 appear blurry compared to methods 2 and 3 because of anti‐ringing filters. While small vasculatures appear very sharp in the ppm maps of methods 2 and 3, method 3 appears to have less smoothed magnitude images.Conclusion:To obtain useful blood vessel delineation, low noise susceptibility weighted images are needed. Standard methods like SWI or SWAN require the combination of several slices using a minimum intensity projection to delineate vessels. The method considered here delineates vasculature with high spatial resolution and high SNR in a single slice. Iterative reconstruction methods have superior image quality but also require much more computation time. By reconstructing all echoes simultaneously, group sparse reconstruction produces the sharpest and clearest images.

Group sparse reconstruction for image segmentation

Image segmentation is a fundamental problem in computer vision and image analysis. Specially, the segmentation of medical images can assist doctors in making decisions. Due to the lack of distinctive features to describe the boundary of an organ and match function with high performance for features, medical image segmentation is difficult to be achieved with high accuracy. In this paper, an one-class classifier is proposed as the match function to decide whether the pixel belongs to the boundary or not. The proposed method is comprised of two steps. At first, a feature vector space is built with the gradient feature and its statistical information in the training stage. In the test image, a feature vector of one candidate probably being located on the boundary is reconstructed by sparse coding with the feature vector space. After reconstruction, the candidate is classified belonging to boundary or non-boundary via the reconstruction based one-class classifier. Then, in order to maintain the consistency between the candidates which are neighbors to each other, the neighboring candidates are coded using group lasso with the same dictionary. Compared to the traditional methods, the proposed one has three advantages. Firstly, it solves the non-Gaussian distribution problem of the positive samples. Secondly, it avoids large variation among the negative samples. Thirdly, the relationship of the neighboring candidates is considered and used in classification, which is ignored in other methods. The proposed method is validated on 52 MR images of prostate and outperforms Mahalanobis distance, which is considered as one of the state-of-the-art match functions. The experimental results show that the segmentation accuracy can be significantly improved by the proposed method with one-class classification.

A Greedy Multistage Convex Relaxation Algorithm Applied to Structured Group Sparse Reconstruction Problems Based on Iterative Support Detection

We propose a new effective algorithm for recovering a group sparse signal from very limited observations or measured data. As we know that a better reconstruction quality can be achieved when encoding more structural information besides sparsity, the commonly employedl2,1-regularization incorporating the prior grouping information has a better performance than the plainl1-regularized models as expected. In this paper we make a further use of the prior grouping information as well as possibly other prior information by considering a weightedl2,1model. Specifically, we propose a multistage convex relaxation procedure to alternatively estimate weights and solve the resulted weighted problem. The procedure of estimating weights makes better use of the prior grouping information and is implemented based on the iterative support detection (Wang and Yin, 2010). Comprehensive numerical experiments show that our approach brings significant recovery enhancements compared with the plainl2,1model, solved via the alternating direction method (ADM) (Deng et al., 2013), either in noiseless or in noisy environments.

A Continuous Biomedical Signal Acquisition System Based on Compressed Sensing in Body Sensor Networks

The emerging compressed sensing (CS) holds considerable promise for continuously acquiring biomedical signals in body sensor networks (BSNs), which enables nodes to employ a much lower sampling rate than Nyquist while still able to accurately reconstruct signals. CS-based BSNs are expected to significantly enhance the quality of healthcare and improve the ability of prevention, early diagnosis, and treatment of chronic diseases. However, existing BSNs are still unable to support long-term monitoring in healthcare, as well as providing an energy-efficient low communication burden and inexpensive scheme. Capitalizing on the sparsity of biomedical signals in transfer domains, this paper develops a continuous biomedical signal acquisition system, which explores a sparsification model to find the sparse representation of biomedical signals. The sparsified measurements of signals are wirelessly transmitted to a fusion center through BSNs. Meanwhile, a weighted group sparse reconstruction algorithm is proposed to accurately reconstruct the signals at the fusion center. Simulation results show that, on random sampling over BSN, the proposed group sparse algorithm shows good efficiency, strong stability, and robustness.

Compressed sensing CPMG with group‐sparse reconstruction for myelin water imaging

Myelin content is a marker for nervous system pathology and is quantifiable by myelin water imaging using multi-echo CPMG sequence, which is inherently slow. One way to accelerate the scan is to utilize compressed sensing. However, reconstructing the images piecemeal by standard compressed sensing methods is not the optimal solution, because it only exploits intraimage spatial redundancy. It does not recognize that the different T2 weighted images are scans of the same anatomical volume and hence correlated. The purpose of this work is to test the feasibility of compressed sensed CPMG with group-sparsity promoting optimization for myelin water imaging. Group-sparse reconstruction was performed at various simulated and actual undersampling factors for an electronic phantom, ex vivo rat spinal cord, and in vivo rat spinal cord. Normalized mean square error was used as the metric for comparison. For both simulated undersampling and the actual undersampling, the method was found to minimally impact myelin water fraction map quality (normalized mean square error < 0.25) when acceleration factor was below two. Compressed sensed CPMG with group-sparse reconstruction is useful for achieving a shorter scan time than traditionally possible.

Group sparse reconstruction using intensity-based clustering

Compressed sensing has been of great interest to speed up the acquisition of MR images. The k-t group sparse (k-t GS) method has recently been introduced for dynamic MR images to exploit not just the sparsity, as in compressed sensing, but also the spatial group structure in the sparse representation. k-t GS achieves higher acceleration factors compared to the conventional compressed sensing method. However, it assumes a spatial structure in the sparse representation and it requires a time consuming hard-thresholding reconstruction scheme. In this work, we propose to modify k-t GS by incorporating prior information about the sorted intensity of the signal in the sparse representation, for a more general and robust group assignment. This approach is referred to as group sparse reconstruction using intensity-based clustering. The feasibility of the proposed method is demonstrated for static 3D hyperpolarized lung images and applications with both dynamic and intensity changes, such as 2D cine and perfusion cardiac MRI, with retrospective undersampling. For all reported acceleration factors the proposed method outperforms the original compressed sensing method. Improved reconstruction over k-t GS method is demonstrated when k-t GS assumptions are not satisfied. The proposed method was also applied to cardiac cine images with a prospective sevenfold acceleration, outperforming the standard compressed sensing reconstruction.