Sparse Recovery Methods Research Articles

Joint estimation of DOA and channel errors with sparse recovery for SKA low‐frequency array

Here, the authors present an improved and fast sparse recovery method for joint estimation of channel errors and direction of arrival (DOA) for square kilometre antennas low-frequency array. Since this array is formed of a large number of antennas and distributed in a very large space, array calibration is a vital step to provide accurate signal information. Then, channel errors are the concerns here, which are assumed to be localised in a priori known interval. To achieve the joint estimation, an approach is proposed by using the alternative optimisation strategy, which theoretically gives convergence results. In detail, the basis pursuit de-noising (BPDN) algorithm and the proximal algorithm are used to estimate the DOA and the array errors, respectively, and the final results are obtained by alternatively solving these two algorithms. Finally, numerical simulation results are presented to demonstrate the effectiveness of their proposed method.

Proposal of a Geometric Calibration Method Using Sparse Recovery to Remove Linear Array Push-Broom Sensor Bias.

The rational function model (RFM) is widely used in the most advanced Earth observation satellites, replacing the rigorous imaging model. The RFM method achieves the desired calibration performance when image distortion is caused by long-period errors. However, the calibration performance of the RFM method deteriorates when short-period errors—such as attitude jitter error—are present, and the insufficient and uneven ground control points (GCPs) can also lower the calibration precision of the RFM method. Hence, this paper proposes a geometric calibration method using sparse recovery to remove the linear array push-broom sensor bias. The most important issue regarding this method is that the errors related to the imaging process are approximated to the equivalent bias angles. By using the sparse recovery method, the number and distribution of GCPs needed are greatly reduced. Meanwhile, the proposed method effectively removes short-period errors by recognizing periodic wavy patterns in the first step of the process. The image data from Earth Observing 1 (EO-1) and the Advanced Land Observing Satellite (ALOS) are used as experimental data for the verification of the calibration performance of the proposed method. The experimental results indicate that the proposed method is effective for the sensor calibration of both satellites.

Super-resolution ISAR imaging based on the modified iterative reweighted approach

High-resolution inverse synthetic aperture radar (ISAR) imaging of fast rotating targets is a complicated task. Targets’ fast rotational motion always introduces migration through range cells (MTRC) when we use the conventional range Doppler algorithm. We mainly focus on the ISAR imaging of a fast rotating target. In that case, the samples in the cross-range dimension are insufficient, which is the undersampling case. Compressed sensing-based ISAR imaging methods are generally faced with the problem of basis mismatch, which may degrade the ISAR image. A two-dimensional iterative reweighted super-resolution algorithm is proposed by iteratively decreasing a surrogate function. We also compared the performance of the proposed method with other state-of-the-art sparse recovery methods. Simulation results show that the proposed method can achieve the high-resolution ISAR imaging of fast rotating targets. Moreover, the MTRC and the basis mismatch problems can be effectively solved.

Compressive spectral imaging with diffractive lenses.

Compressive spectral imaging enables the reconstruction of an entire 3D spectral cube from a few multiplexed images. Here we develop a novel compressive spectral imaging technique using diffractive lenses. Our technique uses a coded aperture to spatially modulate the optical field from the scene and a diffractive lens such as a photon sieve for both dispersion and focusing. Measurement diversity is achieved by changing the focusing behavior of the diffractive lens. The 3D spectral cube is then reconstructed from highly compressed measurements taken with a monochrome detector. A fast sparse recovery method is developed to solve this large-scale inverse problem. The performance is illustrated for various scenarios with different compression ratios through simulations. The results demonstrate that promising reconstruction performance can be achieved at high compression levels. This opens up new possibilities for high-resolution spectral imaging with simpler and low cost designs.

One-Bit Compressive Radar Sensing in the Presence of Clutter

We propose a compressive pulse-Doppler radar that works through one-bit quantization of the received noisy signal by comparing it with a time-varying reference level. Considering the sparsity of the targets in the range-Doppler domain, we solve the problem by sparse recovery methods in both the absence and presence of clutter. The proposed method leads to an optimization problem that can be tackled by a convex approximation. Numerical examples confirm the effectiveness of the proposed method.

Methods for Sparse and Low-Rank Recovery under Simplex Constraints

The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The situation is analogous for the use of nuclear norm regularization for low-rank recovery of Hermitian positive semidefinite matrices with given trace. In the present paper, we discuss several strategies to deal with this situation, from simple to more complex. As a starting point, we consider empirical risk minimization (ERM). It follows from existing theory that ERM enjoys better theoretical properties w.r.t.~prediction and $\ell_2$-estimation error than $\ell_1$-regularization. In light of this, we argue that ERM combined with a subsequent sparsification step like thresholding is superior to the heuristic of using $\ell_1$-regularization after dropping the sum constraint and subsequent normalization. At the next level, we show that any sparsity-promoting regularizer under simplex constraints cannot be convex. A novel sparsity-promoting regularization scheme based on the inverse or negative of the squared $\ell_2$-norm is proposed, which avoids shortcomings of various alternative methods from the literature. Our approach naturally extends to Hermitian positive semidefinite matrices with given trace. Numerical studies concerning compressed sensing, sparse mixture density estimation, portfolio optimization and quantum state tomography are used to illustrate the key points of the paper.

A fast decoupled ISAR high-resolution imaging method using structural sparse information under low SNR

Inverse synthetic aperture radar (ISAR) image can be represented and reconstructed by sparse recovery (SR) approaches. However, the existing SR algorithms, which are used for ISAR imaging, have suffered from high computational cost and poor imaging quality under a low signal to noise ratio (SNR) condition. This paper proposes a fast decoupled ISAR imaging method by exploiting the inherent structural sparse information of the targets. Firstly, the ISAR imaging problem is decoupled into two sub-problems. One is range direction imaging and the other is azimuth direction focusing. Secondly, an efficient two-stage SR method is proposed to obtain higher resolution range profiles by using jointly sparse information. Finally, the residual linear Bregman iteration via fast Fourier transforms (RLBI-FFT) is proposed to perform the azimuth focusing on low SNR efficiently. Theoretical analysis and simulation results show that the proposed method has better performance to efficiently implement higher-resolution ISAR imaging under the low SNR condition.

Dynamic ISAR Imaging and Autofocusing of Maneuvering Targets Based on Sequential GP-SOONE Method and Eigenvalue Decomposition

A long coherent processing interval (CPI) is needed for achieving a high-resolution inverse synthetic aperture radar (ISAR) image. However, for a maneuvering target, the time-varying Doppler shifts cause a blurring effect on the ISAR image. Sparse representation-based algorithms can obtain a high-resolution image in a short CPI, while the Doppler shifts remain constant. Recently, a sequential order one negative exponential (SOONE) function has been introduced to measure the sparsity, and a gradient projection (GP) method has been used to solve the SOONE function and recover the sparse signal. In this paper, a 2D sequential GP-SOONE method for sparse recovery and dynamic ISAR imaging is proposed, which has a lower computational complexity than that of the 2D-GP-SOONE algorithm. Moreover, the performance of the proposed approach is the same as the 2D-GP-SOONE and better than the 2D smoothed L0 algorithm. Another problem of dynamic ISAR imaging is sequentially autofocusing the image. Hence, a fast parametric method based on eigenvalue decomposition and minimum entropy for dynamic ISAR autofocusing is proposed which has a faster convergence than the conventional methods. The proposed method has also comparable performance with the conventional ones. Several simulations and real data are used to show the superiority of the proposed methods.

Reconstruction of jointly sparse vectors via manifold optimization

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This result reveals a reduction in the computational complexity of the original problem and enables a simple implementation of joint sparse recovery algorithms for full-rank setting. Secondly, we propose a new method for joint sparse recovery in the form of a non-convex optimization problem on a non-compact Stiefel manifold. In our numerical experiments our method outperforms the commonly used ℓ2,1 minimization in the sense that much fewer measurements are required for accurate sparse reconstructions. We postulate this approach possesses the desirable rank aware property, that is, being able to take advantage of the rank of the unknown matrix to improve the recovery.

Exploiting Channel Crosstalk for Polarimetric SAR Compressive Sensing

We propose a new compressive sensing scheme that enables fully polarimetric radar imaging from a subset of channel measurements. Previous sparse recovery methods for polarimetric radar have not modeled channel coupling. We recognize that mixing of information through coupling is key to dropping a channel. Our method complements fast and slow time sampling and may reduce hardware and communications costs. This paper provides the signal model and examples of successful four-channel recovery when only three are measured.

Evolutionary algorithms for sparse signal reconstruction

This study includes an evolutionary algorithm technique for sparse signal reconstruction in compressive sensing. In general, l1 minimization and greedy algorithms are used to reconstruct sparse signals. In addition to these methods, recently, heuristic algorithms have begun to be used to reconstruct sparse signals. Heuristic algorithms are used in the field of compressive sensing by creating a hybrid structure with other methods or by optimizing the problem of sparse signal reconstruction on its own. This proposed method for evolutionary algorithms has a strategy similar to the sparse signal recovery method of greedy algorithms used in compressive sensing. In addition, this method has been applied for genetic and differential evolution algorithms. Firstly, the reconstruction performance of genetic and differential evolution algorithms is compared among each other. And then, the reconstruction performance of them is compared with l1 minimization method and greedy approaches. As a result from these studies, the proposed method for genetic and differential evolution algorithms can be used as the sparse signal recovery algorithm.

Dynamical sparse signal recovery with fixed-time convergence

Arising in a large number of application areas, sparse recovery (SR) has been exhaustively investigated and many algorithms have been proposed. Different from the numerical methods realized by iterative algorithm, the recent continuous approach is realized through analog circuit, which takes advantage of short time-delay and fast convergence. However, the existing continuous method for SR still has the space to further improve the convergence speed. Consequently, in this paper, we propose a new dynamical continuous system to solve the sparse signal recovery problem with fixed-time convergence property.

BreathTrack: Tracking Indoor Human Breath Status via Commodity WiFi

In this paper, we propose a contact-free breath tracking system, BreathTrack, to track the status of breath using the off-the-shelf WiFi devices. BreathTrack exploits the phase variation of the channel state information (CSI) to track human breath. To resolve the phase distortions introduced by the hardware imperfection of the commodity WiFi chips, BreathTrack utilizes both the hardware and software correction methods. The time-invariant PLL phase offset is calibrated by the hardware correction using cables and splitters, while the time-varying carrier frequency offset, sampling frequency offset and packet detection delay are removed by the software corrections using the phase difference between the CSI at the receiver antennas and that at the reference antenna connected from the transmitter. Moreover, BreathTrack utilizes the sparse recovery method to find the dominant path in the multipath indoor environment and derive the corresponding complex attenuation coefficient. Then, the phase variation of the complex attenuation coefficient is utilized to extract the detailed breath status and the breath rate. Extensive experiments are conducted to show that BreathTrack could estimate the breath rate with the median accuracy of over 99% in most scenarios, and could track the detailed status of breath directly using the raw phase variation.

ADMM based low-rank and sparse matrix recovery method for sparse photoacoustic microscopy

Photoacoustic microscopy (PAM) has evolved into a new promising medical imaging tool available for both in vivo surficial and deep-tissue imaging with a high spatial resolution. However, the long data acquisition time has made real-time imaging highly challenging. This paper presents an Alternating Direction Method of Multipliers (ADMM) based low-rank and sparse matrix recovery method for a sparse optical-scanning PAM system to realize fast PAM vascular imaging.For our system, an x-y galvanometer scanner is used to achieve compressive sampling, and the associated image recovery process is formulated as a matrix completion problem. The sparse scanning scheme might be easy to integrate with several other optical-resolution PAM modalities. Further, the sparse constraint (the total variation norm) and the low-rank constraint (nuclear norm) are combined for solving the optimization program under ADMM framework for matrix recovery in order to achieve better PAM image recovery even for images that are not well-approximated by their low-rank components.A prototype PAM system has been implemented and the recovery method has been validated. From both visual effects and quantitative parameters, such as PSNR, SSIM, Rerr and MSE, comparable image qualities with conventional full sampling optical resolution PAM could be acquired by just half of the data acquisition time. Besides, the ADMM based low-rank and sparse matrix recovery method could show better results than GoDec. The obtained results demonstrate the preclinical and clinical potential of sparse PAM system in investigating vascular diseases.

Reweighted Regularized Sparse Recovery for DOA Estimation With Unknown Mutual Coupling

In this letter, the direction-of-arrival (DOA) estimation of uniform linear array under unknown mutual coupling is dealt with by proposing a reweighted regularized sparse recovery algorithm. The proposed method first formulates a block-sparse representation model without mutual coupling compensation and array aperture loss. Then, a reweighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization scheme is formulated to recover the block-sparse matrix, in which a weighted matrix is designed with a novel MUSIC-Like spectrum function for enhancing the sparsity of solution. Finally, the spatial spectrum of the recovered matrix is utilized to estimate DOAs. Due to using the whole array aperture and enhanced sparsity of solution, the proposed method can achieve superior performance than the existing regularized sparse recovery methods. Some simulation results are carried out to demonstrate the superiority of the proposed method.

Cascaded Interference and Multipath Suppression Method Using Array Antenna for GNSS Receiver

The space-time adaptive processing method has been widely used for both narrowband and wideband interference suppression in GNSS receiver equipped with array antenna. However, the use of space-time filter may cause satellite signal distortion and lead to bias in pseudo-range measurement. In addition, multipath is one of the main error sources that will have a serious influence on the performance of the GNSS receiver. For precise applications, the error induced by space-time filter and multipath should be reduced. In this paper, a cascaded interference and multipath suppression method using an array antenna are proposed. In the first stage, the interference is suppressed by projecting the received array signal into the interference orthogonal subspace using subspace projection method. In the second stage, the directions of arrival (DOA) of the direct signal and the multipath signal are estimated using sparse recovery method. The DOA parameters enable the receiver to construct a space-time distortionless beamformer, which is used to null the multipath signals and maximize the signal-to-noise ratio. The method does not require the prior knowledge of the direction of the direct signal and achieves unbiased measurement while suppressing the interference and multipath. The simulation results demonstrate that the proposed method can achieve the interference and multipath suppression effectively, and have a distortionless response for the direct signal.

Radio Frequency Interference Suppression for SAR via Block Sparse Bayesian Learning

Radio frequency interference (RFI) can severely degrade the image quality for synthetic aperture radar (SAR). Traditional sparse recovery-based RFI suppression methods construct a joint dictionary to represent both the time-domain RFI and the useful target echo (UTE), thus, transforming the task of RFI suppression into a signal recovery problem. However, these methods generally have poor performance when the one-dimensional (1-D) range profiles are nonsparse. To overcome this problem, two RFI suppression algorithms are proposed based on a modified block sparse Bayesian learning (BSBL). In the first algorithm, the vector to be recovered is divided into several blocks of identical size. The Bayesian hyper-parameters corresponding to the RFI and UTE are learned separately by exploiting the temporal intrablock correlation, and then the nonsparse vector can be successfully recovered. In the second algorithm, the dictionary is adaptively tuned during the iteration process of BSBL, thus reducing the computational load. After recovering the UTE, a well-focused 2-D image can be obtained by traditional SAR imaging algorithms. With the use of properties of both the RFI and UTE, and by exploiting the intrablock correlation, the proposed RFI suppression methods outperform other sparse recovery methods, especially when the range profile is nonsparse. Simulation results demonstrate the superior performance of the proposed algorithms.

An Improved Trilinear Model-Based Angle Estimation Method for Co-Prime Planar Arrays.

Angle estimation methods in two-dimensional co-prime planar arrays have been discussed mainly based on peak searching and sparse recovery. Peak searching methods suffer from heavy computational complexity and sparse recovery methods face some problems in selecting the regularization parameters. In this paper, we propose an improved trilinear model-based method for angle estimation for co-prime planar arrays in the view of trilinear decomposition, namely parallel factor analysis. Due to the principle of trilinear decomposition, our method does not require peak searching and can conduct auto-pairing easily, which can reduce the computational loads and avoid parameter selection problems. Furthermore, we exploit the virtual array concept of the whole co-prime planar array through the cross-correlation matrix obtained from the received signal data and present a matrix reconstruction method using the Khatri–Rao product to tackle the matrix rank deficiency problem in the virtual array condition. The simulation results show that our proposed method can not only achieve high estimation accuracy with low complexity compared to other similar approaches, but also utilize limited sensor number to implement the angle estimation tasks.

Sparsity-based time-frequency representation of FM signals with burst missing samples

Abstract In this paper, we present an effective time-frequency (TF) analysis of non-stationary frequency modulated (FM) signals in the presence of burst missing data samples. The key concept of the proposed work lies in the reliable sparse recovery of non-parametric FM signals in the joint-variable domains. Specifically, by utilizing the one-dimensional Fourier relationship between the instantaneous auto-correlation function (IAF) and the TF representation (TFR), the proposed approach iteratively recovers missing samples in the IAF domain through sparse reconstruction using, e.g., the orthogonal matching pursuit (OMP) method, while maintaining the TF-domain sparsity. The proposed method, referred to as missing data iterative sparse reconstruction (MI-SR), achieves reliable TFR recovery from the observed data with a high proportion of burst missing samples. This is in contrast to the existing sparse TFR recovery methods which work well only for random missing data samples. In particular, when applied in conjunction with signal-adaptive TF kernels, the proposed method achieves effective suppression of both cross-terms and artifacts due to burst missing samples. The superiority of the proposed technique is verified through analytical results and numerical examples.

A Noise Reduced Hard Thresholding method for Noisy Sparse Reconstruction

The problem of noisy sparse signal recovery has been studied in this paper. The generalized expectation maximization (GEM) algorithm provides solutions over state of the art convex relaxation methods for sparse signal recovery by considering the noisy measurements as missing data. However, in the case of images, artifacts in the reconstructed signal renders it to have low quality, especially based on qualitative performance metrics and so are unsuitable for further application specific processing. The problem may be reduced significantly by minimizing the total variation in the signal considering the constraints created by the statistics of noise in the reconstructed image. A modified iterative GEM for low noise reconstruction is presented and analyzed. Even though time consuming, simulations and numerical analysis show significantly higher performance metrics, especially PSNR and Structural Similarity, which imply reconstructed images may be suitable for further processing.