Sparse Learning Via Iterative Minimization Research Articles

Space-Time Adaptive Processing Based on Modified Sparse Learning via Iterative Minimization for Conformal Array Radar.

Space-time adaptive processing (STAP) is a well-known technique for slow-moving target detection in the clutter spreading environment. For an airborne conformal array radar, conventional STAP methods are unable to provide good performance in suppressing clutter because of the geometry-induced range-dependent clutter, non-uniform spatial steering vector, and polarization sensitivity. In this paper, a knowledge aided STAP method based on sparse learning via iterative minimization (SLIM) combined with Laplace distribution is proposed to improve the STAP performance for a conformal array. The proposed method can avoid selecting the user parameter. the proposed method constructs a dictionary matrix that is composed of the space-time steering vector by using the prior knowledge of the range cell under test (CUT) distributed in clutter ridge. Then, the estimated sparse parameters and noise power can be used to calculate a relatively accurate clutter plus noise covariance matrix (CNCM). This method could achieve superior performance of clutter suppression for a conformal array. Simulation results demonstrate the effectiveness of this method.

Parameter Estimation in PMCW MIMO Radar Systems With Few-Bit Quantized Observations

We consider the problem of target parameter estimation in phase modulated continuous wave (PMCW) multiple-input multiple-output (MIMO) radar systems with quantized observations. We derive the Cramér-Rao bound (CRB) for jointly estimating targets’ amplitudes, time delays, Doppler shifts, and directions. The derived bound provides an efficient method to analyze the estimation performance achieved by different quantization schemes. We also devise the maximum likelihood (ML) estimator for the considered parameters, and a direct grid-based method (DGM) is introduced to obtain the ML estimates. To obtain the ML estimates more efficiently, a two-stage scheme is proposed. In the proposed scheme, we first formulate the estimation problem as a sparse signal recovery problem and modify the sparse learning via iterative minimization (SLIM) approach to solve it. Next, a RELAX-based iterative algorithm is proposed to refine the estimates. Simulation results show that the proposed scheme can approach the CRB. Simulation results also show that using quantized observations does not affect the estimation performance significantly when the targets’ amplitudes are similar.

Estimation of Complex High-Resolution Range Profiles of Ships by Sparse Recovery Iterative Minimization Method

It is always an important problem to recover sparse signals from observations corrupted by Gaussian noise and has been extensively investigated. In high-resolution maritime surveillance radars working at scan mode, ship classification, and recognition need to recover high-resolution range profiles (HRRPs) of ships from radar returns of several pulses with severe range sidelobe effect. Multipulse synthetic data by the aid of ship Doppler information are complex sparse signals corrupted by non-Gaussian correlated interference. In this article, a sparse recovery via iterative minimization (SRIM) method is proposed to estimate complex HRRPs of ships from multipulse synthetic data. The SRIM method adapts the non-Gaussianity nature of the interference in the multipulse synthetic data and ship complex HRRPs are modeled by the random sequences of the biparametric generalized Gaussian distributions (GGDs) (0 < <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> ≤ 1). In the SRIM method, the parameters of the GGD model are iteratively searched by the minimal criterion of the Kolmogorov–Smirnov distance of the residue and the interference model. The SRIM method is compared with the recent linear-programming-based method and the classic sparse learning via iterative minimization (SLIM) method by using simulated and measured radar data and the results show that the SRIM method obtains the better performance.

Analysis and Evaluation of Data-Adaptive Spectral Estimation Algorithms for Processing MST Radar Data

The National Atmospheric Research Laboratory (NARL) situated at Gadanki, Andhra Pradesh, constitutes the primary source for Indian MST radar data (Mesosphere-Stratosphere-Troposphere). The primary purpose of the MST radar is to analyze and explore the atmospheric dynamics. The MST radar is developed with an array antenna in the active phase and consists of 1024 Yagi-Uda antennas being operated at a frequency of 53 MHz. The NARL provides atmospheric wind data by using MST radar. The wind speed parameters are calculated from the radar echo signals by using spectral estimation. In this paper, the analysis and evaluation of data-adaptive spectral estimation algorithms namely nonparametric iterative adaptive approach (IAA) and semiparametric methods—sparse learning via iterative minimization (SLIM) and sparse iterative covariance-based estimation (SPICE)—have been presented. These algorithms exhibit high resolution and low sidelobe levels. The detectability of the radar signals is improved at low signal-to-noise (SNR) conditions. The zonal speed (U), meridional speed (V) and wind speed (W) are computed and are validated using the Global Positioning System (GPS) radiosonde data. From the results, the SPICE algorithm outperforms the other two data-adaptive algorithms and the existing periodogram method.

High-Resolution Multiple-Input Multiple-Ouput FLGPR Imaging

Multiple-input multiple-output forward-looking ground-penetrating radar (GPR) systems can be used to detect landmines. To enhance its performance, two data-dependent imaging algorithms, based on the sparse learning via iterative minimization (SLIM) and sparse covariance-based estimation (SPICE) techniques for high-resolution imaging, applied to the time-domain GPR data, were previously developed. Time-domain SLIM (TD-SLIM) and time-domain SPICE (TD-SPICE) yield higher resolution and lower sidelobe compared with data-independent approaches such as delay-and-sum and recursive sidelobe minimization. However, the two data-dependent imaging algorithms are computationally expensive. To provide both improved landmine detection performance and significantly reduced computational time compared with the TD-SLIM and TD-SPICE algorithms, we propose herein the frequency-domain SLIM algorithm.

Adaptive Range-Doppler Imaging and Target Parameter Estimation in Multistatic Active Sonar Systems

Multistatic active sonar systems involve the transmission and reception of multiple probing sequences. Since the multiple simultaneously transmitted probing sequences act as interferences to one another, adaptive receiver filters are needed for interference suppression and for target range-Doppler imaging. Two adaptive receiver designs, namely, the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) method, are considered for range-Doppler imaging via multistatic active sonar. The so-obtained range-Doppler images allow us to further estimate the target parameters. Specifically, we use the popular quasi-Newton method for target position estimation and the least squares (LS) fitting approach for target velocity determination. The effectiveness of the proposed multistatic active sonar signal processing techniques is verified using numerical examples.

On Bayesian Channel Estimation and FFT-Based Symbol Detection in MIMO Underwater Acoustic Communications

Reliable channel estimation and effective interference cancellation are essential for enhancing the performance of multiple-input-multiple-output (MIMO) underwater acoustic communication (UAC) systems. In this paper, an efficient user-parameter-free Bayesian approach, referred to as sparse learning via iterative minimization (SLIM), is presented. SLIM provides good channel estimation performance along with reduced computational complexity compared to iterative adaptive approach (IAA). Moreover, RELAX-BLAST, which is a linear minimum mean-squared error (MMSE)-based symbol detection scheme, is implemented efficiently by making use of the conjugate gradient (CG) method and diagonalization properties of circulant matrices. The proposed algorithm requires only simple fast Fourier transform (FFT) operations and facilitates parallel implementations. These MIMO UAC techniques are evaluated using both simulated and in-water experimental examples. The 2008 Surface Processes and Acoustic Communications Experiment (SPACE08) experimental results show that the proposed MIMO UAC schemes can enjoy almost error-free performance even under severe ocean environments.

Moving Target Imaging for MIMO Radar Using CS-SLIM

Multiple-input Multiple-output (MIMO) radar can achieve superior performance through waveform diversity over conventional phased-array radar systems. Many methods were proposed to provide accurate MIMO angle-range-Doppler images of moving targets. Sparse Learning via Iterative Minimization (SLIM) can provide more accurate estimates in that case. However, when using the Bayesian Information Criterion (BIC) to determine the user parameter automatically for a less sparse scene, SLIM has high complexity. In this paper, we propose an improved approach as Sparse Learning via Iterative Minimization based on Compressive Sampling (CS-SLIM) for targets imaging. CS-SLIM can provide targets imaging as almost accurate as but with a lower computational burden than SLIM. The measurement matrix and the computational complexity for CS-SLIM are discussed. Mean Squared Errors (MSEs) at various measurement samples are provided to demonstrate the performance of the proposed approach in sparse scenes

Wideband source localization using sparse learning via iterative minimization

In this paper, two extensions of the Sparse Learning via Iterative Minimization (SLIM) algorithm are presented for wideband source localization using a sensor array. The proposed methods exploit the joint sparse structure across all frequency bins, and estimate the spatial pseudo-spectra at various frequency bins jointly and iteratively. Via several numerical examples, we show that the proposed methods can provide high-resolution angle estimates and excellent source localization performance, and are able to resolve the left–right ambiguity problem, when used together with the vector sensor array technology.

Non-Parametric High-Resolution SAR Imaging

The development of high-resolution two-dimensional spectral estimation techniques is of notable interest in synthetic aperture radar (SAR) imaging. Typically, data-independent techniques are exploited to form the SAR images, although such approaches will suffer from limited resolution and high sidelobe levels. Recent work on data-adaptive approaches have shown that both the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) algorithm offer excellent performance with high-resolution and low side lobe levels for both complete and incomplete data sets. Regrettably, both algorithms are computationally intensive if applied directly to the phase history data to form the SAR images. To help alleviate this, efficient implementations have also been proposed. In this paper, we further this work, proposing yet further improved implementation strategies, including approaches using the segmented IAA approach and the approximative quasi-Newton technique. Furthermore, we introduce a combined IAA-MAP algorithm as well as a hybrid IAA- and SLIM-based estimation scheme for SAR imaging. The effectiveness of the SAR imaging algorithms and the computational complexities of their fast implementations are demonstrated using the simulated Slicy data set and the experimentally measured GOTCHA data set.

Computationally efficient sparsity-inducing coherence spectrum estimation of complete and non-complete data sets

The magnitude squared coherence (MSC) spectrum is an often used frequency-dependent measure for the linear dependency between two stationary processes, and the recent literature contain several contributions on how to form high-resolution data-dependent and adaptive MSC estimators, and on the efficient implementation of such estimators. In this work, we further this development with the presentation of computationally efficient implementations of the recent iterative adaptive approach (IAA) estimator, present a novel sparse learning via iterative minimization (SLIM) algorithm, discuss extensions to two-dimensional data sets, examining both the case of complete data sets and when some of the observations are missing. The algorithms further the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices, extending these formulations to the coherence estimation using IAA and SLIM formulations. The performance of the proposed algorithms and implementations are illustrated both with theoretical complexity measures and with numerical simulations.

Nonparametric Missing Sample Spectral Analysis and Its Applications to Interrupted SAR

We consider nonparametric adaptive spectral analysis of complex-valued data sequences with missing samples occurring in arbitrary patterns. We first present two high-resolution missing-data spectral estimation algorithms: the Iterative Adaptive Approach (IAA) and the Sparse Learning via Iterative Minimization (SLIM) method. Both algorithms can significantly improve the spectral estimation performance, including enhanced resolution and reduced sidelobe levels. Moreover, we consider fast implementations of these algorithms using the Conjugate Gradient (CG) technique and the Gohberg-Semencul-type (GS) formula. Our proposed implementations fully exploit the structure of the steering matrices and maximize the usage of the fast Fourier transform (FFT), resulting in much lower computational complexities as well as much reduced memory requirements. The effectiveness of the adaptive spectral estimation algorithms is demonstrated via several numerical examples including both 1-D spectral estimation and 2-D interrupted synthetic aperture radar (SAR) imaging examples.

Probing waveforms and adaptive receivers for active sonar

Active sonar systems involve the transmission and reception of one or more probing sequences, which provide a basis for extraction of target information in a region of interest. The probing sequences at the transmitter and signal processing at the receiver play crucial roles in the overall system performance. In this paper, CAN (cyclic algorithm-new) is employed to synthesize probing sequences with good aperiodic autocorrelation properties. The performance of the CAN sequences will be compared with those of pseudo random noise and random phase sequences. Two adaptive receiver designs, namely the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) method, will also be considered. IAA and SLIM will be compared with the conventional matched filter method. The performances of the algorithms will be illustrated via numerical examples, which show that CAN, IAA, and SLIM can contribute to the overall performance improvement of the active sonar systems.

Sparse Learning via Iterative Minimization With Application to MIMO Radar Imaging

Through waveform diversity, multiple-input multiple-output (MIMO) radar can provide higher resolution, improved sensitivity, and increased parameter identifiability compared to more traditional phased-array radar schemes. Existing methods for target estimation, however, often fail to provide accurate MIMO angle-range-Doppler images when there are only a few data snapshots available. Sparse signal recovery algorithms, including many <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$l_{1}$</tex></formula> -norm based approaches, can offer improved estimation in that case. In this paper, we present a regularized minimization approach to sparse signal recovery. Sparse learning via iterative minimization (SLIM) follows an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$l_{q}$</tex></formula> -norm constraint (for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$0&lt;q\leq 1$</tex></formula> ), and can thus be used to provide more accurate estimates compared to the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$l_{1}$</tex></formula> -norm based approaches. We herein compare SLIM, through imaging examples and examination of computational complexity, to several well-known sparse methods, including the widely used CoSaMP approach. We show that SLIM provides superior performance for sparse MIMO radar imaging applications at a low computational cost. Furthermore, we will show that the user parameter <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex></formula> can be automatically determined by incorporating the Bayesian information criterion.