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This paper concerns the sparse Bayesian learning (SBL) problem for group sparse signals. Group sparsity means that the signal coefficients can be divided into groups and that the entries in one group are simultaneously zero or nonzero. In SBL, each group is controlled by a hyperparameter, which is estimated by solving the marginal likelihood maximization (MLM) problem. MLM is used to maximize the marginal likelihood of a given hyper-parameter by fixing all others. The main contribution of this paper is to extend the fast marginal likelihood maximization (FMLM) method to the group sparsity case. The key process of realizing FMLM in the group sparsity case is solved by finding the roots of a polynomial. Hence, the local maximum of the marginal likelihood can be found exactly, and the final estimation is obtained more efficiently. Furthermore, most large matrix inverses involved in MLM are replaced with the eigenvalue decompositions of much smaller matrices, which substantially reduces the computational complexity. Numerical results with both simulated and real data demonstrate the excellent performance and relatively high computational efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

Compressive sensing (CS) provides a new perspective for data reduction without compromising performance when the signal of interest is sparse or has intrinsically low-dimensional structure. The theoretical foundation for most of the existing studies on CS is based on the stable embedding (i.e., a distance-preserving property) of vectors that are sparse or in a union of subspaces via random measurement matrices. To the best of our knowledge, few existing literatures of CS have clearly discussed the stable embedding of linear subspaces via compressive measurement systems. In this paper, we explore a volume-based stable embedding of multidimensional signals based on Grassmann manifold, via Gaussian random measurement matrices. The Grassmann manifold is a topological space, in which each point is a linear vector subspace, and is widely regarded as an ideal model for multidimensional signals generated from linear subspaces. In this paper, we formulate the linear subspace spanned by multidimensional signal vectors as points on the Grassmann manifold, and use the volume and the product of sines of principal angles (also known as the product of principal sines) as the generalized norm and distance measure for the space of Grassmann manifold. We prove a volume-preserving embedding property for points on the Grassmann manifold via Gaussian random measurement matrices, i.e., the volumes of all parallelotopes from a finite set in Grassmann manifold are preserved upon compression. This volume-preserving embedding property is a multidimensional generalization of the conventional stable embedding properties, which only concern the approximate preservation of lengths of vectors in certain unions of subspaces. In addition, we use the volume-preserving embedding property to explore the stable embedding effect on a generalized distance measure of Grassmann manifold induced from volume. It is proved that the generalized distance measure, i.e., the product of principal sines between different points on the Grassmann manifold, is well preserved in the compressed domain via Gaussian random measurement matrices. Numerical simulations are also provided for validation. [ABSTRACT FROM AUTHOR]

Based on the linear relationship between the chirp rate of cross-range inverse synthetic aperture radar (ISAR) signal and the slant range, a parametric sparse representation method is proposed for ISAR imaging of rotating targets. The ISAR echo is formulated as a parametric joint-sparse signal and the chirp rates at all range bins are estimated by maximizing the contrast of sparse ISAR image. Comparing with homologous algorithms, the computational complexity of the proposed method is significantly reduced. [ABSTRACT FROM AUTHOR]

Random stepped frequency (RSF) radar, which transmits random-frequency pulses, can suppress the range ambiguity, improve convert detection, and possess excellent electronic counter-countermeasures (ECCM) ability [1]. In this paper, we apply a sparse recovery method to estimate the range and Doppler of targets. We also propose a cognitive mechanism for RSF radar to further enhance the performance of the sparse recovery method. The carrier frequencies of transmitted pulses are adaptively designed in response to the observed circumstance. We investigate the criterion to design carrier frequencies, and efficient methods are then devised. Simulation results demonstrate that the adaptive frequency-design mechanism significantly improves the performance of target reconstruction in comparison with the nonadaptive mechanism. [ABSTRACT FROM AUTHOR]

It has been shown in the literature that, the inverse synthetic aperture radar (ISAR) echo can be seen as sparse and the ISAR imaging can be implemented by sparse recovery approaches. In this paper, we propose a new parametric weighted L1 minimization algorithm for ISAR imaging based on the parametric sparse representation of ISAR signals. Since the basis matrix used for sparse representation of ISAR signals is determined by the unknown rotation parameter of a moving target, we have to estimate both the ISAR image and basis matrix jointly. The proposed algorithm can adaptively refine the basis matrix to achieve the best sparse representation for the ISAR signals. Finally the high-resolution ISAR image is obtained by solving a weighted L1 minimization problem. Both numerical and real experiments are implemented to show the effectiveness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

Abstract: Space–time adaptive processing (STAP) is a well-known technique in detecting slow-moving targets in the clutter-spreading environment. When considering the STAP system with conformal radar array (CFA), the training data are range-dependent, which results in poor detection performance of traditional statistical-based algorithms. Current registration-based compensation (RBC) is implemented based on a sub-snapshot spectrum using temporal smoothing. In this case, the estimation accuracy of the configuration parameters and the clutter power distribution is limited. In this paper, the technique of sparse representation is introduced into the spectral estimation, and a new compensation method is proposed, namely RBC with sparse representation (SR-RBC). This method first establishes the relationship between the clutter covariance matrix (CCM) and the clutter spectral distribution. Based on this, it avoids the problem of lacking stationary training data and converts the CCM estimation into the solving of the underdetermined equation only with the test cell. Then sparse representation method, like iterative reweighted least square (IRLS) is used to guide the solution of the underdetermined equation towards the actual clutter distribution. Finally, the transform matrix is designed using the CCM estimation so that the processed training data behaves nearly stationary with the test cell. Because the configuration parameters and the clutter spectral response are obtained with full-snapshot using sparse representation, SR-RBC provides more accurate clutter spectral estimation, and the transformed training data are more stationary so that better signal-clutter-ratio (SCR) improvement is achieved. [Copyright &y& Elsevier]

Abstract: In the field of space–time adaptive processing (STAP), direct data domain (D3) methods avoid non-stationary training data and can effectively suppress the clutter within the test cell. However, this benefit comes at the cost of a reduced system degree of freedom (DOF), which results in performance loss. In this paper, by exploiting the intrinsic sparsity of the spectral distribution, a new direct data domain approach using sparse representation (D3SR) is proposed, which seeks to estimate the high-resolution space–time spectrum only with the test cell. The simulation of both side-looking and non-side-looking cases has illustrated the effectiveness of the D3SR spectrum estimation using focal underdetermined system solution (FOCUSS) and L1 norm minimization. Then the clutter covariance matrix (CCM) and the corresponding adaptive filter can be effectively obtained. D3SR maintains the full system DOF so that it can achieve better performance of output signal-clutter-ratio (SCR) and minimum detectable velocity (MDV) than current D3 methods, e.g., direct data domain least squares (D3LS). Therefore D3SR can deal with the non-stationary clutter scenario more effectively, where both the discrete interference and range-dependent clutter exists. [Copyright &y& Elsevier]