Huiping Duan

Pattern-Coupled Sparse Bayesian Learning for Inverse Synthetic Aperture Radar Imaging

We propose a pattern-coupled sparse Bayesian learning method for inverse synthetic aperture radar (ISAR) imaging by exploiting a block-sparse structure inherent in ISAR target images. A two-dimensional pattern-coupled hierarchical Gaussian prior is proposed to model the pattern dependencies among neighboring scatterers on the target scene. An expectation-maximization (EM) algorithm is developed to infer the maximum a posterior (MAP) estimate of the hyperparameters, along with the posterior distribution of the sparse signal. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.

Pattern-coupled sparse Bayesian learning for recovery of block-sparse signals

We consider the problem of recovering block-sparse signals whose cluster patterns are unknown a priori. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block partition is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. A pattern-coupled hierarchical Gaussian prior is introduced to characterize the pattern dependencies among neighboring coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients. The proposed hierarchical model is similar to that for the conventional sparse Bayesian learning. However, unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also its immediate neighbor hyperparameters. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters are learned by maximizing their posterior probability. We exploit an expectation-maximization (EM) formulation to develop an iterative algorithm that treats the signal as hidden variables and iteratively maximizes a lower bound on the posterior probability. In the M-step, a simple suboptimal solution is employed to replace a gradient-based search to maximize the lower bound. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.

Robust Bayesian compressed sensing with outliers

Abstract We consider the problem of robust compressed sensing where the objective is to recover a high-dimensional sparse signal from compressed measurements partially corrupted by outliers. A new sparse Bayesian learning method is developed for this purpose. The basic idea of the proposed method is to identify the outliers and exclude them from sparse signal recovery. To automatically identify the outliers, we employ a set of binary indicator variables to indicate which observations are outliers. These indicator variables are assigned a beta-Bernoulli hierarchical prior such that their values are confined to be binary. In addition, a Gaussian-inverse Gamma prior is imposed on the sparse signal to promote sparsity. Based on this hierarchical prior model, we develop a variational Bayesian method to estimate the indicator variables as well as the sparse signal. Simulation results show that the proposed method achieves a substantial performance improvement over existing robust compressed sensing techniques.

Fast Inverse-Free Sparse Bayesian Learning via Relaxed Evidence Lower Bound Maximization

Sparse Beyesian learning is a popular approach for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless, the sparse Bayesian learning algorithm involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size, which hinders its application to many practical problems even with moderately large datasets. To address this issue, in this letter, we develop a fast inverse-free sparse Bayesian learning method. Specifically, by invoking a fundamental property for smooth functions, we obtain a relaxed evidence lower bound (relaxed-ELBO) that is computationally more amiable than the conventional ELBO used by sparse Bayesian learning. A variational expectation-maximization (EM) scheme is then employed to maximize the relaxed-ELBO, which leads to a computationally efficient inverse-free sparse Bayesian learning algorithm. Simulation results show that the proposed algorithm has a fast convergence rate and achieves lower reconstruction errors than other state-of-the-art fast sparse recovery methods in the presence of noise.

Agent Identification Using a Sparse Bayesian Model

Identifying agents in a linear mixture is a fundamental problem in spectral sensing applications including chemical and biological agent identification. In general, the size of the spectral signature library is usually much larger than the number of agents really present. Based on this fact, the sparsity of the mixing coefficient vector can be utilized to help improve the identification performance. In this paper, we propose a new agent identification method by using a sparse Bayesian model. The proposed iterative algorithm takes into account the nonnegativity of the abundance fractions and is proved to be convergent. Numerical studies with a set of ultraviolet (UV) to infrared (IR) spectra are carried out for demonstration. The effect of the signature mismatch is also studied using a group of terahertz (THz) spectra.

Real-valued Khatri-Rao subspace approaches on the ULA and a new nested array

In underdetermined direction-of-arrival (DOA) estimation using the covariance-based signal models, the computational complexity turns into a noticeable issue because of the high dimension of the virtual array manifold. In this paper, real-valued Khatri-Rao (KR) approaches are developed on the uniform linear array (ULA) and the nested array. The complexities of subspace decomposition and spectral search are reduced compared with the complex-valued KR approach. By designing a special transformation matrix, the influence of the noise is removed in the mean time while the data is transformed from the complex domain to the real domain. Deploying the sensors with nonuniform spacings can raise the degree of freedom (DOF) and hence help detect more sources in the underdetermined situation. To increase the DOF further, a new nested array geometry is designed. The real-valued denoising KR approach developed on the new nested array can resolve more sources with reduced complexities. The performance improvement is demonstrated by numerical studies.

Off-grid DOA estimation using temporal block sparse Bayesian inference

By considering the off-grid distance in the sparse reconstruction model, off-grid direction-of-arrival (DOA) estimation can achieve better performance. Most existing off-grid algorithms consider that the snapshots of each source are independent with each other. This contradicts with the realworld scenario, where sources often have temporal structures. To address this issue, we present a new off-grid DOA estimation method, which brings the temporal structures into the off-grid model and a temporal block sparse Bayesian inference is derived. In comparison with the off-grid block sparse Bayesian inference method, the proposed approach achieves higher estimation accuracy for off-grid source directions in low SNR situations. Numerical simulations demonstrate the preferable performance of our method.

A new sparse Bayesian learning method for inverse synthetic aperture radar imaging via exploiting cluster patterns

The application of sparse representation to SAR/ISAR imaging has attracted much attention over the past few years. This new class of sparse representation based imaging methods present a number of unique advantages over conventional range-Doppler methods, the basic idea behind these works is to formulate SAR/ISAR imaging as a sparse signal recovery problem. In this paper, we propose a new two-dimensional pattern-coupled sparse Bayesian learning(SBL) method to capture the underlying cluster patterns of the ISAR target images. Based on this model, an expectation-maximization (EM) algorithm is developed to infer the maximum a posterior (MAP) estimate of the hyperparameters, along with the posterior distribution of the sparse signal. Experimental results demonstrate that the proposed method is able to achieve a substantial performance improvement over existing algorithms, including the conventional SBL method.