Cognitive radar framework has recently been proposed in radar signal processing to develope algorithms for target detection, tracking, and waveform design in the presence of nonstationary environmental (clutter) characteristics. In this framework, there are the three main steps: sensing the environmental changes, learning the new environmental statistical characteristics, and adapting the radar algorithms to the new characteristics. Here, we focus on the second step of the framework to identify the new clutter characteristics after a change is detected in the environment. We form a dictionary of various clutter distributions and identify the distribution of the new clutter data through matching pursuit using probabilistic similarity and distance measures under sparsity constraints. Specifically, we use inner-product as a similarity measure, and we apply three different L 1 -norm type probabilistic distance measures. We both numerically and analytically analyze their clutter-distribution identification performances and show that Kulczynski is the best distance measure for distribution identification.

The low-rank approximation problem has recently attracted wide concern due to its excellent performance in real-world applications such as image restoration, traffic monitoring, and face recognition. Compared with the classic nuclear norm, the Schatten-p norm is stated to be a closer approximation to restrain the singular values for practical applications in the real world. However, Schatten-p norm minimization is a challenging non-convex, non-smooth, and non-Lipschitz problem. In this paper, inspired by the reweighted ℓ1 and ℓ2 norm for compressive sensing, the generalized iterative reweighted nuclear norm (GIRNN) and the generalized iterative reweighted Frobenius norm (GIRFN) algorithms are proposed to approximate Schatten-p norm minimization. By involving the proposed algorithms, the problem becomes more tractable and the closed solutions are derived from the iteratively reweighted subproblems. In addition, we prove that both proposed algorithms converge at a linear rate to a bounded optimum. Numerical experiments for the practical matrix completion (MC), robust principal component analysis (RPCA), and image decomposition problems are illustrated to validate the superior performance of both algorithms over some common state-of-the-art methods.

Graph matching plays a central role in such fields as computer vision, pattern recognition, and bioinformatics. Graph matching problems can be cast as two types of quadratic assignment problems (QAPs): Koopmans-Beckmann's QAP or Lawler's QAP. In our paper, we provide a unifying view for these two problems by introducing new rules for array operations in Hilbert spaces. Consequently, Lawler's QAP can be considered as the Koopmans-Beckmann's alignment between two arrays in reproducing kernel Hilbert spaces (RKHS), making it possible to efficiently solve the problem without computing a huge affinity matrix. Furthermore, we develop the entropy-regularized Frank-Wolfe (EnFW) algorithm for optimizing QAPs, which has the same convergence rate as the original FW algorithm while dramatically reducing the computational burden for each outer iteration. We conduct extensive experiments to evaluate our approach, and show that our algorithm significantly outperforms the state-of-the-art in both matching accuracy and scalability.

A synthetic aperture radar (SAR) system is severely affected by radio frequency systems, such as TV and cellular networks. Previous studies showed that narrowband radio frequency interference (RFI) is low rank and used the nuclear norm as a low-rank regularization to extract the RFI from the received signal. However, the nuclear norm is not an appropriate approximation of the true rank function. Hence, in this paper, the reweighted matrix-factorization (RMF) algorithm and the matrix-factorization decomposition (MFD) algorithm are proposed to suppress narrowband RFI for SAR systems, where the RMF algorithm uses the reweighted scheme to approximate the rank function, while the MFD algorithm restrains the upper bound of the rank as a prior condition. Moreover, the introduction of the MF scheme dramatically decreases the computational complexity and efficiently suppresses RFI. In addition, we further show that the sparse regularization of the useful signal (i.e., the useful SAR echo) not only protects the strong scatterers of the useful signal but also avoids low-rank overfitting. We employ the real SAR signals of both the sparse scene and the nonsparse scene with the measured RFI to verify the effectiveness of the proposed methods, and the proposed methods outperform the other methods for RFI suppression.

Synthetic aperture radar (SAR), as a wideband radar system, is subject to interference by radio frequency systems, such as radio, TV, and cellular networks. Since the narrowband radio frequency interference (RFI) has a stable frequency in a snapshot sequence, it has a low-rank property that can be used to substract RFI from the received signal. The nuclear norm is a common convex relaxation to constrain the rank, but it is optimized by the singular value thresholding (SVT) algorithm, which uses a single threshold to treat all singular values and greatly over-punishes large singular values. Hence, in this paper, we propose two methods, the reweighted nuclear norm (RNN) algorithm and the reweighted Frobenius norm (RFN) algorithm, to separate the RFI and the useful signal. The RNN and RFN minimization problems are the approximations of the real rank function, which can protect large singular values and restrict the rank. As a result, the RFI is accurately extracted and the useful signal is successfully protected. Also, we strictly derive the closed-form solutions of the RNN and RFN minimization problems for complex radar signals, and we also employ downsampling to extract the mainband of the signal spectrum to speed up the convergence. Real SAR data is applied to demonstrate the effectiveness of the proposed methods for RFI suppression.

Radio-frequency systems, such as TV and cellular networks, severely interfere with synthetic aperture radar (SAR) systems. Narrowband radio-frequency interference (RFI) has a special low-rank property in the received signal matrix, because it performs like a sinusoid with nearly invariant frequency as the slow time proceeds. Exploiting this special property, in this paper, we divide the received signal matrix into several small matrices, in each of which the RFI is also low rank. Without losing the connection between these small matrices, we stack them into a three-mode tensor to separate the low-rank RFI tensor and recover the informative signal tensor. Previous studies employed the nuclear norm to regularize the low-rank RFI, which is not a good choice. Hence, we propose two reweighted algorithms, the reweighted tensor nuclear norm (RTNN) and the reweighted tensor Frobenius norm (RTFN) algorithms, to approximate the rank function in a tensor and accurately extract the low-rank RFI tensor from the received signal tensor. As a result, the introduction of the tensor structure dramatically decreases the computational cost. Furthermore, the reweighted scheme helps suppressing the RFI and recovering the useful signal with excellent performance. Finally, real SAR data with measured RFI is employed to demonstrate the effectiveness of the proposed methods for RFI mitigation.

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform other state-of-the-art approaches in both accuracy and computational efficiency.

In recent years, many researchers have focused on the automatic target recognition problem for high-resolution synthetic aperture radar (SAR) systems. Most have directly employed the training data as the dictionary, which introduces error from speckle noise. In this letter, a joint low-rank and sparse multiview denoising (JLSMD) dictionary is generated, which combines multiview training samples for denoising. To extract the dictionary, we fully consider the low-rank property of multiview target images and the sparsity of speckle noise for SAR systems. The designed dictionary is more accurate than the training data in representing the target. With the help of the proposed JLSMD dictionary, we develop three algorithms based on the sparse representation classification and the support vector machine approach. We carry out experiments on the moving and stationary target acquisition and recognition public data set to evaluate the excellent performance of the proposed methods against several state-of-the-art methods, including deep learning methods.

In this paper, we provide a novel regression algorithm based on a Gaussian random field (GRF) indexed by a Riemannian manifold (M, g). We utilize both the labeled and unlabeled data sets to exploit the geometric structure of M. We use the recovered heat (H) kernel as the covariance function for the GRF (HGRF). We propose a Monte Carlo integral theorem on Riemannian manifolds and derive the corresponding convergence rate and approximation error. Based on this theorem, we correctly normalize the recovered eigenvector to make it compatible with Riemannian measure. More importantly, we prove that the HGRF is intrinsic to the original data manifold by comparing the pullback geometry and the original geoemtry of M. Essentially it is a semi-supervised learning method, which means the unlabeled data can be utilized to help identify the geometry structure of the unknown manifold M.

We propose an analytical model to estimate the depth-error-induced virtual view synthesis distortion (VVSD) in 3D video, taking the distance between reference and virtual views (virtual view position) into account. In particular, we start with a comprehensive preanalysis and discussion over several possible VVSD scenarios. Taking intrinsic characteristic of each scenario into consideration, we specifically classify them into four clusters: 1) overlapping region; 2) disocclusion and boundary region; 3) edge region; and 4) infrequent region. We propose to model VVSD as the linear combination of the distortion under different scenarios (DDSs) weighted by the probability under different scenarios (PDSs). We show analytically that DDS and PDS can be related to the virtual view position using quadratic/biquadratic models and linear models, respectively. Experimental results verify that the proposed model is capable of estimating the relationship between VVSD and the distance between reference and virtual views. Therefore, our model can be used to inform a reference view setup for capturing, or distortion at certain virtual view positions, when depth information is compressed.

We propose an analytical model to estimate the depth-error-induced virtual view synthesis distortion (VVSD) in 3D video, taking into account the configuration of the cameras. Focusing on view synthesis under depth error, we carefully analyze the merging operations under different situations that affect pixel availability: overlapping region, disocclusion and boundary region, disparity error region, and infrequent region. The analysis leads to quadratic/biquadratic models and linear models that explicitly relate the distance between camera positions (reference/virtual view) to Distortion under Different Situations (DDS) and Probability under Different Situations (PDS), respectively. We also show that VVSD is the linear combination of DDS weighted by PDS. Our careful analysis results in state-of-the-art estimation accuracy. Experimental results verify that the proposed model is capable to produce accurate estimates of VVSD based on the distance between reference/virtual views. Therefore, our model can effectively inform camera setup for capturing, in particular, the set-up of the cameras in situation where depth information will be compressed subsequently.

We propose an analytical model to estimate the depth-error-induced synthesis distortion in 3D video, taking into account the configuration of the cameras. In particular, the model mathematically relates the Distance between camera positions (reference view and virtual view) to the Virtual View Distortion (VVD), thus it is denoted as DVVD model. Specifically, the DVVD model accounts for two modules: distribution of disparity errors and shift-induced distortion. The former one is derived under a Laplacian distribution assumption of depth errors, and the latter one is estimated under a Quadratic model. We further propose a linear Steady-State model by performing Taylor series approximation of the DVVD model over a region of practical interest. Experiment results demonstrate that both the DVVD and Steady-State models are capable of estimating the relationship between VVD and the distance between virtual/reference view. Therefore, our model can effectively inform camera setup for capturing, in particular, the setup of the cameras in situation where depth information will be compressed subsequently.