We present an image reconstruction method for diffuse optical tomography (DOT) by using the sparsity regularization and expectation-maximization (EM) algorithm. Typical image reconstruction approaches in DOT employ Tikhonov-type regularization, which imposes restrictions on the L ₂ norm of the optical properties (absorption/scattering coefficients). It tends to cause a blurring effect in the reconstructed image and works best when the unknown parameters follow a Gaussian distribution. In reality, the abnormality is often localized in space. Therefore, the vector corresponding to the change of the optical properties compared with the background would be sparse with only a few elements being nonzero. To incorporate this information and improve the performance, we propose an image reconstruction method by regularizing the L ₁ norm of the unknown parameters and solve it iteratively using the expectation-maximization algorithm. We verify our method using simulated 3D examples and compare the reconstruction performance of our approach with the level-set algorithm, Tikhonov regularization, and simultaneous iterative reconstruction technique (SIRT). Numerical results show that our method provides better resolution than the Tikhonov-type regularization and is also efficient in estimating two closely spaced abnormalities.

In this paper, we present a mathematical and computational framework for comparing and matching distributions in reproducing kernel Hilbert spaces (RKHS). This framework, called optimal transport in RKHS, is a generalization of the optimal transport problem in input spaces to (potentially) infinite-dimensional feature spaces. We provide a computable formulation of Kantorovich's optimal transport in RKHS. In particular, we explore the case in which data distributions in RKHS are Gaussian, obtaining closed-form expressions of both the estimated Wasserstein distance and optimal transport map via kernel matrices. Based on these expressions, we generalize the Bures metric on covariance matrices to infinite-dimensional settings, providing a new metric between covariance operators. Moreover, we extend the correlation alignment problem to Hilbert spaces, giving a new strategy for matching distributions in RKHS. Empirically, we apply the derived formulas under the Gaussianity assumption to image classification and domain adaptation. In both tasks, our algorithms yield state-of-the-art performances, demonstrating the effectiveness and potential of our framework.

Network science plays a central role in understanding and modeling complex systems in many areas including physics, sociology, biology, computer science, economics, politics, and neuroscience. One of the most important features of networks is community structure, i.e., clustering of nodes that are locally densely interconnected. Communities reveal the hierarchical organization of nodes, and detecting communities is of great importance in the study of complex systems. Most existing community-detection methods consider low-order connection patterns at the level of individual links. But high-order connection patterns, at the level of small subnetworks, are generally not considered. In this paper, we develop a novel community-detection method based on cliques, i.e., local complete subnetworks. The proposed method overcomes the deficiencies of previous similar community-detection methods by considering the mathematical properties of cliques. We apply the proposed method to computer-generated graphs and real-world network datasets. When applied to networks with known community structure, the proposed method detects the structure with high fidelity and sensitivity. When applied to networks with no a priori information regarding community structure, the proposed method yields insightful results revealing the organization of these complex networks. We also show that the proposed method is guaranteed to detect near-optimal clusters in the bipartition case.

In this paper, we study the joint design of a transmit sequence and a receive filter for an airborne multiple-input multiple-output (MIMO) radar system to improve its moving target detection performance in the presence of signal-dependent interference. The optimization problem is formulated to maximize the output signal-to-noise-plus-interference ratio (SINR), subject to the waveform constant envelope (CE) constraint. To address the challenge of this non-convex problem, we propose a novel optimization framework for solving the problem over a Riemannian manifold which is the product of complex circles and a Euclidean space. Manifold optimization views the constrained optimization problem as an unconstrained one over a restricted search space. The Riemannian gradient descent algorithms and the Riemannian trust-region algorithm are then developed to solve the reformulated problem efficiently with low iteration complexity. In addition, the proposed manifold-based algorithms provably converge to an approximate local optimum from an arbitrary initialization point. Numerical experiments demonstrate the algorithmic advantages and performance gains of the proposed algorithms.

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.

We consider a multiple input multiple output (MIMO) radar that works through one-bit sampling of received radar echoes. The application of one-bit sampling significantly reduces the hardware cost, energy consumption, and systematic complexity, but it also poses serious challenges to extracting highly accurate target information from one-bit quantized data. In this paper, we propose a maximum likelihood (ML)-based method that first iteratively maximizes the likelihood function to recover a virtual array data matrix, then jointly estimates the angle and Doppler parameters from the recovered matrix. Because the ML problem is convex, we can successfully apply a computationally efficient gradient descent algorithm to solve it. Based on our analysis of the Cramér-Rao bound (CRB) of the ML-based method, a pre-estimation assisted threshold (PET) strategy is developed to improve the estimation performance. Numerical experiments demonstrate that the proposed ML-based method, combined with the PET strategy, can provide highly accurate parameter estimation performance, close to that of classic MIMO radar.