This letter investigates the problem of direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for non-line-of-sight (NLOS) targets in bistatic multiple-input multiple-output (MIMO) radar systems assisted by an intelligent reflecting surface (IRS). To tackle this issue, we propose a covariance tensor subspace-based algorithm. First, the received data is modeled within a tensor framework to preserve their inherent multi-dimensional spatiotemporal structure. Then, a fourth-order covariance tensor is constructed by computing correlations along the temporal dimension. Using the higher-order singular value decomposition (HOSVD), the signal subspace matrix is derived from this covariance tensor. The receive steering matrix is accurately reconstructed by exploiting the property of the Khatri–Rao product for full-column-rank matrices. Based on the estimated signal subspace and the reconstructed steering matrix, DOD and DOA estimation is efficiently performed via the rotational invariance technique combined with a one-dimensional correlation-based method, which provides automatic parameter pairing. Simulation results validate the superiority and effectiveness of the proposed algorithm in estimating angles.

A fluid reconfigurable intelligent surface (fRIS)-aided integrated sensing and communication (ISAC) system is proposed to enhance multi-target sensing and multi-user communication. Unlike the conventional RIS, the fRIS employs movable elements with adjustable positions, offering additional spatial degrees of freedom. In this system, a joint optimization problem is formulated to minimize sensing beampattern mismatch and symbol estimation error. An algorithm based on alternating minimization is devised to handle the resultant non-convex problem, where the subproblems are solved via augmented Lagrangian method, quadratic programming, semidefinite relaxation, and majorization-minimization. A key challenge is that the element positions affect both incident and reflective channels, leading to the high-order composite objective functions. As a remedy, the high-order terms are transformed into linear and linear-difference forms by exploiting the structural characteristics of fRIS and the channels. Numerical results demonstrate the superiority of the proposed scheme over conventional RIS-aided ISAC and other benchmarks.

Low-cost and low-power consumptions have become the trend for the future communication systems, where one-bit quantization is a promising candidate. However, due to the low resolutions, the performance loss of the one-bit system is serious. To alleviate this issue, we propose leveraging the fluid reconfigurable intelligent surface (fRIS) to compensate for the loss in downlink communication systems with one-bit digital-to-analog converters (DACs). Specifically, we formulate a symbol estimation error minimization problem by jointly optimizing the symbol estimator, the one-bit transmit signal, the fRIS phase shifts, and the element positions. To handle the resultant problem, an alternating algorithm is developed, where four subproblems are solved iteratively by using semidefinite-relaxation, discrete optimization, and quadratic programming. In optimizing fRIS element positions, the positions affect both the incident and reflective channels, leading to the high-order complex objective functions. We show that these terms can be simplified by using the characteristics of channels. Numerical results validate that the introduction of fRIS can alleviate the performance loss caused by one-bit quantization.

Active reconfigurable intelligent surface (A-RIS) aided integrated sensing and communications (ISAC) system has been considered as a promising paradigm to improve spectrum efficiency. However, massive energy-hungry radio frequency (RF) chains hinder its large-scale deployment. To address this issue, an A-RIS-aided ISAC system with antenna selection (AS) is proposed in this work, where a target is sensed while multiple communication users are served with specifically selected antennas. Specifically, a cuckoo search-based scheme is first utilized to select the antennas associated with high-gain channels. Subsequently, with the properly selected antennas, the weighted sum-rate (WSR) of the system is optimized under the condition of radar probing power level, power budget for the A-RIS and transmitter. To solve the highly non-convex optimization problem, we develop an efficient algorithm based on weighted minimum mean square error (WMMSE) and fractional programming (FP). Simulation results show that the proposed AS scheme and the algorithm are effective, which reduces the number of RF chains without significant performance degradation.

Electrical impedance tomography (EIT) is a promising imaging technique in the medical field. However, its clinical application is limited by several challenges, such as poor electrode contact and body movement. These factors introduce impulsive noise in boundary voltage measurement, resulting in the performance degradation of the conventional imaging methods. This letter devises a robust approach to improve the performance in such scenarios. Unlike traditional algorithms that use an identity matrix as the measurement noise weight matrix, the suggested method designs a strategy to update the weight matrix during iteration for outlier resistance. Specifically, we apply the penalty technique to optimize the weight matrix and thus formulate the imaging task as a half-quadratic optimization problem. In addition, we exploit a median absolute deviation based confidence interval to distinguish outlier-contaminated and normal channels, such that the elements of the diagonal weight matrix are either 0 or 1. Subsequently, the resultant optimization task is addressed using the alternating minimization method. Experimental results show that the proposed approach outperforms the state-of-the-art algorithms in the presence of impulsive noise.

Over the past two decades, sparse unmixing (SU) has gained significant attention in the realm of hyperspectral imaging. The aims of SU are to seek a subset of spectral signatures and estimate their fractional abundances to represent each mixed spectral pixel. Conventional SU methods often employ the Frobenius norm and thus cannot work satisfactorily in the presence of non-Gaussian noise. Second, the ideal$\ell _{0}$-norm is usually substituted with its convex or nonconvex approximation in most existing algorithms, which may degrade the recovery performance. To address these issues, this article proposes a novel approach, termed sparse unmixing using$\ell _{0}$-norm constraint and log-cosh loss (SUNNING). We exploit the$\log $-$\cosh $function to minimize the fitting errors subject to three constraints, namely, nonnegativity, sum-to-one, and upper bounded$\ell _{0}$-norm. Then, we adopt the projected gradient descent (PGD) framework to solve such an optimization problem. SUNNING includes two alternating steps, gradient descent and nonconvex projection, where an optimality of the solution is guaranteed. Also, we prove the convergence of SUNNING, including the objective value and variable sequence. In addition, to attain higher unmixing accuracy, we exploit the spectral library pruning (SLP) strategy to eliminate inactive endmembers, yielding an improved SUNNING. Experimental results on synthetic and real-world datasets exhibit improved robustness and effectiveness of the suggested methods over the state-of-the-art algorithms. MATLAB code is available at:https://github.com/freeLix-YY/IEEE_TGRS2024_SparseUnmixing_SUNNING_demo

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the$\ell_{p}$-norm ($0<p<2$) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the$\ell_{p}$-norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

Inspired by sparse learning, the Markowitz mean-variance model with a sparse regularization term is popularly used in sparse portfolio optimization. However, in penalty-based portfolio optimization algorithms, the cardinality level of the resultant portfolio relies on the choice of the regularization parameter. This brief formulates the mean-variance model as a cardinality ($\ell _{0}$-norm) constrained nonconvex optimization problem, in which we can explicitly specify the number of assets in the portfolio. We then use the alternating direction method of multipliers (ADMMs) concept to develop an algorithm to solve the constrained nonconvex problem. Unlike some existing algorithms, the proposed algorithm can explicitly control the portfolio cardinality. In addition, the dynamic behavior of the proposed algorithm is derived. Numerical results on four real-world datasets demonstrate the superiority of our approach over several state-of-the-art algorithms.

Graph signal processing refers to dealing with irregularly structured data. Compared with traditional signal processing, it can preserve the complex interactions within irregular data. In this work, we devise a robust algorithm to recover band-limited graph signals in the presence of impulsive noise. First, the observed data vector is recast, such that the noise component is divided into two vectors, representing the dense-noise component and sparse outliers, respectively. We then exploit ℓ0-norm to characterize the sparse vector as a regularization term. Alternating minimization is subsequently adopted as the solver for the resultant optimization problem. Besides, we suggest an approach to automatically update the penalty parameter of the ℓ0-norm term. In addition, we analyze the computational complexity and the steady-state convergence of our algorithm. Experimental results on synthetic and temperature data exhibit the superiority of the developed method over state-of-the-art algorithms in impulsive noise environments in terms of recovery accuracy and convergence speed.

This letter focuses on the robust low-rank matrix recovery (RLRMR) in the presence of gross sparse outliers. Instead of using$\ell _{1}$-norm to reduce or suppress the influence of anomalies, we aim to eliminate their impact. To this end, we model the RLRMR as a mixed integer programming (MIP) problem based on the$\ell _{0}$-norm. Then, a block coordinate descent (BCD) algorithm is developed to iteratively solve the resultant MIP. At each iteration, the proposed approach first utilizes the$\ell _{0}$-norm optimization theory to assign binary weights to all entries of the residual between the known and estimated matrices. With these binary weights, the optimization over the bilinear term is reduced to a weighted extension of the Frobenius norm. As a result, the optimization problem is decomposed into a group of row-wise and column-wise subproblems with closed-form solutions. Additionally, the convergence of the proposed algorithm is studied. Simulation results demonstrate that the proposed method is superior to five state-of-the-art RLRMR algorithms.

In this paper, we devise a sparse-coded orthogonal frequency division multiplexing (OFDM) differential chaos shift keying (DCSK) communication system based on low-rank matrix recovery which can handle Gaussian background noise and outlier-contaminated symbols simultaneously. As the noise-free OFDM-DCSK symbol matrix has rank 1, we exploit the vector outer product for its modeling, while sparse coding is also applied to reduce the transmission energy. To demodulate information bits from the sparse-coded signal, we formulate an objective function which consists of a sum of Frobenius norm for rank-1 matrix recovery and$\ell _{0}$-norm for identifying the possibly outlier-contaminated symbols, with a self-adaptive weight parameter. The resultant optimization problem is solved iteratively via block coordinate descent, and the Laplacian kernel with the Silverman’s rule is adopted for outlier detection. Theoretical analysis including convergence of the objective function, bit error rate (BER), energy efficiency and computational complexity, are provided. Simulation results show that the proposed system has comparable mean square error and BER performance with the$\ell _{p}$-norm minimization based matrix recovery approach at$p=2$in additive white Gaussian noise, and is superior to that of$p=1$in Middleton class A noise, even when sparse coding is applied. Moreover, compared with other binary DCSK systems, our system achieves higher energy efficiency thanks to the sparse coding.

Robust matrix completion refers to recovering a low-rank matrix given a subset of the entries corrupted by gross errors, and has various applications since many real-world signals can be modeled as low-rank matrices. Most of the existing methods only perform well for noise-free data or those with zero-mean white Gaussian noise, and their performance will be degraded in the presence of outliers. In this paper, based on the factorization framework, we propose a novel robust matrix completion scheme via using the truncated-quadratic loss function, which is non-convex and non-smooth, and half-quadratic theory is adopted for its optimization. By introducing an auxiliary variable, half-quadratic optimization (HO) can transform the loss function into two tractable forms, that is, additive and multiplicative formulations. Block coordinate descent method is then exploited as their solver. Compared with the additive form, the multiplicative variant has lower computational cost since we attempt to take the observations contaminated by outliers as missing entries. Numerical simulations and experimental results based on image inpainting and hyperspectral image recovery demonstrate that our algorithms are superior to the state-of-the-art methods in terms of restoration accuracy and runtime. MATLAB code is available athttps://github.com/bestzywang.

Matrix completion refers to recovering a matrix from a small subset of its entries. It is an important topic because numerous real-world data can be modeled as low-rank matrices. One popular approach for matrix completion is based on low-rank matrix factorization, but it requires knowing the matrix rank, which is difficult to accurately determine in many practical scenarios. We propose a novel algorithm based on rank-one approximation that a matrix can be decomposed as a sum of outer products. The key idea is to find the basis vectors of the underlying matrix according to the observed entries, and gradually increase the vector number until an appropriate rank estimate is reached. In contrast to the conventional rank-one schemes that employ unchanging rank-one basis matrices, our algorithm performs completion from the vector viewpoint and is able to generate continuously updated rank-one basis matrices. Besides, we theoretically show that the developed method has a linear convergence rate and a smaller recovery error than existing rank-one based algorithms. Experimental results using both synthetic data and real-world images demonstrate that our solution has the best recovery performance among the competing algorithms when the observations are contaminated by Gaussian noise.

Matrix completion (MC) aims at recovering missing entries, given an incomplete matrix. Existing algorithms for MC are mainly designed for noiseless or Gaussian noise scenarios and, thus, they are not robust to impulsive noise. For outlier resistance, entry-wise$\ell _{p}$-norm with$0 < p < 2$and M-estimation are two popular approaches. Yet the optimum selection of$p$for the entrywise$\ell _{p}$-norm-based methods is still an open problem. Besides, M-estimation is limited by a breakdown point, that is, the largest proportion of outliers. In this article, we adopt entrywise$\ell _{0}$-norm, namely, the number of nonzero entries in a matrix, to separate anomalies from the observed matrix. Prior to separation, the Laplacian kernel is exploited for outlier detection, which provides a strategy to automatically update the entrywise$\ell _{0}$-norm penalty parameter. The resultant multivariable optimization problem is addressed by block coordinate descent (BCD), yielding$\ell _{0}$-BCD and$\ell _{0}$-BCD-F. The former detects and separates outliers, as well as its convergence is guaranteed. In contrast, the latter attempts to treat outlier-contaminated elements as missing entries, which leads to higher computational efficiency. Making use of majorization–minimization (MM), we further propose$\ell _{0}$-BCD-MM and$\ell _{0}$-BCD-MM-F for robust non-negative MC where the nonnegativity constraint is handled by a closed-form update. Experimental results of image inpainting and hyperspectral image recovery demonstrate that the suggested algorithms outperform several state-of-the-art methods in terms of recovery accuracy and computational efficiency.

Sparse index tracking, as one of the passive investment strategies, is to track a benchmark financial index via constructing a portfolio with a few assets in a market index. It can be considered as parameter learning in an adaptive system, in which we periodically update the selected assets and their investment percentages based on the sliding window approach. However, many existing algorithms for sparse index tracking cannot explicitly and directly control the number of assets or the tracking error. This article formulates sparse index tracking as two constrained optimization problems and then proposes two algorithms, namely, nonnegative orthogonal matching pursuit with projected gradient descent (NNOMP-PGD) and alternating direction method of multipliers for$\ell _{0}$-norm (ADMM-$\ell _{0}$). The NNOMP-PGD aims at minimizing the tracking error subject to the number of selected assets less than or equal to a predefined number. With the NNOMP-PGD, investors can directly and explicitly control the number of selected assets. The ADMM-$\ell _{0}$aims at minimizing the number of selected assets subject to the tracking error that is upper bounded by a preset threshold. It can directly and explicitly control the tracking error. The convergence of the two proposed algorithms is also presented. With our algorithms, investors can explicitly and directly control the number of selected assets or the tracking error of the resultant portfolio. In addition, numerical experiments demonstrate that the proposed algorithms outperform the existing approaches.

Background subtraction refers to extracting the foreground from an observed video, and is the fundamental problem of various applications. There are two kinds of popular methods to deal with background separation, namely, robust principal component analysis (RPCA) and low-rank matrix factorization (LRMF). Nevertheless, the drawback of RPCA requires tuning penalty parameter to attain an ideal result. Compared with RPCA, the$\ell _{1}$-norm based LRMF does not involve extra parameters tuning, but it is challenging to optimize the$\ell _{1}$-norm based minimization because of the nonsmooth$\ell _{1}$-norm. In addition, it becomes time-consuming to find the optimal solution. In this work, we propose to employ smooth$\ell _{1,\epsilon }$-norm, an approximation of$\ell _{1}$-norm, to tackle background subtraction. Thus, the proposed model inherits the superiority of LRMF and even becomes tractable. Then the resultant optimization problem is solved by alternating minimization and gradient descent where the step-size of the gradient descent is adaptively updated via backtracking line searching approach. The proposed method is proved to be locally convergent. Experimental results on synthetic and real-world data demonstrate that our method outperforms the state-of-the-art algorithms in terms of reconstruction loss, computational speed and hardware performance.

Low-rank tensor completion (LRTC) that aims to restore the latent clean data from an incomplete and/or degraded observation, shows promising results in ubiquitous tensorial data completion applications. Most tensor completion approaches are vulnerable to outliers since their derivations are based on$\ell _{2}$-space to be robust against Gaussian noise. In this work, to tackle this issue,$\ell _{p}$-regression$(0 < p < 2)$is employed to achieve outlier resistance, where a factored form of tensor train (TT)-format representation is regularized by the low-TT-rank prior to exploit the inter-fibers correlation. On the basis of that, an effective iterative$\ell _{p}$-regression TT completion method (referred to$\ell _{p}$-TTC) is proposed, with the advantage of not requiring the hard-to-determine user-defined weights in TT rank model. Extensive experiment results are presented to demonstrate the outlier resistance of the proposed$\ell _{p}$-TTC, and showing the effective and superior performance in both bistatic MIMO radar localization and color image inpainting and denoising, compared with state-of-the-art tensor completion approaches.

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. In this article, a novel type-2 fuzzy-based filter is proposed for denoising images corrupted by impulse noise, especially for the high density of salt-and-pepper noise. It operates two stages, namely, type-2 fuzzy identifier and matrix completion denoiser. In the proposed method, the type-2 fuzzy identifier is first employed to identify and trim the entries contaminated by impulse noise in the data matrix from fuzzy system. Then, the trimmed data matrix is utilized to retrieve the noiseless data matrix with the matrix completion technology. Herein, a novel matrix completion technique is developed without$a$$priori$rank information compared to its counterparts. Simulation results are presented, which vividly show the denoised images obtained by the proposed method can achieve crystal clear image with strong structural integrity, and are showing good performance in terms of peak signal-to-noise ratio.

In the problem of image inpainting, one popular approach is based on low-rank matrix completion. Compared with other methods which need to convert the image into vectors or dividing the image into patches, matrix completion operates on the whole image directly. Therefore, it can preserve latent information of the two-dimensional image. An efficient method for low-rank matrix completion is to employ the matrix factorization technique. However, conventional low-rank matrix factorization-based methods often require a prespecified rank, which is challenging to determine in practice. The proposed method factorizes an image matrix as a sum of rank-one matrices so that it does not require rank information in advance as it can be automatically estimated by the algorithm itself when the algorithm has satisfactorily converged. In our study, matching pursuit is applied to search for the best rank-one matrix at each iteration. To be robust against impulsive noise, the residual error between the observed and estimated matrices is minimized by ℓp-norm with 0p-norm minimization is solved by the iteratively reweighted least squares method. The proposed model is beneficial for the robustness against outliers, and does not require rank information. Experimental results verify the effectiveness and higher accuracy of the proposed method with comparison to several state-of-the-art matrix completion-based image inpainting approaches.