Sparse Blind Deconvolution with Nonconvex Optimization for Ultrasonic NDT Application.

Recently, a new two-step tensor-based distributed epileptic source localization method was proposed. Firstly, it performs Canonically Polyiadic (CP) decomposition of a Space-Time-Spike (STS) tensor capturing the occurrence of epileptic events in the ElectroEncephaloGraphic (EEG) data. This with the aim at estimating the spatial map of those distributed sources. Secondly, a source localization step is performed using the well-known Alternating Direction Method of Multipliers (ADMM) algorithm. This paper investigates to what extent this brain epileptic source imaging problem could be properly solved when a proximal gradient-based algorithm, the Proximal Alternating Linearized Minimization (PALM) technique, is used instead of the ADMM when the source localization step is considered. The convergence issue of the PALM scheme in this particular problem is discussed and a link with the one of the ADMM method is established. Furthermore, realistic simulations with epileptic EEG data show the efficiency of the new proposed PALM-based scheme.

ABSTRACTThis study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly limited, and a simple straight CT trajectory is preferable. This method could also be applied in X-ray inspection lines in factories and airports. In the medical field, this method would complement the tomosynthesis in mammography. When using a translational trajectory, the dispersion of the fan- or cone-beam creates projection data with the angular information of the sample object. However, the angular information inevitably becomes insufficient when using a translational trajectory, which degrades the reconstruction accuracy. In this case, CS is considered suitable for reconstruction because it has been successfully used for reconstructions from sparse-view and limited-angle data. For reconstruction from the translational trajectory projection, a new concept of directional difference (DD) regularization was proposed. An algorithm was developed based on the alternating direction method of multipliers (ADMM) algorithm to solve the regularization problem. Numerical reconstruction experiments from noisy projection data were conducted and the results were compared with those from other reconstruction methods. The convergence performance of the total variation (TV), DD, and mixed TV-DD regularization methods were examined. The proposed DD and TV-DD methods showed better performance than the TV only regularization. Reconstruction from Monte-Carlo simulated projection data was also demonstrated.

Enhanced robust multimode process monitoring under dirty data via difference-based decomposition of matrix

The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of ADMM for solving a nonconvex nonsmooth optimization problem, whose objective is the sum of a number of component functions. The proposed algorithm allows the problem to be solved in a distributed, asynchronous, and incremental manner. First, the component functions can be distributed to different computing nodes, which perform the updates asynchronously without coordinating with each other. Two sources of asynchrony are covered by our algorithm: One is caused by the heterogeneity of the computational nodes and the other arises from unreliable communication links. Second, the algorithm can be viewed as implementing an incremental algorithm where at each step the (possibly delayed) gradients of only a subset of component functions are updated. We show that when certain bounds are imposed on the level of asynchrony, the proposed algorithm converges to the set of stationary solutions (resp. optimal solutions) for the nonconvex (resp. convex) problem, with a global sublinear rate.

An efficient non-convex total variation approach for image deblurring and denoising

Deploying multiple unmanned aerial vehicles (UAVs) to locate a signal-emitting source covers a wide range of military and civilian applications like rescue and target tracking. It is well known that the UAVs-source (sensors-target) geometry, namely geometric configuration, significantly affects the final localization accuracy. This paper focuses on the geometric configuration optimization for received signal strength difference (RSSD)-based passive source localization by drone swarm. Different from prior works, this paper considers a general measuring condition where the spread angle of drone swarm centered on the source is constrained. Subject to this constraint, a geometric configuration optimization problem with the aim of maximizing the determinant of Fisher information matrix (FIM) is formulated. After transforming this problem using matrix theory, an alternating direction method of multipliers (ADMM)-based optimization framework is proposed. To solve the subproblems in this framework, two global optimal solutions based on the Von Neumann matrix trace inequality theorem and majorize-minimize (MM) algorithm are proposed respectively. Finally, the effectiveness as well as the practicality of the proposed ADMM-based optimization algorithm are demonstrated by extensive simulations.

Task offloading in edge computing is important for the Industrial Internet of Things (IIoT) to implement computation-intensive applications in real time. However, achieving efficient task offloading in IIoT is very challenging due to the limited computing resources of IIoT devices, the coupling of computing and communication resources, and the unreliability in multihop wireless transmission. In this article, we construct a link model by considering the influence of unreliable links in multihop transmission to reveal the relationship between reliability and transmission delay. Then, a nonconvex optimization problem that minimizes task processing delay is formulated, and task offloading is decided by considering transmission path selection, bandwidth allocation, and computational resource allocation. To solve this problem, an algorithm based on the alternating direction method of multipliers (ADMM) is designed using auxiliary variables and reformulation linearization technology (RLT). The simulation results show that our proposed algorithm can fully utilize the computing power of the edge server and reduce the task processing delay. Compared with the centralized algorithms, the performance of the proposed scheme is only 1% worse, but the calculation time can be reduced by 40%.

Wireless network visualization is envisioned as a promising framework to provide efficient and customized services for next-generation wireless networks. In wireless virtualized networks (WVNs), limited radio resources are shared among different service providers for providing services to different users with heterogeneous demands. In this work, we propose a distributed resource allocation scheme for a wireless virtualized small cell networks. The SBSs in the considered system are equipped with self-backhaul and energy harvesting capabilities in order to reduce the operation cost. In particular, with the objective to obtain the utility maximization, a joint user association, time, spectrum and power allocation problem is presented. To tackle the formulated mixed combinatorial and non-convex optimization problem, the original problem is divided into three low-complexity subproblems and we propose an alternating direction method of multipliers (ADMM)-based distributed algorithm to address them efficiently and effectively. Simulation studies are conducted to demonstrate the advantages of our presented system architecture and proposed schemes.

Melamine is an organic base and a trimer of cyanamide, with a 1, 3, 5-triazine skeleton. It is usually used for the production of plastics, glue and flame retardants. Melamine combines with acid and related compounds to form melamine cyanurate and related crystal structures, which have been implicated as contaminants or biomarkers in protein adulterations by lawbreakers, especially in milk powder. This paper is focused on developing an available method for quantitative detection of melamine in the fields of security inspection and nondestructive testing based on THz-TDS. Terahertz (THz) technology has promising applications for the detection and identification of materials because it exhibits the properties of spectroscopy, good penetration and safety. Terahertz time-domain spectroscopy (THz-TDS) is a key technique that is applied to spectroscopic measurement of materials based on ultrafast femtosecond laser. In this study, the melamine and its mixture with polyethylene powder in different consistence are measured using the transmission THz-TDS. And we obtained the refractive index spectra and the absorption spectrum of different concentrations of melamine on 0.2-2.8THz. In the refractive index spectra, it is obvious to see that decline trend with the decrease of concentration; and in the absorption spectrum, two peaks of melamine at 1.98THz and 2.28THz can be obtained. Based on the experimental result, the absorption coefficient and the consistence of the melamine in the mixture are determined. Finally, methods for quantitative detection of materials in the fields of nondestructive testing and quality control based on THz-TDS have been studied.

Recently, infrared small target detection problem has attracted substantial attention. Many works based on local low-rank model have been proven to be very successful for enhancing the discriminability during detection. However, these methods construct patches by traversing local images and ignore the correlations among different patches. Although the calculation is simplified, some texture information of the target is ignored, and targets of arbitrary forms cannot be accurately identified. In this paper, a novel target-aware method based on a non-local low-rank model and saliency filter regularization is proposed, with which the newly proposed detection framework can be tailored as a non-convex optimization problem, therein enabling joint target saliency learning in a lower dimensional discriminative manifold. More specifically, non-local patch construction is applied for the proposed target-aware low-rank model. By combining similar patches, we reconstruct them together to achieve a better generalization of non-local spatial sparsity constraints. Furthermore, to encourage target saliency learning, our proposed saliency filtering regularization term based on entropy is restricted to lie between the background and foreground. The regularization of the saliency filtering locally preserves the contexts from the target and surrounding areas and avoids the deviated approximation of the low-rank matrix. Finally, a unified optimization framework is proposed and solved with the alternative direction multiplier method (ADMM). Experimental evaluations of real infrared images demonstrate that the proposed method is more robust under different complex scenes compared with some state-of-the-art methods.

This article investigates the problem of frequency-invariant (FI) beamforming of wideband multiple-input multiple-output (MIMO) radars and presents two design criteria to synthesize wideband FI beampatterns under peak-to-average power ratio (PAPR) and nulling constraints. Precisely, the two criteria are to apply the least-squares and absolute errors, respectively, to approximate a desired transmit beampattern. Both criteria result in nonconvex constrained optimization problems. For the former, the solution is derived via reformulating the initial problem into a quadratic form, which can be solved by alternating direction method of multipliers (ADMM). For the latter, the design problem is formulated into an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${l_{1}}$</tex-math></inline-formula> -norm real-valued form, which is solved iteratively by using a nested ADMM (N-ADMM) algorithm. Moreover, both the convergence and computational complexities of these two algorithms are discussed. Numerical simulations show that the obtained beampatterns by the proposed algorithms can well approximate the given beampattern under the required constraints.

Integrated sensing and communication (ISAC) has been envisioned to play a more important role in future wireless networks. However, the design of ISAC networks is challenging, especially when there are multiple communication and sensing (C&S) nodes and multiple sensing targets. We investigate a multi-base station (BS) ISAC network in which multiple BSs equipped with multiple antennas simultaneously provide C&S services for multiple ground communication users (CUs) and targets. To enhance the overall performance of C&S, we formulate a joint user association (UA) and multi-BS transmit beamforming optimization problem with the objective of maximizing the total sum rate of all CUs while ensuring both the minimum target detection and parameter estimation requirements in terms of the radar signal-to-noise ratio (SNR) and the Cramér-Rao bound (CRB), respectively. To efficiently solve the highly non-convex mixed integer nonlinear programming (MINLP) optimization problem, we propose an alternating optimization (AO)-based algorithm that decomposes the problem into two sub-problems, i.e., UA optimization and multi-BS transmit beamforming optimization. Inspired by the huge potential of large language models (LLMs) for prediction and inference, we propose a unified framework integrating LLMs with convex-based optimization methods to benefit from the theoretical rigor and convergence guarantees of convex-based methods, and the adaptability and flexibility of LLMs. First, we propose a comprehensive design of prompt engineering based on in-context, few-shot, chain of thought, and self-reflection techniques to guide LLMs in solving the binary integer programming UA optimization problem. Second, we utilize convex-based optimization methods to handle the non-convex beamforming optimization problem based on fractional programming (FP), majorization minimization (MM), and the alternating direction method of multipliers (ADMM) with an optimized UA from LLMs. Numerical results demonstrate that our proposed LLM-enabled AO-based algorithm achieves fast convergence and near upper-bound performance with the GPT-o1 model, outperforming various benchmark schemes, which shows the advantages of integrating LLMs into convex-based optimization for wireless networks.

Compression Based Identification of PWA Systems

We present single-shot high-performance quantitative phase imaging with a physics-inspired plug-and-play denoiser for polarization differential interference contrast (PDIC) microscopy. The quantitative phase is recovered by the alternating direction method of multipliers (ADMM), balancing total variance regularization and a pre-trained dense residual U-net (DRUNet) denoiser. The custom DRUNet uses the Tanh activation function to guarantee the symmetry requirement for phase retrieval. In addition, we introduce an adaptive strategy accelerating convergence and explicitly incorporating measurement noise. After validating this deep denoiser-enhanced PDIC microscopy on simulated data and phantom experiments, we demonstrated high-performance phase imaging of histological tissue sections. The phase retrieval by the denoiser-enhanced PDIC microscopy achieves significantly higher quality and accuracy than the solution based on Fourier transforms or the iterative solution with total variance regularization alone.

This paper addresses time-domain frequency-invariant beampattern synthesis under multiple constraints. Mainlobe spatial response variation is introduced to characterize the frequency invariance. Peak constraints and norm constraints are imposed to control the sidelobe response and robustness of the beamformer, respectively. Such constraints are separated with the help of the alternating direction method of multipliers (ADMM), and an iterative solution is derived. Unlike the traditional interior-point approach with cubic complexity, the proposed algorithm shows quadratic complexity in a single iteration. Simulation results demonstrate that the proposed algorithm can achieve satisfactory performance in less time.