Sparse Optimization Techniques Research Articles

Dynamical Soft Sensors from Scarce and Irregularly Sampled Outputs Using Sparse Optimization Techniques

In process industries, quality variables such as concentrations and viscosity usually require offline laboratory analysis due to difficulties associated with online sensing and are often sampled slowly or irregularly compared to other variables such as temperatures and flow rates. Dynamical soft sensors, which relate the uniformly fast sampled variables to irregularly sampled quality variables, are crucial in control and process monitoring applications. Most identification approaches for soft sensing assume that all the variables are sampled regularly and uniformly. The existing auxiliary model (AM)-based approaches for dealing with irregular sampling suffer from drawbacks such as nonconvex optimization, lack of model parsimony and require prior information about the system dynamics. This work addresses a few of these issues by developing a flexible AM that can accommodate complex linear process dynamics without assuming any prior knowledge and compromising on model parsimony by using redundant Laguerre filters and casting the model learning in the sparse optimization framework. The developed AM is utilized to efficiently reconstruct the measurements at the base sampling interval, which further serves as a foreground for the traditional parametric model identification techniques or the expectation maximization algorithm to obtain optimal parameter estimates. The efficacy of the proposed AM-based soft sensor algorithm is demonstrated through synthetic as well as industrial simulation case studies. Finally, a few guidelines on effective sampling of quality variables to generate informative experiments for soft sensor development are also presented.

Cell fate conversion prediction by group sparse optimization method utilizing single-cell and bulk OMICs data.

Cell fate conversion by overexpressing defined factors is a powerful tool in regenerative medicine. However, identifying key factors for cell fate conversion requires laborious experimental efforts; thus, many of such conversions have not been achieved yet. Nevertheless, cell fate conversions found in many published studies were incomplete as the expression of important gene sets could not be manipulated thoroughly. Therefore, the identification of master transcription factors for complete and efficient conversion is crucial to render this technology more applicable clinically. In the past decade, systematic analyses on various single-cell and bulk OMICs data have uncovered numerous gene regulatory mechanisms, and made it possible to predict master gene regulators during cell fate conversion. By virtue of the sparse structure of master transcription factors and the group structure of their simultaneous regulatory effects on the cell fate conversion process, this study introduces a novel computational method predicting master transcription factors based on group sparse optimization technique integrating data from multi-OMICs levels, which can be applicable to both single-cell and bulk OMICs data with a high tolerance of data sparsity. When it is compared with current prediction methods by cross-referencing published and validated master transcription factors, it possesses superior performance. In short, this method facilitates fast identification of key regulators, give raise to the possibility of higher successful conversion rate and in the hope of reducing experimental cost.

Underwater channel estimation exploiting multipath feature morphology.

Real-time accurate channel estimation has been an ongoing challenge because of diverse oceanic events that cause rapid fluctuations of high-energy multipath activity across the delay spread. This work leverages current compressed sensing and sparse optimization techniques with topological signal processing to improve estimation time and localize channel estimation to salient parts of the delay spread. This work improves the estimation time by tracking the channel as a union of overlapping multipath and other scattering events, which are modeled as "feature braids" in the delay-time domain. A channel feature braid may be intuitively visualized as the topologically connected trajectory of a group of channel delay taps, which represent the support of dominant or persistent scattering events, e.g., surface bounce multipath scattering. We present algorithms that harness support-constrained mixed norm optimization techniques to track the evolving support of channel feature braids. We validate our channel feature tracking algorithm independently in experimental field data as well as BELLHOP channel simulations across a diversity of oceanic conditions. This work shows that braiding used in estimation can improve estimation time and track high-energy events that develop within the delay vs time channel representation.

A Computerized Bioinspired Methodology for Lightweight and Reliable Neural Telemetry.

Personalized health monitoring of neural signals usually results in a very large dataset, the processing and transmission of which require considerable energy, storage, and processing time. We present bioinspired electroceptive compressive sensing (BeCoS) as an approach for minimizing these penalties. It is a lightweight and reliable approach for the compression and transmission of neural signals inspired by active electroceptive sensing used by weakly electric fish. It uses a signature signal and a sensed pseudo-sparse differential signal to transmit and reconstruct the signals remotely. We have used EEG datasets to compare BeCoS with the block sparse Bayesian learning-bound optimization (BSBL-BO) technique—A popular compressive sensing technique used for low-energy wireless telemonitoring of EEG signals. We achieved average coherence, latency, compression ratio, and estimated per-epoch power values that were 35.38%, 62.85%, 53.26%, and 13 mW better than BSBL-BO, respectively, while structural similarity was only 6.295% worse. However, the original and reconstructed signals remain visually similar. BeCoS senses the signals as a derivative of a predefined signature signal resulting in a pseudo-sparse signal that significantly improves the efficiency of the monitoring process. The results show that BeCoS is a promising approach for the health monitoring of neural signals.

Ultrasonic Thickness Measurements Using Machine Learning

Abstract Thickness measurements using an ultrasonic contact test is a well-known nondestructive evaluation technique. However, its implementation in a robotic system with a closed-loop feedback control for artificial intelligent measurements requires precise information of positioning and force of the ultrasonic probe. In this work, we describe an ultrasonic probe developed in our lab that uses a semispherical soft membrane made from an elastomer. The aim is to develop a methodology for precise positioning and force control of a dry contact ultrasonic probe based on the ultrasonic signal information processed using sparse matrix optimization and Fourier analysis techniques. The results show that the proposed methodology makes easy to achieve a fine tuning of the probe orientation with high sensitivity to load and misalignment in order to perform accurate thickness measurements.

Online Estimation of Missing Data Using Sparse Optimization Techniques With Applications to Classical Control

This paper proposes and describes a method based on sparse optimization techniques for online estimation of missing data. The basic idea of the proposed method is to represent the noise-free signal of interest sparsely in a composite dictionary. The proposed algorithm offers three prime advantages: 1) handles nonlinear processes that are locally linearizable; 2) requires lower computational power than the existing algorithms; and 3) adapts to the changing process conditions by optimally selecting the most relevant feature for that window of time. Results show that the proposed algorithm outperforms the existing neural network-based method. An application of the proposed algorithm to classical (PID) control using measurements with missing data is presented. In this context, an added benefit of the proposed method is that it serves as a feature selection operator for the process, which can be useful in other applications. Numerical (simulation) studies are carried out to study the influence of user-defined parameter in the algorithm and two stochastic factors, namely, the random sampling scheme and noise , on the stability and performance of the closed-loop system. Results show that the closed-loop system with the proposed algorithm is stable and yields a satisfactory performance.

Barrier-Certified Adaptive Reinforcement Learning With Applications to Brushbot Navigation

This paper presents a safe learning framework that employs an adaptive model learning algorithm together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique. We use the learned model in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding particular undesirable regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate an action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring the greedy policy improvement under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has previously been used under stationarity assumptions in the safe learnings literature, and is then tested on a real robot, the brushbot, whose dynamics is unknown, highly complex and nonstationary.

Sparse optimization for image reconstruction in Electrical Impedance Tomography

Abstract Electrical Impedance Tomography (EIT) can be used to obtain phase boundaries and gas holdups in multiphase flows. The main challenge in image reconstruction using EIT is the low spatial resolution. In this paper, a reconstruction algorithm using sparse optimization techniques is presented. For multiphase flows, gradients in the conductivity vector are sparse. Therefore, the reconstruction problem is formulated as identification of this sparse vector given the current-voltage measurements. A new iterative algorithm is proposed to estimate the conductivity values. The accuracy of the proposed method is demonstrated with the help of several examples and comparison with an existing technique.

Data-Driven and Low-Sparsity False Data Injection Attacks in Smart Grid

Recent researches on data-driven and low-sparsity data injection attacks have been presented, respectively. To combine the two main goals (data-driven and low-sparsity) of research, this paper presents a data-driven and low-sparsity false data injection attack strategy. The proposed attacking strategy (EID: Eliminate-Infer-Determine) is divided into three stages. In the first step, the intercepted data is preprocessed by sparse optimization techniques to eliminate the outliers. The recovered data is then exploited to learn about the system matrix based on the parallel factorization algorithm in the second step. In the third step, the approximated system matrix is applied for the design of sparse attack vector based on the convex optimization. The simulation results show that the EID attack strategy achieves a better performance than the improved ICA-based attack strategy in constructing perfect sparse attack vectors. What is more, data-driven implementation of the proposed strategy is also presented which ensures attack performance even without the prior information of the system.

A D2D-Based Protocol for Ultra-Reliable Wireless Communications for Industrial Automation

As one indispensable use case for the 5G wireless systems on the roadmap, ultra-reliable and low latency communications (URLLC) is a crucial requirement for the coming era of wireless industrial automation. This paper aims to develop communication techniques for making such a paradigm shift from the conventional human-type broadband communications to the emerging machine-type URLLC. One fundamental task for URLLC is to deliver a short command from the controller to each actuator within the stringent delay requirement and also with high-reliability in the downlink. Motivated by the geographic feature in industrial automation that in the factories many tasks are assigned to different groups of devices who work in close proximity to each other and thus can form clusters of reliable device-to-device (D2D) networks, this paper proposes a novel two-phase transmission protocol for achieving the above goal. Specifically, in the first phase within the latency requirement, the multi-antenna base station (BS) combines the messages of each group together and multicasts them to the corresponding groups; while in the second phase, the devices that have decoded the messages successfully, who are defined as the leaders, help relay the messages to the other devices in their groups. Under this protocol, we further design an innovative leader selection based beamforming strategy at the BS by utilizing the sparse optimization technique, which leads to the desired sparsity pattern in user activity, i.e., at least one leader exists in each group, in the first phase, thus making full utilization of the reliable D2D networks in the second phase. Simulation results are provided to show that the proposed two-phase transmission protocol considerably improves the reliability of the whole system within the stringent latency requirement as compared to other existing schemes for URLLC such as Occupy CoW.

Computing medial axis transformations of 2D point clouds

In this paper, we propose a robust method to compute the medial axis transformation of a 2D point cloud with noise and/or missing data. The basic approach is to first compute the signed distance function of the point cloud by solving the Eikonal equation, and then an approximation of the signed distance function is obtained by sparse optimization technique. The medial axis of the point cloud corresponds to the non-smooth ridge of the distance function which can be extracted by checking the norm of the gradient of the distance function. The medial axis is segmented into branches and a compact spline representation of each branch can be obtained. We perform experiments on various examples and compare our method with state-of-the-art methods. Experimental results demonstrate that our method outperforms previous methods in obtaining accurate and reliable representations for medial axis transformations of noisy 2D point clouds.

SINR Balancing via Base Station Association, Beamforming, and Power Control in Downlink Multicell MISO Systems

This paper considers the downlink channel of multicell multiuser multiple-input single-output systems with arbitrary architecture. We aim to maximize the minimum weighted signal-to-interference-plus-noise ratio (SINR) through user-base station (BS) association, coordinated beamforming among BSs, and power control subject to per BS power constraints. The problem is known to be NP-hard. In the high-SNR regime, where the performance is interference-limited, we globally optimize the upper bound, which is achieved asymptotically, of the balanced SINR. In the low-SNR regime, where the performance is restricted by the tightest per BS power constraint, we balance the transmit power using relaxed integer programming and group sparse optimization techniques. The two goals can be integrated to achieve a universally better performance. From the perspective of optimization methods, the corresponding algorithms are based on Lagrangian relaxation and are guaranteed to converge. Simulation results show that the proposed algorithms outperform the existing algorithms designed for the downlink single-input single-output systems.

The total variation constrained data divergence minimization model for image reconstruction and its Chambolle-Pock solving algorithm

Image reconstruction is an important inverse problem to reconstruct images from its transform. The two main reconstruction methods are the analytic method and the iterative method. The analytic method, for example, the filtered backprojection algorithm, needs complete projection data, so it is not competent to accurately reconstruct an image from sparse data. Thus the iterative method combined with optimization techniques has received more and more attention. The optimization-based iterative image reconstruction algorithm may accurately reconstruct images by the use of compressed sensing, low rank matrix and other sparse optimization techniques. Among them, the total variation (TV) minimization model is a simple but effective optimization model. The traditional, constrained TV model employs the data fidelity term as the constraint term and the TV regularization term as the objective function. In the present work, we study a novel, TV constrained, data divergence minimization (TVcDM) model and its solver. We derive in detail the Chambolle-Pock (CP) algorithm for solving the TVcDM model, verify the correctness of the model and its solver, analyze the convergence behavior of the algorithm, evaluate the sparse reconstruction ability of the TVcDM-CP algorithm and finally analyze the influence of the model parameters on reconstruction and the effect of algorithm parameters on convergence rate. The studies show that the TVcDM model may accurately reconstruct images from sparse-view projections. The TVcDM-CP algorithm may ensure convergence but the vibration phenomena may be observed in the convergence process. The model parameter, TV tolerance, has important influence on reconstruction quality, i. e. too big a value introduces noise whereas too small a value may smoothen the image details. Also, the studies reveal that different algorithm-parameter selections may lead to different convergence rates. The TVcDM-CP algorithm may be tailored and applied to other computed tomography scanning configurations and other imaging modalities. The necessary key work is just to design the corresponding system matrix and select the optimal model parameters and algorithm parameters according to the insights gained in the work.

A Network Model for an Urban Bike Sharing System

In this paper, we study and implement a model of the “ToBike” bike sharing system, located in the city of Turin, Italy. The system is modeled through a closed queuing network. A thorough data analysis phase is executed on the logged dataset provided by the service provider, to assess the stationarity properties of the system and to estimate the system parameters. In particular, customer arrival rates, not directly available, are estimated from station throughput measurements through a sparse optimization technique. The parameters are then used to perform predictions of the system behavior over an unseen validation dataset. While the accuracy provided by asymptotic methods, like mean value analysis, is quite limited, numerical simulations of the closed queueing network offer viable predictions, especially when realistic behavioral patterns for the customer behavior are considered.

An Efficient Reactive Power Control Method for Power Network Systems with Solar Photovoltaic Generators Using Sparse Optimization

With the incremental introduction of solar photovoltaic (PV) generators into existing power systems, and their fast-growing share in the gross electricity generation, system voltage stability has become a critical issue. One of the major concerns is voltage fluctuation, due to large and random penetration of solar PV generators. To suppress severe system voltage deviation, reactive power control of the photovoltaic system inverter has been widely proposed in recent works; however, excessive use of reactive power control would increase both initial and operating costs. In this paper, a method for efficient allocation and control of reactive power injection using the sparse optimization technique is proposed. Based on a constrained linearized model describing the influence of reactive power injection on voltage magnitude change, the objective of this study is formulated as an optimization problem, which aims to find the best reactive power injection that minimizes the whole system voltage variation. Two types of formulations are compared: the first one is the conventional least-square optimization, while the second one is adopted from a sparse optimization technique, called the constrained least absolute shrinkage and selection operator (LASSO) method. The constrained LASSO method adds ℓ 1 -norm penalty to the total reactive power injection, which contributes to the suppression of the number of control nodes with non-zero reactive power injection. The authors analyzed the effectiveness of the constrained LASSO method using the IEEE 39-bus and 57-bus power network as benchmark examples, under various PV power generation and allocation patterns. The simulation results show that the constrained LASSO method automatically selects the minimum number of inverters required for voltage regulation at the current operating point.

Distributed Scheduling of Network Connectivity Using Mobile Access Point Robots

In this paper, we consider scenarios where mobility can be exploited to enable reliable communications in wireless networks with scarce resources that are unable to concurrently service their nodes. Specifically, we consider cases where a team of robots operate as mobile access points (APs) that provide service, namely sufficient end-to-end communication routes, to a multihop network of static source nodes which generate data. We introduce the connectivity scheduling problem, a novel framework that combines motion planning of the APs with service scheduling of the source nodes and network routing control so that integrity of communications is guaranteed over time. We formulate the connectivity scheduling problem as a multistage mixed integer programming (MIP) problem, where path planning, service scheduling, and routing decisions are all jointly optimized over a discrete-time horizon. Since MIP problems can grow intractable quickly, we further consider a continuous convex reformulation of the problem and employ sparse optimization techniques, specifically the reweighted $\ell _1$ regularization scheme, to recover the desired integrality structure of the solution. We propose a decentralized method to solve the above relaxation that is based on the recently developed accelerated distributed augmented Lagrangians (ADAL) algorithm. Specifically, we modify ADAL by incorporating in the algorithm the reweighted $\ell _1$ scheme, which enables us to recover the desired sparsity structure of the original MIP at the final solution. Numerical results are presented that validate the effectiveness of the proposed framework.

Shallow water acoustic channel estimation across fluctuations in channel support

Estimating the shallow water acoustic channel across rapidly varying multipath fluctuations have been an open challenge for decades. Recently, sparse sensing techniques have been employed to take advantage of the heavy-tailed distribution of channel components in the Delay-Doppler domain. Despite noticeable improvement over channel estimator performance by exploiting channel sparsity compared to traditional least-squared based techniques, a key challenge remains. Most sparse recovery techniques are designed to estimate high-amplitude components across static or slowly varying support. Depending on wind and sea conditions, the underlying distribution of the channel components may change unpredictably, leading to fluctuations in the channel support that are difficult to model or track efficiently with high precision. Furthermore, not all channel components are high-energy and therefore, may be unintentionally suppressed by a sparse optimization technique. We will present the current state-of-the-art on applying sparse sensing, particularly mixed norm techniques, to shallow water channel tracking. In particular, we will present extensions to prior work on channel estimation that exploit a non-convex metric to converge faster to the same solution offered by the traditional (and convex) Lasso metric. We will present how non-convex optimization can navigate varying channel sparsity and present results based on experimental field data.

Radial Basis Function Interpolation for Signal-Model-Independent Localization

In this paper, we propose a novel localization algorithm to be used in applications where the measurement model is neither accurate nor complete. In our algorithm, we apply radial basis function (RBF) interpolation to evaluate the measurement function on the entire surveillance area and, then, estimate the target position. Since the signal function is sparse in the spatial domain, we also propose to use sparse optimization techniques (LASSO) both to efficiently compute the weights for the RBF and to improve the interpolated function quality. Simulation results show good performance in the localization of single and multiple targets.

Traffic demand-aware topology control for enhanced energy-efficiency of cellular networks

The service provided by mobile networks operated today is not adapted to spatio-temporal fluctuations in traffic demand, although such fluctuations offer opportunities for energy savings. In particular, significant gains in energy efficiency are realizable by disengaging temporarily redundant hardware components of base stations. We therefore propose a novel optimization framework that considers both the load-dependent energy radiated by the antennas and the remaining forms of energy needed for operating the base stations. The objective is to reduce the energy consumption of mobile networks, while ensuring that the data rate requirements of the users are met throughout the coverage area. Building upon sparse optimization techniques, we develop a majorization-minimization algorithm with the ability to identify energy-efficient network configurations. The iterative algorithm is load-aware, has low computational complexity, and can be implemented in an online fashion to exploit load fluctuations on a short time scale. Simulations show that the algorithm can find network configurations with the energy consumption similar to that obtained with global optimization tools, which cannot be applied to real large networks. Although we consider only one currently deployed cellular technology, the optimization framework is general, potentially applicable to a large class of access technologies.

A fast time-difference inverse solver for 3D EIT with application to lung imaging.

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.