Group Sparse Optimization Research Articles

Wideband Millimeter Wave Communication With Lens Antenna Array: Joint Beamforming and Antenna Selection With Group Sparse Optimization

For millimeter wave (mm-wave) communication systems, a lens antenna array with single-carrier transmission and path delay compensation is a promising technique for realizing cost-effective large multiple-input multiple-output communications with limited number of radio frequency chains. In this paper, we study the multi-user mm-wave downlink lens antenna array system for the general frequency-selective channels. By leveraging the angle-dependent energy focusing property of the lens antenna array and the angular sparsity of mm-wave channels, we investigate the low-complexity single-carrier transmission scheme with path delay pre-compensation applied at the base station (BS). The resulting signal-to-interference-plus-noise ratio (SINR) is derived by taking into account both the residual inter-symbol interference and inter-user interference. Based on the derived SINR expression, we propose an effective joint antenna selection and beamforming scheme by utilizing the group sparse optimization to accommodate for the limited number of RF chains at the BS. Thus, the proposed scheme can obtain the approximate performance with the fully digital case and has a better performance than the conventional orthogonal frequency-division multiplexing mode for the frequency-selectivity channels. Numerical results are provided to verify the effectiveness of the proposed schemes.

Twitter Summarization Based on Social Network and Sparse Reconstruction

With the rapid growth of microblogging services, such as Twitter, a vast of short and noisy messages are produced by millions of users, which makes people difficult to quickly grasp essential information of their interested topics. In this paper, we study extractive topic-oriented Twitter summarization as a solution to address this problem. Traditional summarization methods only consider text information, which is insufficient in social media situation. Existing Twitter summarization techniques rarely explore relations between tweets explicitly, ignoring that information can spread along the social network. Inspired by social theories that expression consistence and expression contagion are observed in social network, we propose a novel approach for Twitter summarization in short and noisy situation by integrating Social Network and Sparse Reconstruction (SNSR). We explore whether social relations can help Twitter summarization, modeling relations between tweets described as the social regularization and integrating it into the group sparse optimization framework. It conducts a sparse reconstruction process by selecting tweets that can best reconstruct the original tweets in a specific topic, with considering coverage and sparsity. We simultaneously design the diversity regularization to remove redundancy. In particular, we present a mathematical optimization formulation and develop an efficient algorithm to solve it. Due to the lack of public corpus, we construct the gold standard twitter summary datasets for 12 different topics. Experimental results on this datasets show the effectiveness of our framework for handling the large scale short and noisy messages in social media.

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.

Compressive sensing of wireless sensors based on group sparse optimization for structural health monitoring

Vibration signals of most civil infrastructures have sparse characteristics (i.e. only a few modes contribute to the vibration of the structures). Therefore, the vibration data usually have sparse representation. Additionally, the vibration data measured by the sensors placed on different locations of structure have almost the same sparse structure in the frequency domain. On basis of the group sparsity of the structural vibration data, we proposed a group sparse optimization algorithm based on compressive sensing for wireless sensors. Different from the Nyquist sampling theorem, the data are first acquired by a nonuniform low-rate random sampling method according to compressive sensing theory. We then developed the group sparse optimization algorithm to reconstruct the original data from incomplete measurements. By conducting a field test on Xiamen Haicang Bridge with wireless sensors, we illustrate the effectiveness of the proposed approach. The results show that smaller reconstruction errors can be achieved using data from multiple sensors with the group sparse optimization method than using data from only single sensor. Even using only 10% random sampling data, the original data can be reconstructed using the group sparse optimization method with a small reconstruction error. In addition, the modal parameters can also be identified from the reconstruction data with small identification errors.

Group sparse optimization for learning predictive state representations

Predictive state representations (PSRs) are a commonly used approach for agents to summarize the information from history generated during their interaction with a dynamical environment and the agents may use PSRs to predict the future observation. Existing works have shown the benefits of PSRs for modelling partially observable dynamical systems. One of the key issues in PSRs is to discover a set of tests for representing states, which is called core tests. However, there is no very efficient technique to find the core tests for a large and complex problem in practice. In this paper, we formulate the discovering of the set of core tests as an optimization problem and exploit a group sparsity of the decision-making matrix to solve the problem. Then the PSR parameters can be obtained simultaneously. Hence, the model of the underlying system can be built immediately. The new learning approach doesn’t require the specification of the number of core tests. Furthermore, the embedded optimization method for solving the considered group Lasso problem, called alternating direction method of multipliers (ADMM), can achieve a global convergence. We conduct experiments on three problem domains including one extremely large problem domain and show promising performances of the new approach.

Passive localization and classification of cavitation activity using group sparsity

In therapeutic high intensity focused ultrasound (HIFU) applications, cavitation mapping is a powerful tool to monitor and guide the treatment procedure. Furthermore, the frequency spectrum of the cavitation activity can be used to classify the mode of cavitation (stable/inertial), enabling a means for increasing the safety of the application. In this study, we formulate the cavitation mapping as a group sparse constrained optimization problem, minimizing l2,1-norm of the solution. The frequency bins related to a class of cavitation activity (harmonic, ultra-harmonic, or broadband) are grouped using l2-norm for each voxel, and l1-norm of the image is minimized. We solve this problem using an Augmented Lagrangian Method, specifically the Alternating Direction Method of Multipliers (ADMM). We used a simulation model to test this method on a 300 mm diameter 128-element hemispherical receiver array application. We calculate the radiated pressure from the microbubbles inside the HIFU beam using a rigid vessel bubble dynamics model. Then, we reconstruct the image associated with the bubble activity at the focal region using the received signals for various focal pressure distribution scenarios. The results show that the proposed method provide improved resolution and sensitivity, especially for localizing inertial cavitation activity.

Group sparse optimization via lp,q regularization

In this paper, we investigate a group sparse optimization problem via lp,q regularization in three aspects: theory, algorithm and application. In the theoretical aspect, by introducing a notion of ...

Queue-Aware Energy-Efficient Joint Remote Radio Head Activation and Beamforming in Cloud Radio Access Networks

In this paper, we study the stochastic optimization of cloud radio access networks (C-RANs) by joint remote radio head (RRH) activation and beamforming in the downlink. Unlike most previous works that only consider a static optimization framework with full traffic buffers, we formulate a dynamic optimization problem by explicitly considering the effects of random traffic arrivals and time-varying channel fading. The stochastic formulation can quantify the tradeoff between power consumption and queuing delay. Leveraging on the Lyapunov optimization technique, the stochastic optimization problem can be transformed into a per-slot penalized weighted sum rate maximization problem, which is shown to be non-deterministic polynomial-time hard. Based on the equivalence between the penalized weighted sum rate maximization problem and the penalized weighted minimum mean square error (WMMSE) problem, the group sparse beamforming optimization based WMMSE algorithm and the relaxed integer programming based WMMSE algorithm are proposed to efficiently obtain the joint RRH activation and beamforming policy. Both algorithms can converge to a stationary solution with low-complexity and can be implemented in a parallel manner, thus they are highly scalable to large-scale C-RANs. In addition, these two proposed algorithms provide a flexible and efficient means to adjust the power-delay tradeoff on demand.

Multi-document summarization via group sparse learning

Multi-document summarization (MDS) aims to capture the core information from a set of topic-specific documents. Most existing extractive methods evaluate sentences individually and select summary sentences one by one, which may ignore the hidden structure patterns among sentences and fail to keep less redundancy from the global perspective. We study this task from the perspective of compressive sensing, consider sentences in documents as a kind of signals, which are usually sparse or compressible in the sense that they have concise representation pattern expressed in the proper sentence basis and transform it to a group sparse representation issue. A novel multi-document Summarization with Group Sparse learning (SGS) framework is proposed, which can maximally reconstruct the original documents via minimizing the approximation error and jointly select summary sentences with the learnt group structure information among sentences. The summary relatedness can be modeled by constraining the reconstruction models to be close to each other, and make multiple sentences share a common underlying structure to form the summary content. With this model, we take the global information into account in evaluating the importance of sentences and further reduce the redundancy. In order to solve this group sparse convex optimization problem for MDS, we also develop an efficient algorithm based on the Nesterov’s method, which leads to much faster convergence rate than some traditional methods. Experimental results on DUC 2006 and TAC 2007 main task corpora show the effectiveness of our proposed framework. The relevant experiments are conducted to demonstrate the working mechanism of main components in the SGS framework.

Downlink and Uplink Energy Minimization Through User Association and Beamforming in C-RAN

The cloud radio access network (C-RAN) concept, in which densely deployed access points (APs) are empowered by cloud computing to cooperatively support mobile users (MUs), to improve mobile data rates, has been recently proposed. However, the high density of active APs results in severe interference and also inefficient energy consumption. Moreover, the growing popularity of highly interactive applications with stringent uplink (UL) requirements, e.g., network gaming and real-time broadcasting by wireless users, means that the UL transmission is becoming more crucial and requires special attention. Therefore in this paper, we propose a joint downlink (DL) and UL MU-AP association and beamforming design to coordinate interference in the C-RAN for energy minimization, a problem which is shown to be NP hard. Due to the new consideration of UL transmission, it is shown that the two state-of-the-art approaches for finding computationally efficient solutions of joint MU-AP association and beamforming considering only the DL, i.e., group-sparse optimization and relaxed-integer programming, cannot be modified in a straightforward way to solve our problem. Leveraging on the celebrated UL-DL duality result, we show that by establishing a virtual DL transmission for the original UL transmission, the joint DL and UL optimization problem can be converted to an equivalent DL problem in C-RAN with two inter-related subproblems for the original and virtual DL transmissions, respectively. Based on this transformation, two efficient algorithms for joint DL and UL MU-AP association and beamforming design are proposed, whose performances are evaluated and compared with other benchmarking schemes through extensive simulations.

Finding sparse solutions of systems of polynomial equations via group-sparsity optimization

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of linear equations. Then, two approaches are considered to find these group-sparse solutions. The first one is based on a convex relaxation resulting in a second-order cone programming formulation which can benefit from efficient reweighting techniques for sparsity enhancement. For this approach, sufficient conditions for the exact recovery of the sparsest solution to the polynomial system are derived in the noiseless setting, while stable recovery results are obtained for the noisy case. Though lacking a similar analysis, the second approach provides a more computationally efficient algorithm based on a greedy strategy adding the groups one-by-one. With respect to previous work, the proposed methods recover the sparsest solution in a very short computing time while remaining at least as accurate in terms of the probability of success. This probability is empirically analyzed to emphasize the relationship between the ability of the methods to solve the polynomial system and the sparsity of the solution.

Compressed sensing of color images

This work proposes a method for color imaging via compressive sampling. Random projections from each of the color channels are acquired separately. The problem is to reconstruct the original color image from the randomly projected (sub-sampled) data. Since each of the color channels are sparse in some domain (DCT, Wavelet, etc.) one way to approach the reconstruction problem is to apply sparse optimization algorithms. We note that the color channels are highly correlated and propose an alternative reconstruction method based on group sparse optimization. Two new non-convex group sparse optimization methods are proposed in this work. Experimental results show that incorporating group sparsity into the reconstruction problem produces significant improvement (more than 1 dB PSNR) over ordinary sparse algorithm.