Group replicator dynamics: a novel group-wise evolutionary approach for sparse brain network detection

Functional magnetic resonance imaging (fMRI) is increasingly used for studying functional integration of the brain. However, large inter-subject variability in functional connectivity, particularly in disease populations, renders detection of representative group networks challenging. In this paper, we propose a novel technique, "group replicator dynamics" (GRD), for detecting sparse functional brain networks that are common across a group of subjects. We extend the replicator dynamics (RD) approach, which we show to be a solution of the nonnegative sparse principal component analysis problem, by integrating group information into each subject's RD process. Our proposed strategy effectively coaxes all subjects' networks to evolve towards the common network of the group. This results in sparse networks comprising the same brain regions across subjects yet with subject-specific weightings of the identified brain regions. Thus, in contrast to traditional averaging approaches, GRD enables inter-subject variability to be modeled, which facilitates statistical group inference. Quantitative validation of GRD on synthetic data demonstrated superior network detection performance over standard methods. When applied to real fMRI data, GRD detected task-specific networks that conform well to prior neuroscience knowledge.     

Image representation by compressive sensing for visual sensor networks

This paper addresses the image representation problem in visual sensor networks. We propose a new image representation method for visual sensor networks based on compressive sensing (CS). CS is a new sampling method for sparse signals, which is able to compress the input data in the sampling process. Combining both signal sampling and data compression, CS is more capable of image representation for reducing the computation complexity in image/video encoder in visual sensor networks where computation resource is extremely limited. Since CS is more efficient for sparse signals, in our scheme, the input image is firstly decomposed into two components, i.e., dense and sparse components; then the dense component is encoded by the traditional approach (JPEG or JPEG 2000) while the sparse component is encoded by a CS technique. In order to improve the rate distortion performance, we leverage the strong correlation between dense and sparse components by using a piecewise autoregressive model to construct a prediction of the sparse component from the corresponding dense component. Given the measurements and the prediction of the sparse component as initial guess, we use projection onto convex set (POCS) to reconstruct the sparse component. Our method considerably reduces the number of random measurements needed for CS reconstruction and the decoding computational complexity, compared to the existing CS methods. In addition, our experimental results show that our method may achieves up to 2 dB gain in PSNR over the existing CS based schemes, for the same number of measurements.     

Machine learning-based regression models for predicting signal quality of dense wavelength division multiplexing (DWDM) optical communication network

Over the years, optical communication systems have been a significant source of fast and secure communication. However, factors like noise and mitigation error can degrade the bit error rate (BER) and quality factor (Q factor) of optical communication systems. Predicting the optimal threshold, Q factor, and BER is usually a difficult task. Therefore, in this paper, machine learning-based linear regression, least absolute shrinkage and selection operator (LASSO) regression, and Ridge regression have been used for a dense wavelength division multiplexing (DWDM)-based optical communication network to predict the signal quality. These techniques have been used to predict the desired BER, Q factor, threshold, and eye height of the system. To demonstrate this research concept, a DWDM-based optical communication network of 50 km length is designed and simulated using Optisystem-14.0. After data preparation, regression models have been developed and validated through diagnostic plots. Results show that mean square error (MSE) has a significant decline with an increase in the number of epochs for all four models. LASSO and Ridge regression have effectively resolved the issue of overfitting, which occurred in the linear regression case. Furthermore, the mean MSE plot proved the significant reduction of mean MSE in the case of LASSO regression. Results show that min BER for LASSO regression came out to be −173,627.14, providing a robust and cost-efficient process.     

On the trade-off between energy efficiency and estimation error in compressive sensing

Compressive sensing (CS) refers to the process of reconstructing a signal that is supposed to be sparse or compressible. CS has wide applications, such as in cognitive radio networks. In this paper, we investigate effective CS schemes for the trade-off between energy efficiency and estimation error. We propose an enhancement to a Bayesian estimation approach and an enhancement to the isotonic regression approach that is based on nearly isotonic regression. We also show how to compute the routing matrix for selecting active sensor nodes. The proposed enhancements are evaluated with trace-driven simulations. Considerable gaps are observed between the original approaches and the proposed enhancements in the simulation results. The near isotonic regression method achieves the best performance among all the CS schemes examined in this paper.     

Analytical multipoint moment matching reduction of distributed thermal networks

In this paper, the multipoint moment matching method for model order reduction of discretized linear thermal networks is extended to distributed linear thermal networks. As a result, from the analytical canonical forms of distributed linear thermal networks, reduced thermal networks are derived analytically. This direct construction of the reduced network, from the exact analytical solutions, avoids the inevitable inaccuracies inherent in conventional surface and volume meshing. It allows nearly exact reduced thermal network construction by domain decomposition for arbitrarily complicated structures.     

Sparse signal transmission under lossy wireless links based on double process of compressive sensing

In resource-limited wireless sensor networks,links with poor quality hinder its large-scale applications seriously.Thanks to the inherent sparse property of signals in WSN,the framework of sparse signal transmission based on double process of compressive sensing was proposed,providing an insight into a new way of real-time,accurate and energy-efficient sparse signal transmission.Firstly,the random packet loss during transmission under lossy wireless links was modeled as a linear dimension-reduced measurement process of CS (a passive process of CS).Then,considering that a large packet was often adopted in WSN for higher transmission efficiency,a random linear dimension-reduced projection (a simple source coding operation) was employed at the sender node (an active process of CS) to prevent block data loss.Now,the raw signal could be recovered from the lossy data at the receiver node using CS reconstruction algorithms.Furtherly,according to the theory of CS reconstruction and the formula of packet reception rate in wireless communication,the minimum compression ratio and the maximum packet length allowed were obtained.Extensive simulations demonstrate that the reliability of data transmission and its accuracy,the data transmission volume,the transmission delay and energy consumption could be greatly optimized by means of proposed method.     

基于压缩感知的随机噪声成像雷达

近年来提出的压缩感知(CS)理论指出可以从很少的采样点中以很大的概率准确重建原始的未知稀疏信号。该文将压缩感知与随机噪声雷达相结合,提出了基于压缩感知的随机噪声雷达,并给出了该雷达系统的基本原理框图,从理论上证明了基于压缩感知的随机噪声雷达的回波观测矩阵具有很好的等容性质,在目标场景稀疏或可以稀疏表示时,基于压缩感知的随机噪声雷达可以采集远小于常规随机噪声雷达成像所需的回波数据并能实现准确成像,最后通过仿真实验验证了该文的结论。     

Bias and variance of validation methods for function approximationneural networks under conditions of sparse data

Neural networks must be constructed and validated with strong empirical dependence, which is difficult under conditions of sparse data. The paper examines the most common methods of neural network validation along with several general validation methods from the statistical resampling literature, as applied to function approximation networks with small sample sizes. It is shown that an increase in computation, necessary for the statistical resampling methods, produces networks that perform better than those constructed in the traditional manner. The statistical resampling methods also result in lower variance of validation, however some of the methods are biased in estimating network error     

An evaluation of distributed wavelength provisioning in WDM optical networks with sparse wavelength conversion

Distributed wavelength provisioning is becoming one of the most important technologies for supporting next-generation optical networks. This paper describes the evaluation of the performance of distributed wavelength provisioning in wavelength-division-multiplexing (WDM) optical networks with sparse wavelength conversion (i.e., where wavelength conversion is available at only a subset of network nodes). Using the well-known destination-initiated reservation method as a case study, a highly accurate analytical model supported by comprehensive simulation validation is proposed. Both analytical and simulation results show that, in optical networks with distributed wavelength provisioning, sparse wavelength conversion still helps to significantly lower the connection-blocking probabilities. However, unlike that in centralized wavelength provisioning, sparse wavelength conversion may not easily achieve nearly the same performance as that of full wavelength conversion, especially under light traffic loads. This paper evaluates how the potential contribution of sparse wavelength conversion depends on different factors, such as the number of wavelength converters, the number of wavelength channels per fiber, the burstiness of traffic loads, and the network size, and discusses the influence of the signaling scheme.     

Sparse support recovery using correlation information in the presence of additive noise

The correlation based framework has recently been proposed for sparse support recovery in noiseless case. To solve this framework, the constrained least absolute shrinkage and selection operator (LASSO) was employed. The regularization parameter in the constrained LASSO was found to be a key to the recovery. This paper will discuss the sparse support recoverability via the framework and adjustment of the regularization parameter in noisy case. The main contribution is to provide noise-related conditions to guarantee the sparse support recovery. It is pointed out that the candidates of the regularization parameter taken from the noise-related region can achieve the optimization and the effect of the noise cannot be ignored. When the number of the samples is finite, the sparse support recoverability is further discussed by estimating the recovery probability for the fixed regularization parameter in the region. The asymptotic consistency is obtained in probabilistic sense when the number of the samples tends to infinity. Simulations are given to demonstrate the validity of our results.     

On Energy-Based Quality of Detection (QoD) for Cognitive Radio Sensor Networks

An energy-based primary signal detection framework is proposed to study the quality of detection (QoD) performance for cognitive radio sensor networks (CRSNs) under single cognitive sensor (CS) detection and multiple CS detection. We use hypothesis testing to first derive the exact solution and then the approximate solution (with less computational complexity) of the QoD metrics. Based on the approximate solution, we develop an adaptive QoD control scheme to maintain the QoD requirements. Numerical simulations are provided to validate the analysis. The proposed framework and analytic results are expected to be applied to different aspects (e.g., protocol design, network deployment) of CRSNs.     

基于CS的LFM信号脉冲压缩实现算法研究

针对传统的脉冲压缩方法存在着副瓣降低与主瓣展宽的矛盾问题,基于压缩感知理论提出了一种实现对LFM信号脉冲压缩的CS脉压算法。首先在分析传统脉冲压缩与压缩感知的关系的基础上,构建了适用于复数域重构的稀疏基,然后提出了采用构建的稀疏基结合平滑0-范数算法实现脉冲压缩的算法,最后证明了所提的算法脉压后信号不仅能重构出回波的幅度,且保留了信号的相位信息,最后对研究的算法从幅度、相位的重构精度以及重构误差等方面进行了仿真,仿真结果表明CS脉压算法能够在不降低距离分辨率的同时达到降低副瓣的目的,同时能保留回波信号的相位历程,具有较高的重构精度。     

Bayesian Compressive Sensing Via Belief Propagation

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(K log(N)) measurements and O(N log²(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.     

A Robust and Efficient Cross-Layer Optimal Design in Wireless Sensor Networks

When using wireless sensor networks (WSNs) for data transmission, some critical respects should be considered. These respects are limited computational power, storage capability and energy consumption. To save the energy in WSNs and prolong the network lifetime, we design for the signal control input, routing selection and capacity allocation by the optimization model based on compressed sensing (CS) framework. The reasonable optimization model is decomposed into three subsections for three layers in WSNs: congestion control in transport layer, scheduling in link layer and routing algorithm in network layer, respectively. These three functions interact and are regulated by congestion ratio so as to achieve a global optimality. Congestion control can be robust and stable by CS theory that a relatively small number of the projections for a sparse signal contain most of its salient information. Routing selection is abided by fair resource allocation principle. The resources can be allocated more and more to the channel in the case of not causing more severe congestion, which can avoid conservatively reducing resources allocation for eliminating congestion. Simulation results show the stability of our algorithm, the accurate ratio of CS, the throughput, as well as the necessity of considering congestion in WSNs.     

采用时域联合稀疏恢复的多输入多输出水声信道压缩感知估计

多输入多输出(MIMO)水声通信技术可以在极其有限的水声信道频带资源内提高信道容量,但多径和同道干扰的同时存在,使传统信道估计算法如最小二乘算法、压缩感知估计算法的性能急剧下降。考虑到通信数据块间水声信道多径结构存在一定的相关性,该文利用这种数据块间多径结构的时间域相关性建立水声MIMO信道的时域联合稀疏模型,并利用同步正交匹配追踪算法进行多个数据块联合稀疏恢复信道估计,提高MIMO信道多径稀疏位置的检测增益并抑制同道干扰,提高水声MIMO信道的估计性能。仿真和MIMO水声通信海试实验表明了所提方法的有效性。     

基于压缩感知的室内场景无线定位算法

The sparse nature of location finding in the spatial domain makes it possible to exploit the Compressive Sensing (CS) theory for wireless location. CS-based location algorithm can largely reduce the number of online measurements while achieving a high level of localization accuracy, which makes the CS-based solution very attractive for indoor positioning. However, CS theory offers exact deterministic recovery of the sparse or compressible signals under two basic restriction conditions of sparsity and incoherence. In order to achieve a good recovery performance of sparse signals, CS-based solution needs to construct an efficient CS model. The model must satisfy the practical application requirements as well as following theoretical restrictions. In this paper, we propose two novel CS-based location solutions based on two different points of view: the CS-based algorithm with raising-dimension pre-processing and the CS-based algorithm with Minor Component Analysis (MCA). Analytical studies and simulations indicate that the proposed novel schemes achieve much higher localization accuracy.     

Networks, Matroids, and Non-Shannon Information Inequalities

We define a class of networks, called matroidal networks, which includes as special cases all scalar-linearly solvable networks, and in particular solvable multicast networks. We then present a method for constructing matroidal networks from known matroids. We specifically construct networks that play an important role in proving results in the literature, such as the insufficiency of linear network coding and the unachievability of network coding capacity. We also construct a new network, from the Vamos matroid, which we call the Vamos network, and use it to prove that Shannon-type information inequalities are in general not sufficient for computing network coding capacities. To accomplish this, we obtain a capacity upper bound for the Vamos network using a non-Shannon-type information inequality discovered in 1998 by Zhang and Yeung, and then show that it is smaller than any such bound derived from Shannon-type information inequalities. This is the first application of a non-Shannon-type inequality to network coding. We also compute the exact routing capacity and linear coding capacity of the Vamos network. Finally, using a variation of the Vamos network, we prove that Shannon-type information inequalities are insufficient even for computing network coding capacities of multiple-unicast networks.     

Sparse Wavelength Conversion in Wavelength-Routed WDM Optical Networks*

A wavelength-routed optical network can suffer inefficiencies due to the wavelength-continuity constraint (under which a signal has to remain on the same wavelength from the source to the destination). In order to eliminate or reduce the effects of this constraint, a device called a wavelength converter may be utilized. Due to the high cost of these wavelength converters, many studies have attempted to determine the exact benefits of wavelength conversion. However, most of these studies have focused on optical networks that implement full wavelength conversion capabilities. An alternative to full wavelength conversion is to employ only a sparse number of wavelength converters throughout the network, thereby reducing network costs. This study will focus on different versions of sparse wavelength conversion--namely, sparse nodal conversion, sparse switch-output conversion, and sparse (or limited) range conversion--to determine if most of the benefits of full conversion can be obtained using only sparse conversion. Simulation and analytical results on these three different classes of sparse wavelength conversion will be presented. In addition, this study will present heuristic techniques for the placement of sparse conversion facilities within an optical network.     

基于压缩感知技术的双向中继信道估计

设计了一种基于压缩感知（compressive sensing, CS）技术的双向中继信道（two-way relay channels, TWRC）估计方法,并具体采用正交匹配追踪算法（orthogonal matching pursuit, OMP）对OFDM系统下的信道脉冲响应进行估计。双向中继信道往往呈现出稀疏多径结构,这种结构会随着信号空间维数的增大而越加明显。传统的线性估计方法没有考虑到TWRC的潜在稀疏性,因而导致了对关键通信资源的过度使用。而基于CS的TWRC估计方法能够很好地利用这种传输信道的稀疏多径结构,与传统线性估计方法相比,在获得同样估计性能的前提下,需要的训练序列长度大大减少,有效地提高了频谱、能量等资源利用率。同时,所采用的OMP算法的时间复杂度主要依赖于信道稀疏度,因此计算效率往往比传统的方法高。仿真也证实了基于CS的TWRC估计算法的优越性。      

基于自学习稀疏先验的三维SAR成像方法

合成孔径雷达三维成像技术(3D SAR)能通过孔径维度扩展实现三维成像能力,但数据维度大、系统实现难、成像分辨率低。压缩感知稀疏重构技术在简化3D SAR系统、提升成像质量等方面展现出巨大潜力,但面临计算复杂度高、参数设置困难、弱稀疏场景适应差等新问题,制约了其实际应用。针对上述问题,该文结合卷积神经网络的特征学习及迭代算法的深度展开理论,提出了基于自学习稀疏先验的3D SAR成像方法。首先,探讨了常规3D SAR稀疏成像中矩阵向量线性表征模型的局限性,引入成像算子提升成像算法处理效率。其次,讨论了迭代算法映射网络的深度展开模型和实现方式,包括网络拓扑结构设计、算法参数的优化约束及网络的训练方法。最后,通过仿真数据和地面实验,证明了所提方法在提升成像精度的同时,其运行时间较传统稀疏成像算法降低一个数量级。