Sparse Detection Research Articles

Distributed Detection of Sparse Stochastic Signals With Quantized Measurements: The Generalized Gaussian Case

In this paper, we consider distributed detection of sparse stochastic signals with quantized measurements. Assume that both the noise and the dominant elements in sparse signals follow the generalized Gaussian (GG) distribution. Since the communication bandwidth in sensor networks is limited, the local sensors send quantized measurements instead of analog data to the fusion center. First, we propose the locally most powerful test (LMPT) detector based on quantized measurements for distributed detection of sparse signals with the GG distribution. Then, the local quantizers are designed by maximizing the efficacy of the proposed quantized LMPT detector. In particular, we obtain the near-optimal closed-form solutions of 1-bit quantizers at the local sensors using the log-concave approximation of efficacy. Multilevel quantizers at the local sensors are numerically obtained using the particle swarm optimization (PSO) algorithm. The asymptotic relative efficiency (ARE) is derived analytically to measure the performance loss of the proposed LMPT detector caused by quantization of local measurements. Simulation results corroborate our theoretical analysis of the proposed quantized LMPT detector.

Secure Distributed Detection of Sparse Signals via Falsification of Local Compressive Measurements

The problem of detecting a high-dimensional signal based on compressive measurements in the presence of an eavesdropper (Eve) is studied in this paper. We assume that a large number of sensors collaborate to detect the presence of sparse signals while the Eve has access to all the information transmitted by the sensors to the fusion center (FC). A strategy to ensure secrecy that has been used in the literature is the injection of artificial noise to the raw observations of some of the nodes. However, this strategy considers a clairvoyant case where it assumes that all the noise injection sensors are aware of the true hypothesis, which may not be practical in some situations. Different from this, we propose a new method, in which falsified data are produced by a fraction of the nodes based on their own observations and sent to the FC. Moreover, we determine the optimal parameters of this system to ensure perfect secrecy at the Eve and maximize the detection performance at the FC. Simulation results demonstrate the superior performance of the proposed method.

Bayesian Matching Pursuit: A Finite-Alphabet Sparse Signal Recovery Algorithm for Quantized Compressive Sensing

In this letter, we consider the problem of detecting finite-alphabet sparse signals from noisy and coarsely quantized measurements. To solve this problem, we propose a greedy sparse signal detection algorithm referred to as Bayesian matching pursuit (BMP). The key idea of BMP is to identify the non-zero elements of a sparse signal that produce the largest a posteriori probabilities in an iterative fashion. Our simulation results show that the BMP algorithm outperforms the existing sparse signal reconstruction algorithms in terms of frame error rates even with a significantly reduced computational complexity.

Sparse signal detection without reconstruction based on compressive sensing

This paper considers the problem of compressive detection of sparse signals without signal reconstruction. In the compressed detection model, we present the design of measurement matrix by using the sparsity of a signal, and prove that the variances of the compressive measurements follow two different Gaussian distributions under the binary hypothesis testing. A single measurement vector (SMV) detector is proposed when the knowledge of noise variance is available. Nevertheless, the theoretical analysis shows that the SMV detector has an inferior perfornance in the low signal-noise-ratio regime. To address this situation, the SMV model is extended to the multiple measurement vectors (MMV) model. In the scenario of unknown noise (UN) variance, we propose the UN-MMV detector which requires less prior knowledge. Moreover, the closed-form expressions for the probabilities of false alarm and detection of each detector are derived, respectively. Numerical simulations are conducted to illustrate the performance of the proposed detectors.

Detection of Sparse Stochastic Signals With Quantized Measurements in Sensor Networks

In this paper, we consider the problem of detection of sparse stochastic signals with quantized measurements in sensor networks. The observed sparse signals are assumed to follow the Bernoulli–Gaussian distribution. Due to the limited bandwidth in sensor networks, the local sensors are required to send quantized measurements to the fusion center. First, we propose a detector using the locally most powerful test (LMPT) strategy, called the quantized LMPT detector, for the problem of distributed detection of sparse signals with quantized measurements. Then, the local quantizers are designed to guarantee the near optimal detection performance of the proposed quantized LMPT detector. When the designed quantization thresholds are applied at the local sensors, we show that 1) the proposed 1-bit LMPT detector with 3.3 L sensors achieves approximately the same detection performance as the clairvoyant LMPT detector with L sensors; 2) the proposed LMPT detector with 3-bit measurements can achieve detection performance comparable to the clairvoyant LMPT detector. Simulation results demonstrate the performance of the proposed quantized LMPT detector and corroborate our theoretical analysis.

Spatial Signal Detection Using Continuous Shrinkage Priors

Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. We apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.

Detection of Sparse Signals in Sensor Networks via Locally Most Powerful Tests

We consider the problem of detection of sparse stochastic signals with a distributed sensor network. Multiple sensors in the network are assumed to observe sparse signals, which share the joint sparsity pattern. The Bernoulli–Gaussian (BG) distribution with sparsity-enforcing capability is imposed on the sparse signals. The sparsity degree in the BG model is positive and close to zero in the presence of the sparse signals and is zero in the absence of the signals. Motivated by this, the problem of detection of the sparse signals with a distributed sensor network is formulated as the problem of close and one-sided hypothesis testing on the sparsity degree. For this problem, we propose a detector based on the locally most powerful test (LMPT) to decide on the presence or absence of sparse signals with sensor networks. The proposed LMPT detector does not require signal recovery, which alleviates the complexity of the detection system in sensor networks. Simulation results illustrate the performance of the proposed LMPT detector and corroborate our theoretical analysis. Simulation results also show that, compared to the detector based on matching pursuit, the proposed LMPT detector significantly reduces the computational burden without noticeable performance loss.

Supplementary score test for sparse signals in large-scale truncated one-sided sequential tests

ABSTRACTFor large-scale one-sided sequential tests from independent panels, the detection of sparse signals is considered when the signals only appear in a small portion of panels. By treating the ...

Intelligent approaches for security technologies

Intelligent approaches for security technologies

The Horseshoe+ Estimator of Ultra-Sparse Signals

We propose a new prior for ultra-sparse signal detection that we term the “horseshoe+ prior.” The horseshoe+ prior is a natural extension of the horseshoe prior that has achieved success in the estimation and detection of sparse signals and has been shown to possess a number of desirable theoretical properties while enjoying computational feasibility in high dimensions. The horseshoe+ prior builds upon these advantages. Our work proves that the horseshoe+ posterior concentrates at a rate faster than that of the horseshoe in the Kullback–Leibler (K-L) sense. We also establish theoretically that the proposed estimator has lower posterior mean squared error in estimating signals compared to the horseshoe and achieves the optimal Bayes risk in testing up to a constant. For one-group global–local scale mixture priors, we develop a new technique for analyzing the marginal sparse prior densities using the class of Meijer-G functions. In simulations, the horseshoe+ estimator demonstrates superior performance in a standard design setting against competing methods, including the horseshoe and Dirichlet–Laplace estimators. We conclude with an illustration on a prostate cancer data set and by pointing out some directions for future research.

Distance-based species tree estimation under the coalescent: Information-theoretic trade-off between number of loci and sequence length

We consider the reconstruction of a phylogeny from multiple genes under the multispecies coalescent. We establish a connection with the sparse signal detection problem, where one seeks to distinguish between a distribution and a mixture of the distribution and a sparse signal. Using this connection, we derive an information-theoretic trade-off between the number of genes, $m$, needed for an accurate reconstruction and the sequence length, $k$, of the genes. Specifically, we show that to detect a branch of length $f$, one needs $m=\Theta(1/[f^{2}\sqrt{k}])$ genes.

Generalized distributed compressive sensing with security challenges for linearly correlated information sources

SummaryDistributed compressive sensing (DCS) usually improves the signal recovery performance of multi‐signal ensembles by exploiting both intra‐ and inter‐signal correlation and sparsity structure. However, the existing DCS had proposed for a very limited ensemble of signals that has only single common information. This paper proposes a generalized DCS (GDCS) framework which can improve sparse signal detection performance given arbitrary types of common information, which are classified into full common information and partial common information after overcoming against existing limitation. Specifically, the theoretical bound on the required number of measurements under the GDCS is obtained. We also develop a practical algorithm to obtain benefits using the GDCS. At the end of this paper, it simply summarizes the potential security issues when it gets all sensing information in a sensor network. Finally, numerical results verify that the proposed algorithm reduces the required number of measurements for correlated sparse signal detection compared to the DCS algorithm. This research lays down the basis for efficient distributed signal detection so that it can improve the detection performance or it can detect the signal reliably when the number of signal observations is limited.

Sparse Simultaneous Signal Detection for Identifying Genetically Controlled Disease Genes

ABSTRACTGenome-wide association studies (GWAS) and differential expression analyses have had limited success in finding genes that cause complex diseases such as heart failure (HF), a leading cause of death in the United States. This article proposes a new statistical approach that integrates GWAS and expression quantitative trait loci (eQTL) data to identify important HF genes. For such genes, genetic variations that perturb its expression are also likely to influence disease risk. The proposed method thus tests for the presence of simultaneous signals: SNPs that are associated with the gene’s expression as well as with disease. An analytic expression for the p-value is obtained, and the method is shown to be asymptotically adaptively optimal under certain conditions. It also allows the GWAS and eQTL data to be collected from different groups of subjects, enabling investigators to integrate public resources with their own data. Simulation experiments show that it can be more powerful than standard approaches and also robust to linkage disequilibrium between variants. The method is applied to an extensive analysis of HF genomics and identifies several genes with biological evidence for being functionally relevant in the etiology of HF. It is implemented in the R package ssa. Supplementary materials for this article are available online.

Sparse Signal Detection With Compressive Measurements via Partial Support Set Estimation

In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals, which share a common but unknown support. While in the traditional compressive sensing framework, the goal is to recover the complete sparse signal, in sparse signal detection, complete signal recovery may not be necessary to make a reliable detection decision. In particular, detection can be performed based on partially or inaccurately estimated signals, which requires less computational burden than that is required for complete signal recovery. To that end, we investigate the problem of sparse signal detection based on partially estimated support set. First, we discuss how to determine the minimum fraction of the support set to be known so that a desired detection performance is achieved in a centralized setting. Second, we develop two distributed algorithms for sparse signal detection when the raw compressed observations are not available at the central fusion center. In these algorithms, the final decision statistic is computed based on locally estimated partial support sets via orthogonal matching pursuit at individual nodes. The proposed distributed algorithms with less communication overhead are shown to provide comparable performance (sometimes better) to the centralized approach when the size of the estimated partial support set is very small.

Double Detector for Sparse Signal Detection From One-Bit Compressed Sensing Measurements

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a double-detector scheme is introduced in which a sensor level threshold detector is integrated into network level GLRT to improve the performance. The detection criteria of oracle and clairvoyant detectors are also derived. Simulation results show that with careful design of the threshold detector, the overall detection performance of double-detector scheme would be better than the sign-GLRT proposed in [1] and close to oracle and clairvoyant detectors. Also, the proposed detector is applied to spectrum sensing and the results are near the well known energy detector which uses the real valued data while the proposed detector only uses the sign of the data.

Compressive detection of sparse signals in additive white Gaussian noise without signal reconstruction

The main motivation behind compressive sensing is to reduce the sampling rate at the input of a digital signal processing system. However, if for processing the sensed signal one requires to reconstruct the corresponding Nyquist samples, then the data rate will be again high in the processing stages of the overall system. Therefore, it is preferred that the desired processing task is done directly on the compressive measurements, without the need for the reconstruction of the Nyquist samples. This paper addresses the case in which the processing task is “detection” (the existence) of a sparse signal in additive white Gaussian noise, with applications e.g. in radar systems. Moreover, we will propose two estimators for estimating the degree of sparsity of the detected signal. We will show that one of the estimators attains the Cramér–Rao lower bound of the problem.

An Optimal Bahadur-Efficient Method in Detection of Sparse Signals with Applications to Pathway Analysis in Sequencing Association Studies.

Next-generation sequencing data pose a severe curse of dimensionality, complicating traditional "single marker—single trait" analysis. We propose a two-stage combined p-value method for pathway analysis. The first stage is at the gene level, where we integrate effects within a gene using the Sequence Kernel Association Test (SKAT). The second stage is at the pathway level, where we perform a correlated Lancaster procedure to detect joint effects from multiple genes within a pathway. We show that the Lancaster procedure is optimal in Bahadur efficiency among all combined p-value methods. The Bahadur efficiency,, compares sample sizes among different statistical tests when signals become sparse in sequencing data, i.e. ε →0. The optimal Bahadur efficiency ensures that the Lancaster procedure asymptotically requires a minimal sample size to detect sparse signals (). The Lancaster procedure can also be applied to meta-analysis. Extensive empirical assessments of exome sequencing data show that the proposed method outperforms Gene Set Enrichment Analysis (GSEA). We applied the competitive Lancaster procedure to meta-analysis data generated by the Global Lipids Genetics Consortium to identify pathways significantly associated with high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, triglycerides, and total cholesterol.

Compressive sensing applied to radar systems: an overview

Modern radar systems tend to utilize high bandwidth, which requires high sampling rate, and in many cases, these systems involve phased array configurations with a large number of transmit–receive elements. In contrast, the ultimate goal of a radar system is often to estimate only a limited number of target parameters. Thus, there is a pursuit to find better means to perform the radar signal acquisition as well as processing with much reduced amount of data and power requirement. Recently, there has been a great interest to consider compressive sensing (CS) for radar system design; CS is a novel technique which offers the framework for sparse signal detection and estimation for optimized data handling. In radars, CS enables the achievement of better range-Doppler resolution in comparison with the traditional techniques. However, CS requires the selection of suitable (sparse) signal model, the design of measurement system as well as the implementation of appropriate signal recovery method. This work attempts to present an overview of these CS aspects, particularly when CS is applied in monostatic pulse-Doppler and MIMO type of radars. Some of the associated challenges, e.g., grid mismatch and detector design issues, are also discussed.

Optimal detection of multi-sample aligned sparse signals

We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and the higher-criticism test statistics evaluated over pooled scans, and an average likelihood ratio over the critical boundary. We show in our results an inter-play between the scale of the sequence length to signal length ratio, and the sparseness of the signals. In particular the difficulty of the detection problem is not noticeably affected unless this ratio grows exponentially with the number of sequences. We also recover the multiscale and sparse mixture testing problems as illustrative special cases.

Adaptive sensing performance lower bounds for sparse signal detection and support estimation

This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting introduced in (IEEE Trans. Inform. Theory 57 (2011) 6222-6235) and show necessary conditions on the minimum signal magnitude for both detection and estimation: if ${\mathbf {x}}\in \mathbb{R}^n$ is a sparse vector with $s$ non-zero components then it can be reliably detected in noise provided the magnitude of the non-zero components exceeds $\sqrt{2/s}$. Furthermore, the signal support can be exactly identified provided the minimum magnitude exceeds $\sqrt{2\log s}$. Notably there is no dependence on $n$, the extrinsic signal dimension. These results show that the adaptive sensing methodologies proposed previously in the literature are essentially optimal, and cannot be substantially improved. In addition, these results provide further insights on the limits of adaptive compressive sensing.