This paper considers asymptotic perfect secrecy and asymptotic perfect estimation in distributed estimation for large sensor networks under threat of an eavesdropper, which has access to all sensor outputs. To measure secrecy, we compare the estimation performance at the fusion center and at eavesdropper in terms of their respective Fisher Information. We analyze the Fisher Information ratio between the fusion center and eavesdropper and derive the maximum achievable ratio when the channels between sensors and eavesdropper are noisy binary symmetric channels. Furthermore, when the fusion center has noiseless channels, we show that the Fisher Information ratio can be made arbitrarily large by careful design of the sensor quantization rules. As a result, asymptotic perfect secrecy can be achieved by making the Fisher Information at Eve arbitrarily small while keeping the Fisher Information at the fusion center arbitrarily large. The secrecy design method in this paper might greatly enhance the secrecy in distributed estimation for large sensor networks.

We address the optimal quantizer design problem for distributed Bayesian parameter estimation with one-bit quantization at local sensors. A performance limit obtained for any distributed parameter estimator with a known prior is adopted as a guidance for quantizer design. Aided by the performance limit, the optimal quantizer and a set of noisy observation models that achieve the performance limit are derived. Further, when the performance limit may not be achievable for some applications, we develop a near-optimal estimator which consists of a dithered noise and a single threshold quantizer. In the scenario where the parameter is Gaussian and signal-to-noise ratio is greater than −1.138 dB, we show that one can construct such an estimator that achieves approximately 99.65% of the performance limit.

This paper examines the secrecy in distributed detection under threat of a global eavesdropper (Eve) which has access to all sensors decisions. To measure secrecy, we compare the detection performance at the fusion center (FC) and at Eve in terms of their respective Kullback-Leibler Divergence (KLD). When the channels between sensors and the FC are noiseless and the channels between sensors and Eve are noisy, we show that the KLD ratio between the FC and Eve can be made arbitrarily large, provided the log-likelihood ratio at local sensors is unbounded. As a result, a perfect secrecy can be achieved asymptotically by making the KLD at Eve arbitrarily small with almost 0 detectability while keeping the KLD at the FC arbitrary large, for an almost error-free detection. This result reveals an intriguing relationship between networks size and networks secrecy.

In this paper, a distributed detection model is introduced for m-ary hypotheses testing where the local sensors quantize their decisions to messages with alphabet size of D and the number of local sensors is random following a Poisson distribution. This model can be applied to a wide variety of distributed detection problems including homogenous and heterogeneous networks, robust detection under security attacks, and sensor failure mode analysis. As an illustrative example, the proposed model is applied to a Cognitive Radio network where the performance and strategies regarding Byzantine attacks are investigated under a game theoretical setting. Performance tradeoff between the detection efficiency and robustness of the sensor network is evaluated under the independent Byzantine attack model, where the malicious nodes attack based solely on their own observations. It is shown that, when the system is designed for maximum efficiency versus optimal robustness, then the malicious users may completely blind the fusion center, with less than one half of the total number of sensors.

Noise, traditionally defined as an unwanted signal or disturbance, has been shown to play an important constructive role in many information processing systems and algorithms. This noise enhancement has been observed and employed in many physical, biological, and engineered systems. Indeed stochastic facilitation (SF) has been found critical for certain biological information functions such as detection of weak, subthreshold stimuli or suprathreshold signals through both experimental verification and analytical model simulations. In this paper, we present a systematic noise-enhanced information processing framework to analyze and optimize the performance of engineered systems. System performance is evaluated not only in terms of signal-to-noise ratio but also in terms of other more relevant metrics such as probability of error for signal detection or mean square error for parameter estimation. As an important new instance of SF, we also discuss the constructive effect of noise in associative memory recall. Potential enhancement of image processing systems via the addition of noise is discussed with important applications in biomedical image enhancement, image denoising, and classification.

Distributed detection with dependent observations is always a challenging problem. In this paper, we consider a special dependent case where sensors share some common information. Specifically, we investigate a tandem network with sensor 1 sending a one-bit decision to sensor 2 where the final decision is made. Along with their common observation X2, sensors 1 and 2 possess their conditionally independent measurements X1and X3, respectively. After obtaining the relationship between the optimal sensor 1 rule and sensor 2 fusion rule, we derive the necessary condition for the optimal sensor decision rules for both sensors. We compare the optimal rules with two suboptimal rules for distributed detection of a constant DC signal in Gaussian noise with various of signal-to-noise ratios.

Uniformly Most Powerful (UMP) centralized detection for the composite binary hypothesis problem has been well researched. This paper extends the UMP methodology to the parallel distributed detection problem, when the local observations are independently distributed. A collection of general theorems and corollaries define sufficient conditions for the existence of a UMP parallel Distributed Detection (UMP-DD) under one set of fusion rules. These same conditions under another set of general fusion rules result in at least a Locally Most Powerful Distributed Detection (LMP-DD) rule. The subtleties of these conclusions are explored using informative examples that highlight the strengths of this approach and introduce new groups of UMP-DD tests.

Registration of two high-dimensional data sets often involves dimensionality reduction to yield a single-band image from each data set followed by pairwise image registration. We develop a new application-specific algorithm for dimensionality reduction of high-dimensional data sets such that the weighted harmonic mean of Cramér-Rao lower bounds for the estimation of the transformation parameters for registration is minimized. The performance of the proposed dimensionality reduction algorithm is evaluated using three remotes sensing data sets. The experimental results using mutual information-based pairwise registration technique demonstrate that our proposed dimensionality reduction algorithm combines the original data sets to obtain the image pair with more texture, resulting in improved image registration.

Without the conditional independence assumption, the problem of distributed detection becomes intractable in general. A promising approach for this problem was proposed recently that utilizes a hierarchical conditional independence model. By inserting a hidden variable in the detection hierarchy that induces conditional independence among sensor observations, it is possible to identify certain conditions under which the detection problems become tractable. This paper generalizes the conditions thereby broadening the classes of distributed detection problems with dependent observations that can be readily solved. An example of distributed detection of a random signal is given to show that the proposed generalization can solve problems that were not possible using the original approach.

This paper considers the problem of Byzantine attacks on cooperative spectrum sensing in cognitive radio networks. Our major contribution is a technique to learn about the cognitive radio (CR) potential malicious behavior over time and thereby identifies the Byzantines and then estimates their probabilities of false alarm (Pfa) and detection (PD). We show that for a given set of data over time, the Byzantines can be identified for any a (percentage of Byzantines). It has also been shown that these estimates of Pfaand Pn of the Byzantines are asymptotically unbiased and converge to their true values at the rate of O(T-1/2). We then use these probabilities to adaptively design the fusion rule. We calculate the Probability of error (Qe) and compare it with the minimum probability of error possible.

Markov random field (MRF) models are powerful tools to model image characteristics accurately and have been successfully applied to a large number of image processing applications. This paper investigates the problem of fusion of remote sensing images, e.g., multispectral image fusion, based on MRF models and incorporates the contextual constraints via MRF models into the fusion model. Fusion algorithms under the maximum a posteriori criterion are developed to search for solutions. Our algorithm is applicable to both multiscale decomposition (MD)-based image fusion and non-MD-based image fusion. Experimental results are provided to demonstrate the improvement of fusion performance by our algorithms.

This paper revisits the interference channels under strong interference and very strong interference, for both discrete memoryless and Gaussian channels. In particular, it is shown that for the classical definitions, while the conditions of strong interference for discrete and Gaussian cases coincide with each other, those of very strong interference are not consistent with each other in terms of mutual information inequalities. Based on this observation, a new class of discrete memoryless interference channels under very strong interference is introduced whose capacity region is characterized. This new class of channels is consistent with the Gaussian interference channel under very strong interference. Moreover, this new class of interference channels is not a subset of any existing classes of discrete memoryless interference channels with known capacity region.

In this paper, we present a unifying framework for distributed detection with dependent or independent observations. This novel framework utilizes an expanded hierarchical model by introducing a hidden variable. Facilitated by this new framework, we identify several classes of distributed detection problems with conditionally dependent observations whose optimal sensor signaling structure resembles that of the independent case. These classes of problems exhibit a decoupling effect on the form of the optimal local decision rules, much in the same way as the conditionally independent case using both the Bayesian and the Neyman-Pearson criteria.

Collaborative (or distributed) spectrum sensing has been shown to have various advantages in terms of spectrum utilization and robustness in cognitive radio networks (CRNs). The data fusion scheme is a key component of collaborative spectrum sensing. We have recently analyzed the problem of Byzantine attacks in CRNs, where malicious users send false sensing data to the fusion center (FC) leading to an increased probability of spectrum sensing error. In this paper, we propose a novel and easy to implement technique to counter Byzantine attacks in CRNs. In this approach, the FC identifies the attackers and removes them from the data fusion process. Our analysis indicates that the proposed scheme is robust against Byzantine attacks and can successfully remove the Byzantines in a short time span.

Registration of remote sensing data often involves dimensionality reduction of high-dimensional data to yield an image from each data set followed by pairwise image registration. We develop a new rule for dimensionality reduction such that the the Crame¿r-Rao lower bound (CRLB) for the estimation of the transformation parameters is minimized. A hyperspectral data set and a multispectral data set are used to evaluate our proposed rule. The experimental results using Mutual Information (MI) based pairwise registration technique demonstrate that our proposed rule can select the image pair with more texture, resulting in improved image registration results.

Distributed detection with conditionally independent observations at local sensors is well understood. The problem becomes significantly more complicated when dependence is present among sensor observations. In this paper, we attempt to make progress in our understanding of the dependent observation case. Toward this end, we present a new hierarchical model by introducing a hidden or latent variable; this model attempts to present a unified framework for distributed detection with conditionally dependent or independent observations. By a close examination of this model, we identify a class of distributed detection problems with conditionally dependent observations whose optimal sensor signaling structure resembles that of the independent case. This class of problems exhibits a decoupling effect on the form of the optimal local decision rules, much in the same way as the conditionally independent case. Important cases of this class of problems include both the previously known Gaussian case under certain parameter regimes as well as several problems first introduced in this paper. An example is given to illustrate the proposed design approach.

In this paper, we consider the design of local decision rules for distributed detection systems where decisions from peripheral detectors are transmitted over dependent nonideal channels. Under the conditional independence assumption among multiple sensor observations, we show that the optimal detection performance can be achieved by employing likelihood-ratio quantizers (LRQ) as local decision rules under both the Bayesian criterion and Neyman-Pearson (NP) criterion even for the cases where the channels between the fusion center and local sensors are dependent and noisy. This work generalizes the previous work where independence among such channels was assumed. A person-by-person optimization (PBPO) procedure to obtain the solution is presented along with an illustrative example.

This paper investigates potential improvement of nonparametric detection performance via addition of noise and evaluates the performance of noise modified nonparametric detectors. Detection performance comparisons are made between the original detectors and noise modified detectors. Conditions for improvability as well as the optimum additive noise distributions of the widely used sign detector, the Wilcoxon detector, and the dead-zone limiter detector are derived. Finally, a simple and fast learning algorithm to find the optimal noise distribution solely based on received data is presented. A near-optimal solution can be found quickly based on a relatively small dataset.

We consider decentralized detection for resource-constrained wireless sensor networks where local sensor decisions need to go through a multi-hop relay network before reaching the fusion center. Our objective is to collectively design sensor decision rules and relay rules for optimum detection performance. Under the Bayesian criterion, we establish the necessary conditions for an optimal system and derive the form of the optimal fusion rule at the fusion center. Under some conditional independence assumptions, we derive the forms of the optimal local decision rules and the optimal relay rules and show that the optimal set of decision rules for the entire system can be specified by a set of parameters. We demonstrate the advantages of our proposed systematic approach against more conventional design approaches through a numerical example.

In this paper, we consider the distributed parameter estimation problem using one-bit quantized data from local sensors. Nonparametric distributed estimators are proposed based on knowledge of the moments of sensor noise. These estimators are shown to be either unbiased or asymptotically unbiased with bounded estimation variance for all possible parameter values. Relationship between the proposed approaches and dithering in quantization is investigated. Performance comparison is made between the proposed estimators and the Sign quantizer via an illustrative example.

In this letter, we present a novel instance of the stochastic resonance effect in sequential detection. For a general binary hypotheses sequential detection problem, the detection performance is evaluated in terms of the expected sample size under both hypotheses. Improvability conditions are established for an injected noise to reduce at least one of the expected sample sizes for a sequential detection system using stochastic resonance. The optimal noise is also determined under such criteria. An illustrative example is presented where performance comparisons are made between the original detector and different noise modified detectors.

This paper considers the decentralized fusion problem involving local sensor detection as well as the fusion of decisions transmitted over non-ideal transmission channels in a wireless sensor network. Prime emphasis is given to the enhancement of several fusion rules using a recently developed stochastic resonance methodology applied at the local sensors. Further, it is shown that the optimal form of the stochastic resonance probability mass density for the decentralized sensor fusion problem retains the same form as that previously developed for the single sensor case.

Hyperspectral imaging is becoming increasingly important in a variety of applications. These images contain a large number of contiguous bands to provide information at a fine spectral resolution and, therefore, cannot be displayed directly using an RGB color display. There has been some recent work on the problem of fusing hyperspectral images to three-band images for color display purposes. In this paper, we evaluate the performance of our recently proposed approach based on independent component analysis, correlation coefficient and mutual information (ICA- CCMI) to fuse the information from a large number of bands to three images suitable for color display. Depending on whether the reference images are available or not, several image quality metrics such as entropy and edge correlation have been proposed and employed to evaluate the fusion performance via three widely used hyperspectral image datasets.

The problem of dimensionality reduction for color representation of hyperspectral images has received recent attention. In this paper, several independent component analysis (ICA) based approaches are proposed to reduce the dimensionality of hyperspectral images for visualization. We also develop a simple but effective method, based on correlation coefficient and mutual information (CCMI), to select the suitable independent components for RGB color representation. Experimental results are presented to illustrate the performance of our approaches.

Stochastic-resonance (SR), a nonlinear physical phenomenon in which the performance of some nonlinear systems can be enhanced by adding suitable noise, has been observed and applied in many areas. However, it has not been shown whether or not this phenomenon plays a role in distributed detection. It seems counterintuitive that adding additional noise to the received decisions at the fusion center can improve detection performance. However, in this paper, we demonstrate the existence of the SR phenomenon in decision fusion by examples. An explanation for its existence is provided

This paper considers the stochastic resonance (SR) effect in the two hypotheses signal detection problem. Performance of a SR enhanced detector is derived in terms of the probability of detection PDand the probability of false alarm PFA. Furthermore, the conditions required for potential performance improvement using SR are developed. Expression for the optimal stochastic resonance noise pdf which renders the maximum po without increasing PFAis derived. By further strengthening the conditions, this approach yields the constant false alarm rate (CFAR) receiver. Finally, detector performance comparisons are made between the optimal SR noise, Gaussian, uniform and optimal symmetric pdf noises

The problem of reducing the probability of decision error of an existing binary receiver that is suboptimal using the ideas of stochastic resonance is solved. The optimal probability density function of the random variable that should be added to the input is found to be a Dirac delta function, and hence, the optimal random variable is a constant. The constant to be added depends upon the decision regions and the probability density functions under the two hypotheses and is illustrated with an example. Also, an approximate procedure for the constant determination is derived for the mean-shifted binary hypothesis testing problem

Feature subset selection is very important in high dimensional datasets such as hyperspectral images. In this paper, we define a new feature redundancy measure. Two different feature selection algorithms are proposed based on this measure. Experimental results on a real hyperspectral dataset are presented to demonstrate the effectiveness of our methodology.