Compressed sensing shows that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Noting that sparse signals can be well modeled by algebraic-tailed impulsive distributions, in this paper, we formulate the sparse recovery problem in a Bayesian framework using algebraic-tailed priors from the generalized Cauchy distribution (GCD) family for the signal coefficients. We develop an iterative reconstruction algorithm from this Bayesian formulation. Simulation results show that the proposed method requires fewer samples than most existing reconstruction methods to recover sparse signals, thereby validating the use of GCD priors for the sparse reconstruction problem.

We consider consensus algorithms in their most general setting and provide conditions under which such algorithms are guaranteed to converge, almost surely, to a consensus. Let {A(t), B(t)} ∈ RN×Nbe (possibly) stochastic, nonstationary matrices and {x(t), m(t)} 6 RN×1be state and perturbation vectors, respectively. For any consensus algorithm of the form x(t + 1) = A(t)x(t) + B(t)m(t), we provide conditions under which consensus is achieved almost surely, i.e., Pr-{limt →∞x(t) = c1} -1 for some c ∈ R. Moreover, we show that this general result subsumes recently reported results for specific consensus algorithms classes, including sum-preserving, nonsum-preserving, quantized, and noisy gossip algorithms. Also provided are the e-converging time for any such converging iterative algorithm, i.e., the earliest time at which the vector x(t) is ε close to consensus, and sufficient conditions for convergence in expectation to the average of the initial node measurements. Finally, mean square error bounds of any consensus algorithm of the form discussed above are presented.

Recent results in compressed sensing show that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Compressive sensing systems are not immune to noise, which is always present in practical acquisition systems. In this paper we propose robust methods for sampling and reconstructing sparse signals in the presence of impulsive noise. Analysis of the proposed methods demonstrates their robustness under heavy-tailed models. Simulations show that the proposed methods outperform existing compressed sensing techniques in impulsive environments, while having similar performance in light-tailed environments.

Most critical component of the cognitive radio paradigm is spectrum sensing and accordingly, detection of primary users. Recently proposed cooperative spectrum sensing methods do not consider errors occurring during the transmission of local cognitive radio decisions to the cognitive base station. However, perfect communication is clearly not the case in realistic cooperative spectrum sensing scenarios and might lead to misleading performance result interpretations. In this paper, we extend the simple cooperative spectrum sensing communication model to admit transmission imperfections. Specifically, we consider the case where the local hard cognitive radio decisions that are based on any local detection scheme are corrupted by additive noise during transmission from cognitive radios to cognitive base station. Utilizing this extended cooperative spectrum sensing model, we present the complex optimal and a practical and effective suboptimal detector that is capable of operating with any local cognitive radio detection scheme: Two-step detector. We present simulation results investigating the performance of the proposed detectors and the effect of parameters of interest such as number of cognitive radios and signal to noise ratio. Moreover, we provide comparisons between non-cooperative and cooperative spectrum sensing performances revealing some cases where non-cooperative scheme is more effective.

Cooperative spectrum sensing for cognitive radio networks is recently being studied to simultaneously minimize uncertainty in primary user detection and solve hidden terminal problem. Sensing wideband spectrum is another challenging task for a single cognitive radio due to large sensing time required. In this paper, we introduce a technique to tackle both wideband and cooperative spectrum sensing tasks. We divide the wideband spectrum into several subbands. Then a group of cognitive radios is assigned for sensing of a particular narrow subband. A cognitive base station is used for collecting the results and making the final decision over the full spectrum. Our proposed algorithm minimizes time and amount of energy spent for wideband spectrum scanning by a cognitive radio, and effectively detects the primary users in the wideband spectrum thanks to cooperative shared spectrum sensing.

We consider consensus algorithms in their most general setting and provide conditions under which such algorithms are guaranteed to converge, almost surely, to a consensus. Let {A(t),B(t)} isin RNtimesNbe (possibly) random, non-stationary matrices and {x(t),m(t)} isin RNtimes1be state and perturbation vectors, respectively. For any consensus algorithm of the form x(t + 1) = A(t)x(t) + B(t)m(t), we provide conditions under which consensus is achieved almost surely, i.e., Pr {limtrarrinfinx(t) = c1} = 1 for some c isin R. Moreover, we show that this general result subsumes recently reported results for specific consensus algorithms classes, including sum-preserving, non-sum-preserving, quantized and noisy gossip algorithms. Also provided are the e-converging time for any such converging iterative algorithm, i.e., the earliest time at which the vector x(t) is e close to consensus, and sufficient conditions for convergence in expectation to the initial node measurements average.

This paper explores the use of multi-bit quantisation of image features for similarity-based image retrieval. Our work builds on multi-resolution image similarity search algorithms which utilise one-bit representation of the largest magnitude wavelet coefficients. Given a query, images are ranked based on the number of quantised coefficients they have in common with the query. We explore the benefits of a finer-level quantisation (specifically with two bits) and one control parameter that can be chosen optimally based on the probability density of the wavelet coefficients. We show that this extension leads to significant performance improvements.

In this paper we consider cooperative localization and tracking of primary users (PU) in a cognitive radio network using Bayesian techniques. We use particle filtering methods to track the location of a PU in the network using cooperative localization techniques and present some results for noisy measurements. The cognitive radio (CR) nodes estimate the information related to the geographical position of the PU based on existing location identification and localization techniques and forward the noisy information to a cognitive radio base station (CRB), which then fuses the information to estimate the position of the PU in the network in order to perform a radio scene analysis. We propose a particle filtering approach that is suitable for tracking Gaussian and non-Gaussian noisy signals at the CRB to estimate the position of a PU, two importance-functions relative to the particle filtering algorithm are also presented. Simulations are performed on the proposed tracking algorithm and the results are presented in terms of the mean squared error of the positional estimates.

The generalized Cauchy distribution (GCD) family has the property that its pdf has closed form for the whole family and also has algebraic tails which makes it suitable to model many impulsive processes in real life. In this paper we propose a robust M-type estimator based on the pdf of the GCD family. Robustness and properties of the new statistics are analyzed and it is noticed that this estimator provide desired characteristics in robust signal processing applications involving non-Gaussian heavy-tailed models. Simulations of the filtering method are performed to evaluate and compare the proposed filtering structure performance to other classic and robust estimators.

The average consensus problem in the distributed signal processing context is addressed by linear iterative algorithms, with asymptotic convergence to the consensus. The convergence of the average consensus for an arbitrary weight matrix satisfying the convergence conditions is unfortunately slow restricting the use of the developed algorithms in applications. In this paper, we propose the use of linear extrapolation methods in order to accelerate distributed linear iterations. We provide analytical and simulation results that demonstrate the validity and effectiveness of the proposed scheme. Finally, we report simulation results showing that the generalized version of our algorithm, when a grid search for the unknown optimum value of mixing parameter is used, significantly outperforms the optimum consensus algorithm based on weight matrix optimization.

Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and for computing in an arbitrarily connected network of nodes. Specifically, we propose a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithms almost surely converge to a consensus. In addition, the random consensus value is, in expectation, equal to the desired value, i.e., the average of initial node measurements. However, the broadcast gossip algorithms do not converge to the initial average in absolute sense because of the fact that the sum is not preserved at every iteration. We provide theoretical results on the mean square error performance of the broadcast gossip algorithms. The results indicate that the mean square error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithms required to achieve a given distance to consensus through numerical simulations.

We consider decentralized estimation of a noise- corrupted deterministic signal in a bandwidth-constrained sensor network communicating through an insecure medium. Each sensor collects a noise-corrupted version, performs a local quantization, and transmits a 1-bit message to an ally fusion center through a wireless medium where the sensor outputs are vulnerable to unauthorized observation from enemy/third-party fusion centers. In this paper, we introduce an encrypted wireless sensor network (eWSN) concept where stochastic enciphers operating on binary sensor outputs are introduced to disguise the sensor outputs, creating an eWSN scheme. Noting that the plaintext (original) and ciphertext (disguised) messages are constrained to a single bit due to bandwidth constraints, we consider a binary channel-like scheme to probabilistically encipher (i.e., flip) the sensor outputs. We first consider a symmetric key encryption case where the “0” and “1” enciphering probabilities are equal. The key is represented by the bit enciphering probability. Specifically, we derive the optimal estimator of the deterministic signal approached from a maximum-likelihood perspective and the Cramer-Rao lower bound for the estimation problem utilizing the key. Furthermore, we analyze the effect of the considered cryptosystem on enemy fusion centers that are unaware of the fact that the WSN is encrypted (i.e., we derive the bias, variance, and mean square error (MSE) of the enemy fusion center). We then extend the cryptosystem to admit unequal enciphering schemes for “0” and “1”, and analyze the estimation problem from both the prospectives of ally (that has access to the enciphering keys) and (third-party) enemy fusion centers. The results show that when designed properly, a significant amount of bias and MSE can be introduced to an enemy fusion center with the cost to the ally fusion center being a marginal increase [factor of$(1-\Omega _{1}-\Omega _{0})^{-2}$, where$1-\Omega _{j}$,$j=0,1$is the “$j$” enciphering probability] in the estimation variance (compared to the variance of a fusion center estimate operating in a vulnerable WSN).

Recently proposed decentralized, distributed estimation and power scheduling methods for wireless sensor networks (WSNs) do not consider errors occurring during the transmission of binary observations from the sensors to fusion center. In this letter, we extend the decentralized estimation model to the case in which imperfect transmission channels are considered. The proposed estimators, which operate on additive channel noise corrupted versions of quantized noisy sensor observations, are approached from a maximum likelihood (ML) perspective. Complicating this approach is the fact that the noise distribution is rarely fully known to the fusion center. Here we assume the distribution is known but not the defining parameters, e.g., variance. The resulting incomplete data estimation problem is approached from a expectation-maximization (EM) perspective. The critical initialization and convergence aspects of the EM algorithm are investigated. Furthermore, the estimation of the source parameter is extended to the blind case where both the channel and sensor noise parameters are unknown. Finally, numerical experiments are provided to show the effectiveness of the proposed estimators.

This paper extends the homogeneous wireless sensor network (WSN) model to possess (possibly) varying levels of noise that represent environment clusters in a WSN. The estimation of the source parameter is approached from maximum likelihood (ML) perspective. The Cramer Rao lower bound (CRLB) for any unbiased estimator operating in a clustered WSN environment is derived. Noting that the ML estimate cannot be found in closed-from, we resort to a numerical search. Although numerically determined, the ML estimate is guaranteed to converge to the optimal solution since it is shown here that the log-likelihood function is concave. Also considered is the estimation of a random parameter with a priori information, which is approached from maximum a posteriori (MAP) perspective. Finally, the proposed MAP and ML optimal are validated and compared to theoretical bounds with illustrative numerical examples.

The linear, median, myriad filtering structures are statistically related to the maximum likelihood (ML) estimates of location under Gaussian, Laplacian, and Cauchy statistics, respectively In this paper, we propose a filtering structure based on the ML estimate of the constructed and so-called meridian statistics. Analysis and simulations presented here indicate that the proposed filtering structure exhibits characteristics more robust than that of mean, median and myriad filtering structures.

Recently proposed decentralized estimation methods do no consider errors occurring during the transmission of binary observations from the sensors to fusion center. In this paper, we extend the decentralized estimation model to the case where imperfect transmission channels are considered. The proposed estimator, which operates on additive channel noise corrupted versions of quantized noisy sensor observations, is approached from maximum likelihood (ML) perspective. The ML estimate unfortunately has no closed-form solution. We analyze the log-likelihood function showing that it is log-concave, thereby indicating that numerical methods, such as Newtons algorithm, can be utilized to obtain the optimal solution. A suboptimal mean estimator that requires minimal information about the channel and sensing environment is also proposed. Simulation results evaluating the variances of the proposed optimal and suboptimal solutions are provided.

In this paper, we extend the decentralized estimation model to the case in which imperfect transmission channels are considered. The proposed estimators, which operate on additive channel noise corrupted versions of quantized noisy sensor observations, are approached from a maximum likelihood (ML) perspective. Complicating this approach is the fact that the noise distribution is rarely fully known to the fusion center. Here we assume the distribution is known but not the defining parameters, e.g., variance. The resulting incomplete data estimation problem is approached from a expectation-maximization (EM) perspective. The critical initialization and convergence aspects of the EM algorithm are investigated. Furthermore, the estimation of the source parameter is extended to the blind case where both the channel and sensor noise parameters are unknown. Finally, numerical experiments are provided to show the effectiveness of the proposed estimators.

Image sequence prediction is widely used in image compression and transmission schemes such as differential pulse code modulation. In traditional predictive coding, linear predictors are usually adopted for simplicity. The nonlinear Volterra predictor can be employed as an alternative to linear predictors to compensate for the nonstationary and non-Gaussian nature of image sequences. Although the Volterra predictor avoids the smoothing effects introduced by linear predictors, it generally amplifies noise contamination present in the images. In this letter, we propose a nonlinear polynomial weighted median (PWM) predictor for image sequence. The proposed PWM predictor is more robust to noise, while still retaining the information of higher order statistics of pixel values. Experimental results illustrate that the PWM predictor yields good results in both high and low motion video. It is especially suitable for high motion sequence in noisy case. The proposed scheme can be incorporated in new predictive coding systems.

Speckle is a multiplicative noise that degrades ultrasound images. Recent advancements in ultrasound instrumentation and portable ultrasound devices necessitate the need for more robust despeckling techniques, for both routine clinical practice and teleconsultation. Methods previously proposed for speckle reduction suffer from two major limitations: 1) noise attenuation is not sufficient, especially in the smooth and background areas; 2) existing methods do not sufficiently preserve or enhance edges--they only inhibit smoothing near edges. In this paper, we propose a novel technique that is capable of reducing the speckle more effectively than previous methods and jointly enhancing the edge information, rather than just inhibiting smoothing. The proposed method utilizes the Rayleigh distribution to model the speckle and adopts the robust maximum-likelihood estimation approach. The resulting estimator is statistically analyzed through first and second moment derivations. A tuning parameter that naturally evolves in the estimation equation is analyzed, and an adaptive method utilizing the instantaneous coefficient of variation is proposed to adjust this parameter. To further tailor performance, a weighted version of the proposed estimator is introduced to exploit varying statistics of input samples. Finally, the proposed method is evaluated and compared to well-accepted methods through simulations utilizing synthetic and real ultrasound data.

In this paper, we propose a novel speckle filtering algorithm based on the maximum likelihood estimate of speckle statistics. The homomorphism approach is utilized to modify the multiplicative noise problem to an additive one. The statistics of the altered noise are derived. The problem is then converted to the statistical M-estimation. Properties of the proposed filtering structure are investigated. Finally, simulations indicating the advantages of the proposed filtering are presented.

Image sequence prediction is widely used in image compression and transmission schemes such as differential pulse code modulation (DPCM). In traditional predictive coding, linear predictors are usually adopted to exploit the inherent redundancy and correlation between neighboring pixels. However, due to the nonstationary and non-Gaussian nature of image sequences, linear predictors are not often very effective. As an alternative, Volterra predictor is able to compensate for the smoothing effects introduced by linear predictor. However, it suffers from noise that may be attributed to quantization errors or image acquisition devices. In this paper, we propose a novel nonlinear polynomial weighted median (PWM) predictor for image sequence prediction. The proposed PWM predictor is more robust to noise, while still retaining the information of higher-order statistics of pixel values. Experimental results illustrate that the PWM predictor yields better results than other predictors especially in noisy case. The proposed scheme can be incorporated in new predictive coding systems.

Quadratic Volterra filters are effective in image sharpening applications. The linear combination of polynomial terms, however, yields poor performance in noisy environments. Weighted median (WM) filters, in contrast, are well known for their outlier suppression and detail preservation properties. The WM sample selection methodology is naturally extended to the quadratic sample case, yielding a filter structure referred to as quadratic weighted median (QWM) that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise. Through statistical analysis of higher order samples, it is shown that, although the parent Gaussian distribution is light tailed, the higher order terms exhibit heavy-tailed distributions. The optimal combination of terms contributing to a quadratic system, i.e., cross and square, is approached from a maximum likelihood perspective which yields the WM processing of these terms. The proposed QWM filter structure is analyzed through determination of the output variance and breakdown probability. The studies show that the QWM exhibits lower variance and breakdown probability indicating the robustness of the proposed structure. The performance of the QWM filter is tested on constant regions, edges and real images, and compared to its weighted-sum dual, the quadratic Volterra filter. The simulation results show that the proposed method simultaneously suppresses the noise and enhances image details. Compared with the quadratic Volterra sharpener, the QWM filter exhibits superior qualitative and quantitative performance in noisy image sharpening.

Polynomial filter theory methods are able to approximate important classes of nonlinear systems. In the impulsive noise environments, however, outliers are amplified by the polynomial structure, yielding poor performance. Median filters are well-known for their impulsive noise suppression and fine-detail preservation. In this paper, we extend the weighted median (WM) filtering to a polynomial class, polynomial weighted median (PWM) filters which exploit higher order statistics while being robust to outliers. The PWM filter class is motivated by a study of the statistics of cross and square terms. The breakdown probability for the PWM is given and weight optimization is presented. Finally, the effectiveness of the PWM filter is shown through simulations.