Large-scale sensor networks that can monitor an environment at close range with high spatial and temporal resolutions are expected to play an important role in various applications, e.g. assessing ``health'' of machines, aerospace vehicles, and civil-engineering structures; environmental, medical, food-safety, and habitat monitoring; energy management, inventory control, home and building automation, etc. Each node in the network will have limited sensing, signal processing, and communication capabilities, but by cooperating with each other they will accomplish tasks that are difficult to perform with conventional centralized sensing systems.
This research focuses on novel solutions for prominent signal processing problems in sensor network design: efficiently extracting information through distributed (neighborhood-based) processing, mitigating practical difficulties such as node localization errors and spatially correlated measurements, and conserving energy through active node selection. Distributed Bayesian algorithms are being developed for estimating physical phenomena in the presence of node location uncertainties; ignoring these uncertainties may lead to poor estimation and detection performance. The investigators also study nonparametric distributed signal processing approaches under the practically important scenario where parametric models for the response function and noise distribution are unknown. Here, the goal is to provide reliable inference about the observed phenomenon that is comparable to that achieved using exact parametric models. Educational goals of the program include incorporating modern teaching techniques and statistical signal processing applications into the undergraduate engineering curriculum and integrating state-of-the-art signal processing into the graduate engineering curriculum at the Iowa State University. The research results and teaching tools developed in this project are made available to a broad scientific community through the Internet and publication in scientific journals.
Research outcomes. We describe our contributions to three major tasks that we have been working on. 1) Distributed Estimation and Detection for Sensor Networks Using Hidden Markov Random Field Models. We developed a hidden Markov random field (HMRF) framework for distributed signal processing in sensor-network environments. Under this framework, spatially distributed observations collected at the sensors form a noisy realization of an underlying random field that has a simple structure with Markovian dependence. We derived iterated conditional modes (ICM) algorithms for distributed estimation of the hidden random field from the noisy measurements. We consider both parametric and nonparametric measurement-error models. The proposed distributed estimators are computationally simple, applicable to a wide range of sensing environments, and localized, implying that the nodes communicate only with their neighbors to obtain the desired results. We demonstrate the performance of the proposed approach via numerical simulations. 2) Decentralized Random-field Estimation for Sensor Networks Using Quantized Measurements and Fusion-center Feedback. We consider a fusion sensor-network architecture where, due to the bandwidth and energy constraints, the nodes transmit quantized data to a fusion center. The fusion center provides feedback by broadcasting summary information to the nodes. In addition to saving energy, this feedback ensures reliability and robustness to node and fusion-center failures. We developed a Bayesian framework for adaptive quantization, fusion-center feedback, and estimation of the random field and its parameters. We demonstrated that, by employing fusion-center feedback, we can reconstruct the phenomenon of interest using very few information bits transmitted from the nodes to the fusion center. We showed that, for the same node transmission budget, fusion-center feedback can bring an order of magnitude improvement in estimation performance, compared with the no-feedback approach. In our framework, each node uses only its local information. Furthermore, the nodes are treated equally by the fusion center and can continue to operate in the same manner even if the fusion center changes. 3) Sparse Signal Reconstruction. (a) We propose a probabilistic model for sparse signal reconstruction and develop several novel algorithms for computing the maximum likelihood (ML) parameter estimates under this model. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. Our reconstruction schemes are based on an expectation-conditional maximization either (ECME) iteration that aims at maximizing the likelihood function with respect to the unknown parameters for a given signal sparsity level. We propose a double overrelaxation (DORE) thresholding scheme for accelerating the ECME iteration. We prove that, under certain mild conditions, the ECME and DORE iterations converge to local maxima of the likelihood function. The ECME and DORE iterations can be implemented exactly in small-scale applications and for the important class of large-scale sensing operators with orthonormal rows used e.g. partial fast Fourier transform (FFT). If the signal sparsity level is unknown, we introduce an unconstrained sparsity selection (USS) criterion and a tuning-free automatic double overrelaxation (ADORE) thresholding method that employs USS to estimate the sparsity level. We compare the proposed and existing sparse signal reconstruction methods via one-dimensional simulation and two-dimensional image reconstruction experiments using simulated and real X-ray CT data. To the best of our knowledge, we are among the first to apply compressive sampling to real NDE data in general and to NDE X-ray CT data in particular. (b) We develop a generalized expectation-maximization (GEM) algorithm for sparse signal reconstruction from quantized noisy measurements. The measurements follow an underdetermined linear model with sparse regression coefficients, corrupted by additive white Gaussian noise having unknown variance. These measurements are quantized into bins and only the bin indices are used for reconstruction. We treat the unquantized measurements as the missing data and propose a GEM iteration that aims at maximizing the likelihood function with respect to the unknown parameters. Under mild conditions, our GEM iteration yields a convergent monotonically non-decreasing likelihood function sequence and the Euclidean distance between two consecutive GEM signal iterates goes to zero as the number of iterations grows. We compare the proposed scheme with the state-of-the-art convex relaxation method for quantized compressed sensing via numerical simulations. Student supervision and outreach activities. Two students, Benhong Zhang and Kun Qiu, received Ph.D. degrees with support from this award and are currently employed as a Senior Vice President at the Bank of America Corporation and a Staff Scientist at the SAS Institute, respectively, where they work onsignal processing for financial applications. Under the PI's supervision, one Hispanic student working on this project has received an M.S. degree. As a part of the outreach effort, the PI organized a premier signal processing workshop (CAMSAP 2011) in San Juan, Puerto Rico, which featured plenary talks from the world's leading researchers in the area, special focus sessions, and contributed papers, including the contributions from Puerto Rico.
