Info-Greedy sequential adaptive compressed sensing

We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of $k$-sparse signals by connecting compressed sensing and blackbox complexity of sequential query algorithms, and present Info-Greedy algorithms for Gaussian and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse Info-Greedy measurements. Numerical examples demonstrate the good performance of the proposed algorithms using simulated and real data: Info-Greedy Sensing shows significant improvement over random projection for signals with sparse and low-rank covariance matrices, and adaptivity brings robustness when there is a mismatch between the assumed and the true distributions.Comment: Preliminary results presented at Allerton Conference 2014. To appear in IEEE Journal Selected Topics on Signal Processin

Localization of DOA trajectories -- Beyond the grid

The direction of arrival (DOA) estimation algorithms are crucial in localizing acoustic sources. Traditional localization methods rely on block-level processing to extract the directional information from multiple measurements processed together. However, these methods assume that DOA remains constant throughout the block, which may not be true in practical scenarios. Also, the performance of localization methods is limited when the true parameters do not lie on the parameter search grid. In this paper we propose two trajectory models, namely the polynomial and bandlimited trajectory models, to capture the DOA dynamics. To estimate trajectory parameters, we adopt two gridless algorithms: i) Sliding Frank-Wolfe (SFW), which solves the Beurling LASSO problem and ii) Newtonized Orthogonal Matching Pursuit (NOMP), which improves over OMP using cyclic refinement. Furthermore, we extend our analysis to include wideband processing. The simulation results indicate that the proposed trajectory localization algorithms exhibit improved performance compared to grid-based methods in terms of resolution, robustness to noise, and computational efficiency

Energy-aware Sparse Sensing of Spatial-temporally Correlated Random Fields

This dissertation focuses on the development of theories and practices of energy aware sparse sensing schemes of random fields that are correlated in the space and/or time domains. The objective of sparse sensing is to reduce the number of sensing samples in the space and/or time domains, thus reduce the energy consumption and complexity of the sensing system. Both centralized and decentralized sensing schemes are considered in this dissertation. Firstly we study the problem of energy efficient Level set estimation (LSE) of random fields correlated in time and/or space under a total power constraint. We consider uniform sampling schemes of a sensing system with a single sensor and a linear sensor network with sensors distributed uniformly on a line where sensors employ a fixed sampling rate to minimize the LSE error probability in the long term. The exact analytical cost functions and their respective upper bounds of these sampling schemes are developed by using an optimum thresholding-based LSE algorithm. The design parameters of these sampling schemes are optimized by minimizing their respective cost functions. With the analytical results, we can identify the optimum sampling period and/or node distance that can minimize the LSE error probability. Secondly we propose active sparse sensing schemes with LSE of a spatial-temporally correlated random field by using a limited number of spatially distributed sensors. In these schemes a central controller is designed to dynamically select a limited number of sensing locations according to the information revealed from past measurements,and the objective is to minimize the expected level set estimation error.The expected estimation error probability is explicitly expressed as a function of the selected sensing locations, and the results are used to formulate the optimal sensing location selection problem as a combinatorial problem. Two low complexity greedy algorithms are developed by using analytical upper bounds of the expected estimation error probability. Lastly we study the distributed estimations of a spatially correlated random field with decentralized wireless sensor networks (WSNs). We propose a distributed iterative estimation algorithm that defines the procedures for both information propagation and local estimation in each iteration. The key parameters of the algorithm, including an edge weight matrix and a sample weight matrix, are designed by following the asymptotically optimum criteria. It is shown that the asymptotically optimum performance can be achieved by distributively projecting the measurement samples into a subspace related to the covariance matrices of data and noise samples

Adaptive sampling and forecasting with mobile sensor networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2009.Includes bibliographical references (p. 213-219).This thesis addresses planning of mobile sensor networks to extract the best information possible out of the environment to improve the (ensemble) forecast at some verification region in the future. To define the information reward associated with sensing paths, the mutual information is adopted to represent the influence of the measurement actions on the reduction of the uncertainty in the verification variables. The sensor networks planning problems are posed in both discrete and continuous time/space, each of which represents a different level of abstraction of the decision space. In the discrete setting, the targeting problem is formulated to determine the sequence of information-rich waypoints for mobile sensors. A backward formulation is developed to efficiently quantify the information rewards in this combinatorial decision process. This approach computes the reward of each possible sensing choice by propagating the information backwards from the verification time/space to the search space/time. It is shown that this backward method provides an equivalent solution to a standard forward approach, while only requiring the calculation of a single covariance update. This work proves that the backward approach works significantly faster than the forward approach for the ensemble-based representation. In the continuous setting, the motion planning problem that finds the best steering commands of the sensor platforms is posed. The main difficulty in this continuous decision lies in the quantification the mutual information between the future verification variables and a continuous history of the measurement.(cont.) This work proposes the smoother form of the mutual information inspired by the conditional independence relations, and demonstrates its advantages over a simple extension of the state-of-the-art: (a) it does not require integration of differential equations for long time intervals, (b) it allows for the calculation of accumulated information on-the-fly, and (c) it provides a legitimate information potential field combined with spatial interpolation techniques. The primary benefits of the presented methods are confirmed with numerical experiments using the Lorenz-2003 idealistic chaos model.by Han-Lim Choi.Ph.D

Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift towards models that are essentially polynomial and whose uniqueness, unlike the matrix methods, is guaranteed under verymild and natural conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints that match data properties, and to find more general latent components in the data than matrix-based methods. A comprehensive introduction to tensor decompositions is provided from a signal processing perspective, starting from the algebraic foundations, via basic Canonical Polyadic and Tucker models, through to advanced cause-effect and multi-view data analysis schemes. We show that tensor decompositions enable natural generalizations of some commonly used signal processing paradigms, such as canonical correlation and subspace techniques, signal separation, linear regression, feature extraction and classification. We also cover computational aspects, and point out how ideas from compressed sensing and scientific computing may be used for addressing the otherwise unmanageable storage and manipulation problems associated with big datasets. The concepts are supported by illustrative real world case studies illuminating the benefits of the tensor framework, as efficient and promising tools for modern signal processing, data analysis and machine learning applications; these benefits also extend to vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker decomposition, HOSVD, tensor networks, Tensor Train