Sparse Signal Recovery Based on Compressive Sensing and Exploration Using Multiple Mobile Sensors

The work in this dissertation is focused on two areas within the general discipline of statistical signal processing. First, several new algorithms are developed and exhaustively tested for solving the inverse problem of compressive sensing (CS). CS is a recently developed sub-sampling technique for signal acquisition and reconstruction which is more efficient than the traditional Nyquist sampling method. It provides the possibility of compressed data acquisition approaches to directly acquire just the important information of the signal of interest. Many natural signals are sparse or compressible in some domain such as pixel domain of images, time, frequency and so forth. The notion of compressibility or sparsity here means that many coefficients of the signal of interest are either zero or of low amplitude, in some domain, whereas some are dominating coefficients. Therefore, we may not need to take many direct or indirect samples from the signal or phenomenon to be able to capture the important information of the signal. As a simple example, one can think of a system of linear equations with N unknowns. Traditional methods suggest solving N linearly independent equations to solve for the unknowns. However, if many of the variables are known to be zero or of low amplitude, then intuitively speaking, there will be no need to have N equations. Unfortunately, in many real-world problems, the number of non-zero (effective) variables are unknown. In these cases, CS is capable of solving for the unknowns in an efficient way. In other words, it enables us to collect the important information of the sparse signal with low number of measurements. Then, considering the fact that the signal is sparse, extracting the important information of the signal is the challenge that needs to be addressed. Since most of the existing recovery algorithms in this area need some prior knowledge or parameter tuning, their application to real-world problems to achieve a good performance is difficult. In this dissertation, several new CS algorithms are proposed for the recovery of sparse signals. The proposed algorithms mostly do not require any prior knowledge on the signal or its structure. In fact, these algorithms can learn the underlying structure of the signal based on the collected measurements and successfully reconstruct the signal, with high probability. The other merit of the proposed algorithms is that they are generally flexible in incorporating any prior knowledge on the noise, sparisty level, and so on. The second part of this study is devoted to deployment of mobile sensors in circumstances that the number of sensors to sample the entire region is inadequate. Therefore, where to deploy the sensors, to both explore new regions while refining knowledge in aleady visited areas is of high importance. Here, a new framework is proposed to decide on the trajectories of sensors as they collect the measurements. The proposed framework has two main stages. The first stage performs interpolation/extrapolation to estimate the phenomenon of interest at unseen loactions, and the second stage decides on the informative trajectory based on the collected and estimated data. This framework can be applied to various problems such as tuning the constellation of sensor-bearing satellites, robotics, or any type of adaptive sensor placement/configuration problem. Depending on the problem, some modifications on the constraints in the framework may be needed. As an application side of this work, the proposed framework is applied to a surrogate problem related to the constellation adjustment of sensor-bearing satellites

On the Stability Analysis of Perturbed Continuous T-S Fuzzy Models

This paper deals with the stability problem of continuous-time Takagi-Sugeno (T-S) fuzzy models. Based on the Tanaka and Sugeno theorem, a new systematic method is introduced to investigate the asymptotic stability of T-S models in case of having second-order and symmetric state matrices. This stability criterion has the merit that selection of the common positive-definite matrix P is independent of the sub-diagonal entries of the state matrices. It means for a set of fuzzy models having the same main diagonal state matrices, it suffices to apply the method once. Furthermore, the method can be applied to T-S models having certain uncertainties. We obtain bounds for the uncertainties under which the asymptotic stability of the system is guaranteed. The obtained bounds are shown to be tight. Finally, the maximum permissible uncertainty bounds are investigated. Several examples are given to illustrate the effectiveness of the proposed method

Exploration vs. Data Refinement via Multiple Mobile Sensors

We examine the deployment of multiple mobile sensors to explore an unknown region to map regions containing concentration of a physical quantity such as heat, electron density, and so on. The exploration trades off between two desiderata: to continue taking data in a region known to contain the quantity of interest with the intent of refining the measurements vs. taking data in unobserved areas to attempt to discover new regions where the quantity may exist. Making reasonable and practical decisions to simultaneously fulfill both goals of exploration and data refinement seem to be hard and contradictory. For this purpose, we propose a general framework that makes value-laden decisions for the trajectory of mobile sensors. The framework employs a Gaussian process regression model to predict the distribution of the physical quantity of interest at unseen locations. Then, the decision-making on the trajectories of sensors is performed using an epistemic utility controller. An example is provided to illustrate the merit and applicability of the proposed framework

New Bayesian Compressive Sensing Algorithms for Sparse Signal Recovery

Compressive sensing (CS) is one of the evolving areas in signal acquisition and reconstruction with many applications including the study of brain activities, recovery of multi-band signals, separating the foreground and background components from the collection of noisy frames of a video recording, reconstruction of hand-written digits, taking images using one-pixel camera, and so forth. It is a promising technique in processing compressible or sparse signals by requiring far few samples than the well-known Nyquist rate. Sparse signals have very few non-zero elements. In CS the goal is to efficiently measure and then reconstruct the signal under the assumption that the underlying signal of interest is sparse but the number and location of the non-zeros are unknown. Here, we provide some of our recently proposed algorithms in this area using Bayesian approach. Bayesian learning models are powerful and flexible to incorporate the prior knowledge on the characteristics of the underlying signals. We evaluate the performance of our proposed algorithms compared to other existing algorithms in terms of the detection and false-alarm rate via receiver operating curves (ROC) on the synthetically generated data. We also illustrate the performance based on some real-world data

CAMP: An Algorithm to Recover Sparse Signals with Unknown Clustering Pattern Using Approximate Message Passing

Recovering clustered sparse signals with an unknown sparsity pattern for the single measurement vector (SMV) problems is considered. The notion of sparsity in this context is referred to the signals having very few non-zero elements in some known basis. In the SMV, the objective is to recover a sparse or compressible signal from a small set of linear non-adaptive measurements. The case considered in this paper is that the signal of interest is not only sparse but also has an unknown clustered pattern, which occurs in many practical situations. In this case, we propose a sparse Bayesian learning algorithm simplified by the approximate message passing to reduce the complexity of the algorithm. In order to encourage the probably existing clustered sparsity pattern, we define a prior which provides a measure of contiguity over the supports of the solution. We refer to the proposed algorithm as CAMP, where the letter C stands for clustered sparsity pattern and AMP denotes approximate message passing. Simulation results show an encouraging result

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs

Sparse Recovery with Unknown Sparsity Pattern via Multiple Measurement Vectors

In this work, we investigate finding the supports of sparse signals via multiple measurement vectors (MMVs). MMV can be thought as a collection of single measurement vectors (SMVs), in which all the SMVs share the same sparsity pattern, referred to as joint sparsity in the literature. The term sparse is referred to the signals that have very few non-zero (active) elements. The SMV problem is essentially a computational problem related to compressive sensing (CS) with the core idea of providing the possibility of measuring and representing a sparse or compressible signal from a small set of non-adaptive linear measurements. Here, we first propose a hierarchical Bayesian model to solve the MMV problem in the presence of noise. Our model decouples the signal into two parts; the supports of the solution and the amplitudes of the non-zero elements in the solution. Supports of the signal are the location of non-zero elements in the solution. In some applications such as magnetoencephalography (MEG), the signal of interest is not only sparse but also exhibits a clustered sparsity pattern. For example, MEG investigates the locations where most brain activities are produced. The brain activities exhibit contiguity, meaning that they occur in localized regions. Such unknown clustered sparsity pattern can be considered as a prior information in our proposed model. For this purpose, we modify our model by incorporating a parameter that accounts for the measure of contiguity (number of transitions) in the supports of the solution. The emphasizing factor on the contiguity measure of the supports will also be learned in our algorithm. Based on the experimental results, we show that our model is capable of learning the unknown sparsity clustered pattern. In this case, we evaluate the performance of our algorithm via receiver operating curves (ROCs)

Estimating Pragmatic Competence of EFL Learners' Listening Comprehension via Gricean Cooperative Principles

Understanding the pragmatic meanings of the utterances in exchanges is a serious challenge among English language learners. This study aimed to estimate the pragmatic competence of EFL learners’ listening comprehension concerned with cooperative principles (CPs) of TOEFL candidates taking the listening modules. The maxims of quantity, quality, relation, and manner helped test takers uncover the indirect or figurative meanings of the speakers' intended meaning of utterances. The design of the study was exploratory-quantitative and interpretative. The participants were 150 high and low achievers of MA students majoring in TEFL. The research instrument was a 50-item listening test that was randomly selected from the Educational Testing Service (ETS). The participants took the listening test in the fall semester of 2022. Data from the listening test were collected and analyzed via t-test and ANOVA. Findings showed understanding CPs was effective in the learners’ listening performance. Furthermore, results indicated high and low achievers' recognition of quantity and manner principles was significantly different. However, there was no such difference in learners’ comprehension regarding the maxims of quality and relevance. Implications of the study suggest that EFL learners must focus more on the pragmatic meanings of quantity and manner rather than quality and relevance maxims

On the Stability Analysis of Linear Continuous-Time Distributed Systems

This paper discusses the stability problem of linear continuous-time distributed systems. When dealing with large-scale systems, usually there is not thorough knowledge of the interconnection models between different parts of the entire system. In this case, a useful stability analysis method should be able to deal with high dimensional systems accompanied with bounded uncertainties for its interconnections. In this paper, in order to formulate the stability criterion for large-scale systems, stability analysis of LTI systems is first considered. Based on the existing methods for estimating the spectra of square matrices, sufficient criteria are proposed to guarantee the asymptotic stability of such systems. One of the advantages of these stability conditions is in analyzing linear systems having uncertainties. In this case, a new sufficient criterion is introduced. Back to the main purpose of the paper, it will be proved that the method can also be used for the stability investigation of large-scale systems accompanied with bounded time-variant uncertainties. Then the maximum permissible bounds for the interconnections while holding the stability will be obtained. Since in analyzing large-scale systems there is hardly thorough knowledge about the interactions between sub- systems, finding such bounds is of great importance. Unlike most of the previous work, this method is not restricted to structured uncertainties belonging to convex sets. The merit of the suggested stability analysis is illustrated via several examples