Constrained Adaptive Sensing

Suppose that we wish to estimate a vector x∈Cn from a small number of noisy linear measurements of the form y=Ax+z, where z represents measurement noise. When the vector x is sparse, meaning that it has only s nonzeros with s≪n, one can obtain a significantly more accurate estimate of x by adaptively selecting the rows of A based on the previous measurements provided that the signal-to-noise ratio (SNR) is sufficiently large. In this paper we consider the case where we wish to realize the potential of adaptivity but where the rows of A are subject to physical constraints. In particular, we examine the case where the rows of A are constrained to belong to a finite set of allowable measurement vectors. We demonstrate both the limitations and advantages of adaptive sensing in this constrained setting. We prove that for certain measurement ensembles, the benefits offered by adaptive designs fall far short of the improvements that are possible in the unconstrained adaptive setting. On the other hand, we also provide both theoretical and empirical evidence that in some scenarios adaptivity does still result in substantial improvements even in the constrained setting. To illustrate these potential gains, we propose practical algorithms for constrained adaptive sensing by exploiting connections to the theory of optimal experimental design and show that these algorithms exhibit promising performance in some representative applications

Resource Constrained Adaptive Sensing.

RESOURCE CONSTRAINED ADAPTIVE SENSING by Raghuram Rangarajan Chair: Alfred O. Hero III Many signal processing methods in applications such as radar imaging, communication systems, and wireless sensor networks can be presented in an adaptive sensing context. The goal in adaptive sensing is to control the acquisition of data measurements through adaptive design of the input parameters, e.g., waveforms, energies, projections, and sensors for optimizing performance. This dissertation develops new methods for resource constrained adaptive sensing in the context of parameter estimation and detection, sensor management, and target tracking. We begin by investigating the advantages of adaptive waveform amplitude design for estimating parameters of an unknown channel/medium under average energy constraints. We present a statistical framework for sequential design (e.g., design of waveforms in adaptive sensing) of experiments that improves parameter estimation (e.g., scatter coefficients for radar imaging, channel coefficients for channel estimation) performance in terms of reduction in mean-squared error (MSE). We derive optimal adaptive energy allocation strategies that achieve an MSE improvement of more than 5dB over non adaptive methods. As a natural extension to the problem of estimation, we derive optimal energy allocation strategies for binary hypotheses testing under the frequentist and Bayesian frameworks which yield at least 2dB improvement in performance. We then shift our focus towards spatial design of waveforms by considering the problem of optimal waveform selection from a large waveform library for a state estimation problem. Since the optimal solution to this subset selection problem is combinatorially complex, we propose a convex relaxation to the problem and provide a low complexity suboptimal solution that achieves near optimal performance. Finally, we address the problem of sensor and target localization in wireless sensor networks. We develop a novel sparsity penalized multidimensional scaling algorithm for blind target tracking, i.e., a sensor network which can simultaneously track targets and obtain sensor location estimates.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57621/2/rangaraj_1.pd

A Practical Study of Longitudinal Reference Based Compressed Sensing for MRI

Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS significantly speeds up scan time by requiring far fewer measurements than standard MRI techniques. Such a reduction in sampling time leads to less power consumption, less need for patient sedation, and more accurate images. This accuracy increase is especially pronounced in pediatric MRI where patients have trouble being still for long scan periods. Although such gains are already significant, even further improvements can be made by utilizing past MRI scans of the same patient. Many patients require repeated scans over a period of time in order to track illnesses and the prior scans can be used as references for the current image. This allows samples to be taken adaptively, based on both the prior scan and the current measurements. Work by Weizman [20] has shown that so-called reference based adaptive-weighted temporal Compressed Sensing MRI (LACS-MRI) requires far fewer samples than standard Compressed Sensing (CS) to achieve the same reconstruction signal-to-noise ratio (RSNR). The method uses a mixture of reference-based and adaptive-sampling. In this work, we test this methodology by using various adaptive sensing schemes, reconstruction methods, and image types. We create a thorough catalog of reconstruction behavior and success rates that is interesting from a mathematical point of view and is useful for practitioners. We also solve a grayscale compensation toy problem that supports the insensitivity of LACS-MRI to changes in MRI acquisition parameters and thus showcases the reliability of LACS-MRI in possible clinical situations

A Practical Study of Longitudinal Reference Based Compressed Sensing for MRI

Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS significantly speeds up scan time by requiring far fewer measurements than standard MRI techniques. Such a reduction in sampling time leads to less power consumption, less need for patient sedation, and more accurate images. This accuracy increase is especially pronounced in pediatric MRI where patients have trouble being still for long scan periods. Although such gains are already significant, even further improvements can be made by utilizing past MRI scans of the same patient. Many patients require repeated scans over a period of time in order to track illnesses and the prior scans can be used as references for the current image. This allows samples to be taken adaptively, based on both the prior scan and the current measurements. Work by Weizman has shown that so-called reference based adaptive-weighted temporal Compressed Sensing MRI (LACS-MRI) requires far fewer samples than standard Compressed Sensing (CS) to achieve the same reconstruction signal-to-noise ratio (RSNR). The method uses a mixture of reference-based and adaptive-sampling. In this work, we test this methodology by using various adaptive sensing schemes, reconstruction methods, and image types. We create a thorough catalog of reconstruction behavior and success rates that is interesting from a mathematical point of view and is useful for practitioners. We also solve a grayscale compensation toy problem that supports the insensitivity of LACS-MRI to changes in MRI acquisition parameters and thus showcases the reliability of LACS-MRI in possible clinical situations