Magnetic Resonance Imaging can now detect cells that are labeled with contrast agents such as superparamagnetic iron oxide (SPIO). Quantitative monitoring, which is desirable for evaluating cellular therapies, remains challenging. In this work, an MRI technique called TurboSPI is implemented for quantitative cellular imaging. TurboSPI acquires maps of the relaxation rate R2', which is directly related to SPIO concentration. Quantification of R2' is demonstrated using micron-sized iron oxide particles and SPIO-labeled cells. To explain experimental results that deviated from predicted behavior, an extended analytical description of MRI signal relaxation near SPIO was developed. This model compares well to Monte Carlo simulations and experimental data, and may allow improved quantification. The slow imaging speed of TurboSPI is overcome using a signal processing technique called compressed sensing to reconstruct undersampled data, enabling in vivo animal imaging with TurboSPI. Such images demonstrate detection of iron with improved specificity and good potential for quantification.

In this thesis, resource allocation and multiple access in cognitive radio (CR) and compressed sensing (CS)-based wireless networks are studied. Energy-efficiency oriented design becomes more and more important in wireless systems, which motivates us to propose a location-aware power strategy for single user and multiple users in CR systems and a CS-based processing in wireless sensor networks (WSNs) which reduces the number of data transmissions and energy consumption by utilizing sparsity of the transmitted data due to spatial correlation and temporal correlation. In particular, the work on location-aware power allocation in CR system gives a brief overview of the existing power allocation design in the literature and unifies them into a general power allocation framework. The impact of the network topology on the system performance is highlighted, which motivates us to propose a novel location-aware strategy that intelligently utilizes frequency and space opportunities and minimizes the overall power consumption while maintaining the quality of service (QoS) of the primary system. This work shows that in addition to exploring the spectrum holes in time and frequency domains, spatial opportunities can be utilized to further enhance energy efficiency for CR systems. Then the work of resource allocation is extended to finding the power strategy and channel allocation optimization for multiple secondary users in an orthogonal frequency division multiplexing (OFDM) based cognitive radio network. Three different spectrum access methods are considered and utilized adaptively according to the different locations of the secondary users, and we unify these spectrum access methods into a general resource allocation framework. An interference violation test is proposed to decide the parameters in this framework that indicate the set of licensed channels to be sensed. The proposed scheme intelligently utilizes frequency and space opportunities, avoids unnecessary spectrum sensing and minimizes the overall power consumption while maintaining the quality of service of the primary system. The uncertainty of channel state information between the secondary users (SUs) and the primary users (PUs) is also taken into account in the study of power and channel allocation optimization of the SUs. Simulation results validate the effectiveness of the proposed method in terms of energy efficiency and show that enhanced performance can be obtained by utilizing spatial opportunities. The work on CS-based WSNs considers the application of compressed sensing to WSNs for data measurement communication and reconstruction, where N sensor nodes compete for medium access to a single receiver. Sparsity of the sensor data in three domains due to time correlation, space correlation and multiple access are being utilized. A CS-based medium access control (MAC) scheme is proposed and an in depth analysis on this scheme from a physical layer perspective is provided to reveal the impact of communication signal-to-noise ratio on the reconstruction performance. We show the process of the sensor data converted to the modulated symbols for physical layer transmission and how the modulated symbols recovered via compressed sensing. This work further identifies the decision problem of distinguishing between active and inactive transmitters after symbol recovery and provides a comprehensive performance comparison between carrier sense multiple access and the proposed CSbased scheme. Moreover, a network data recovery scheme that exploits both spatial and temporal correlations is proposed. Simulation results validate the effectiveness of the proposed method in terms of communication throughput and show that enhanced performance can be obtained by utilizing the sensed signal’s temporal and spatial correlations. / Graduate

No description available.

The problem of reconstruction of digital images from their degraded measurements has always been a problem of central importance in numerous applications of imaging sciences. In real life, acquired imaging data is typically contaminated by various types of degradation phenomena which are usually related to the imperfections of image acquisition devices and/or environmental effects. Accordingly, given the degraded measurements of an image of interest, the fundamental goal of image reconstruction is to recover its close approximation, thereby "reversing" the effect of image degradation. Moreover, the massive production and proliferation of digital data across different fields of applied sciences creates the need for methods of image restoration which would be both accurate and computationally efficient. Developing such methods, however, has never been a trivial task, as improving the accuracy of image reconstruction is generally achieved at the expense of an elevated computational burden. Accordingly, the main goal of this thesis has been to develop an analytical framework which allows one to tackle a wide scope of image reconstruction problems in a computationally efficient manner. To this end, we generalize the concept of variable splitting, as a tool for simplifying complex reconstruction problems through their replacement by a sequence of simpler and therefore easily solvable ones. Moreover, we consider two different types of variable splitting and demonstrate their connection to a number of existing approaches which are currently used to solve various inverse problems. In particular, we refer to the first type of variable splitting as Bregman Type Splitting (BTS) and demonstrate its applicability to the solution of complex reconstruction problems with composite, cross-domain constraints. As specific applications of practical importance, we consider the problem of reconstruction of diffusion MRI signals from sub-critically sampled, incomplete data as well as the problem of blind deconvolution of medical ultrasound images. Further, we refer to the second type of variable splitting as Fuzzy Clustering Splitting (FCS) and show its application to the problem of image denoising. Specifically, we demonstrate how this splitting technique allows us to generalize the concept of neighbourhood operation as well as to derive a unifying approach to denoising of imaging data under a variety of different noise scenarios.

<p>The emerging theory of compressed sensing has been nothing short of a revolution in signal processing, challenging some of the longest-held ideas in signal processing and leading to the development of exciting new ways to capture and reconstruct signals and images. Although the theoretical promises of compressed sensing are manifold, its implementation in many practical applications has lagged behind the associated theoretical development. Our goal is to elevate compressed sensing from an interesting theoretical discussion to a feasible alternative to conventional imaging, a significant challenge and an exciting topic for research in signal processing. When applied to imaging, compressed sensing can be thought of as a particular case of computational imaging, which unites the design of both the sensing and reconstruction of images under one design paradigm. Computational imaging tightly fuses modeling of scene content, imaging hardware design, and the subsequent reconstruction algorithms used to recover the images. </p><p>This thesis makes important contributions to each of these three areas through two primary research directions. The first direction primarily attacks the challenges associated with designing practical imaging systems that implement incoherent measurements. Our proposed snapshot imaging architecture using compressive coded aperture imaging devices can be practically implemented, and comes equipped with theoretical recovery guarantees. It is also straightforward to extend these ideas to a video setting where careful modeling of the scene can allow for joint spatio-temporal compressive sensing. The second direction develops a host of new computational tools for photon-limited inverse problems. These situations arise with increasing frequency in modern imaging applications as we seek to drive down image acquisition times, limit excitation powers, or deliver less radiation to a patient. By an accurate statistical characterization of the measurement process in optical systems, including the inherent Poisson noise associated with photon detection, our class of algorithms is able to deliver high-fidelity images with a fraction of the required scan time, as well as enable novel methods for tissue quantification from intraoperative microendoscopy data. In short, the contributions of this dissertation are diverse, further the state-of-the-art in computational imaging, elevate compressed sensing from an interesting theory to a practical imaging methodology, and allow for effective image recovery in light-starved applications.</p> / Dissertation

Κανάλια με αραιή κρουστική απόκριση εμφανίζονται πάρα πολύ συχνά σε εφαρμογές ασύρματων κυρίως τηλεπικοινωνιακών συστημάτων. Παραδείγματα τέτοιων εφαρμογών είναι η εκπομπή HDTV (HighDefinitionΤelevision) ή εκπομπή μέσω υποθαλλάσιων ακουστικών καναλιών. Σε όλες αυτές τις εφαρμογές η μορφή του καναλιού διαμορφώνεται από το φαινόμενο της πολυδιόδευσης. Συνεπώς ο δέκτης λαμβάνει έναν περιορισμένο αριθμό από διαφορετικές εκδοχές του εκπεμπόμενου σήματος καθεμία με διαφορετική εξασθένιση και καθυστέρηση. Ως εκ τούτου η συνάρτηση της κρουστικής απόκρισης ενός τέτοιου καναλιού αποτελείται από ελάχιστα μη μηδενικά στοιχεία σε συγκριση με το μήκος της, καθένα από τα οποία αντιστοιχεί σε ένα από τα μονοπάτια πολυδιόδευσης. Για την ισοστάθμιση αυτών των καναλιών έχουν προταθεί διάφορες τεχνικές, πολλές από τις οποίες εκμεταλλεύονται την ιδιαίτερη αυτή μορφή της κρουστικής απόκρισης. Πολλοί από τους προτεινόμενους ισοσταθμιστές καναλιών απαιτούν την παρεμβολή ακολουθίων εκμάθησης ανάμεσα στην ακολουθία δεδομένων, οι οποίες είναι εκ των προτέρων γνωστές στον δέκτη. Χρησιμοποιούνται δε προκειμένου ο αλγόριθμος εκτίμησης του καναλιού να συγκλίνει όσο το δυνατόν ταχύτερα στην επιθυμητή τιμή. Μειονέκτημα αυτών των μεθόδων είναι η επιβάρυνση του ωφέλιμου εύρους ζώνης που συνεπάγεται. Ωστόσο η εκ των προτέρων γνώση της αραιής μορφής της κρουστικής απόκρισης εχει δώσει αφορμή για την σχεδίαση ισοσταθμιστών με περιορισμένο μήκος αλλά εξίσου καλή απόδοση. Οι συμβατικές τεχνικές εκτίμησης καναλιών, όπως η Least Square μέθοδος, δεν εκμεταλλεύονται αυτή την γνώση. Οι πρόσφατες δε εξελίξεις στην ανακατασκευή αραιών σημάτων μέσω τεχνικών συμπιεσμένης καταγραφής (compressed sensing) έχουν οδηγήσει στην μελέτη της εφαρμογής τέτοιων τεχνικών στο πρόβλημα της εκτίμησης καναλιού. Η μέθοδος της συμπιεσμένης καταγραφής στηρίζεται στη δυνατότητα ανακατασκευής αραιών σημάτων από πλήθος δειγμάτων αισθητά κατώτερο από αυτό που προβλέπει το θεωρητικό όριο του Nyquist. Έχει αποδειχθεί ότι η ανακατασκευή αυτή είναι δυνατή όταν το σήμα ή έστω κάποιος μετασχηματισμός του περιέχει λίγα μη μηδενικά στοιχεία σε σχέση με το μήκος του. Οι εφαρμογές αυτών των τεχνικών εκτείνονται και σε άλλα πεδία όπως η επεξεργασία εικόνας, η μαγνητική τομογραφία, η ανάλυση γεωφυσικών δεδομένων, η επεξεργασία εικόνας radar, η αστρονομία κ.α. Στα πλαίσια αυτής της εργασίας παρουσιάζονταιοι βασικές αρχές που διέπουν την ανακατασκευή αραιών σημάτων μέσω της επίλυσης υποορισμένων συστημάτων γραμμικών εξισώσεων. Παράλληλα παρουσιάζονται οι κυριότεροι αλγόριθμοι που έχουν προταθεί για την υλοποίηση της και εξετάζονται ως προς την απόδοση και την υπολογιστική πολυπλοκότητα τους. Εν συνεχεία εξετάζεται η εφαρμογή αυτών των αλγορίθμων στο πρόβλημα της εκτίμησης αραιών καναλιών. Προτείνονται δε ισοσταθμιστές αραιών καναλιών βασισμένοι σε εκτιμητές απόκρισης που χρησιμοποιούν τεχνικές συμπιεσμένης καταγραφής. / Channels with sparse impulse response are very common in wireless telecommunications systems applications. Example of such channel is HDTV channel where multipath distribution of the transmitted signal results in a sparse form of the channel impulse response. Several different versions of the same signal are received, each one with its own gain and delay. As a result, channel impulse response has a few non zero taps compared to its length, its one corresponding to a different distribution path. Several techniques for estimating and equalizing such channels have been proposed, most of them taking advantage of this sparse form of the impulse response. The transmission of a training sequence known to the receiver is required for this purpose. It is used so that the channel estimation algorithm at the receiver converges faster. The disadvantage of the use of a training sequence is the fact that the useful bandwidth is reduced. However the a priori knowledge of the sparse form of the training sequence has led to the design of equalizers that require short training sequences but have satisfactory performance. Channel estimation techniques based on least square method do not take advantage of this idea. On the other hand recent progress on sparse signal reconstruction using compressed sensing techniques has led scientists to research the potential use of such algorithms in channel estimation. Compressed sensing is based on the idea of reconstructing a sparse signal using less samples that those predicted by Nyquist theorem. It has been proved that such a reconstruction is feasible if the reconstructed signal is sparse enough. In this dissertation several sparse signal reconstruction algorithms are presented and their performance and complexity are evaluated. Then the application of these algorithms on channel estimation equalization problem is analyzed.

Magnetic resonance imaging is a widely used medical imaging technique, and accelerated data acquisition is critical for clinical utility. In this thesis, new techniques that incorporate radial acquisition, compressed sensing and sparse regularization for improved rapid imaging are presented. Sufficiently accelerated imaging methods can lead to new applications. Here we demonstrate a solution to lung imaging during forced expiration using accelerated MRI. A technique for dynamic 3D imaging of the lungs from highly undersampled data is developed and tested on six subjects. This method takes advantage of image sparsity, both spatially and temporally, including the use of reference frames called bookends. Sparsity, with respect to total variation, and residual from the bookends, enables reconstruction from an extremely limited amount of data. Dynamic 3D images can be captured at an unprecedented sub-150 ms temporal resolution, using only three (or less) acquired radial lines per slice per time point. Lung volume calculations based on image segmentation are compared to those from simultaneously acquired spirometer measurements. Additionally, accelerated imaging methods can be used to improve upon widely used applications; we also present a technique for improved T₂-mapping. A novel model-based compressed sensing method is extended to include a sparse regularization that is learned from the principal component coefficients. The principal components are determined by a range of T₂ decay curves, and the coefficients of the principal components are reconstructed. These coefficient maps share coherent spatial structures, and a spatial patch--based dictionary is a learned for a sparse constraint. This transformation is learned from the coefficients themselves. The proposed reconstruction is suited for non-Cartesian, multi-channel data. The dictionary constraint leads to parameter maps with less noise and less aliasing for high amounts of acceleration.

abstract: This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering. / Dissertation/Thesis / M.S. Electrical Engineering 2011

In this thesis we consider concentration inequalities and the concentration of measure phenomenon from a variety of angles. Sharp tail bounds on the deviation of Lipschitz functions of independent random variables about their mean are well known. We consider variations on this theme for dependent variables on the Boolean cube. In recent years negatively associated probability distributions have been studied as potential generalizations of independent random variables. Results on this class of distributions have been sparse at best, even when restricting to the Boolean cube. We consider the class of negatively associated distributions topologically, as a subset of the general class of probability measures. Both the weak (distributional) topology and the total variation topology are considered, and the simpler notion of negative correlation is investigated. The concentration of measure phenomenon began with Milman's proof of Dvoretzky's theorem, and is therefore intimately connected to the field of high-dimensional convex geometry. Recently this field has found application in the area of compressed sensing. We consider these applications and in particular analyze the use of Gordon's min-max inequality in various compressed sensing frameworks, including the Dantzig selector and the matrix uncertainty selector. Finally we consider the use of concentration inequalities in developing a theoretically sound anomaly detection algorithm. Our method uses a ranking procedure based on KNN graphs of given data. We develop a max-margin learning-to-rank framework to train limited complexity models to imitate these KNN scores. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate α, its decision region converges to the α-percentile minimum volume level set of the unknown underlying density.

abstract: It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter. / Dissertation/Thesis / Measurement Results (part 1) / Measurement Results (part 2) / General Presentation / M.S. Mechanical Engineering 2012