UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Subject: search.filters.subject.Quantization

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    Optimality of Event-Based Policies for Decentralized Estimation over Shared Networks
    (2016) Vasconcelos, Marcos Muller; Martins, Nuno C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Cyber-physical systems often consist of multiple non-collocated components that sense, exchange information and act as a team through a network. Although this new paradigm provides convenience, flexibility and robustness to modern systems, design methods to achieve optimal performance are elusive as they must account for certain detrimental characteristics of the underlying network. These include constrained connectivity among agents, rate-limited communication links, physical noise at the antennas, packet drops and interference. We propose a new class of problems in optimal networked estimation where multiple sensors operating as a team communicate their measurements to a fusion center over an interference prone network modeled by a collision channel. Using a team decision theoretic approach, we characterize jointly optimal communication policies for one-shot problems under different performance criteria. First we study the problem of estimating two independent continuous random variables observed by two different sensors communicating with a fusion center over a collision channel. For a minimum mean squared estimation error criterion, we show that there exist team-optimal strategies where each sensor uses a threshold policy. This result is independent of the distribution of the observations and, can be extended to vector observations and to any number of sensors. Consequently, the existence of team-optimal threshold policies is a result of practical significance, because it can be applied to a wide class of systems without requiring collision avoidance protocols. Next we study the problem of estimating independent discrete random variables over a collision channel. Using two different criteria involving the probability of estimation error, we show the existence of team-optimal strategies where the sensors either transmit all but the most likely observation; transmit only the second most likely observation; or remain always silent. These results are also independent of the distributions and are valid for any number of sensors. In our analysis, the proof of the structural result involves the minimization of a concave functional, which is an evidence of the inherent complexity of team decision problems with nonclassical information structure. In the last part of the dissertation, the assumption on the cooperation among sensors is relaxed, and we show that similar structural results can also be obtained for systems with one or more selfish sensors. Finally the assumption of the independence is lifted by introducing the observation of a common random variable in addition to the private observations of each sensor. The structural result obtained provides valuable insights on the characterization of team-optimal policies for a general correlation structure between the observed random variables.
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    Geometric Issues in Spatial Indexing
    (2006-08-22) Alborzi, Houman; Samet, Hanan; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We address a number of geometric issues in spatial indexes. One area of interest is spherical data. Two main examples are the locations of stars in the sky and geodesic data. The first part of this dissertation addresses some of the challenges in handling spherical data with a spatial database. We show that a practical approach for integrating spherical data in a conventional spatial database is to use a suitable mapping from the unit sphere to a rectangle. This allows us to easily use conventional two-dimensional spatial data structures on spherical data. We further describe algorithms for handling spherical data. In the second part of the dissertation, we introduce the areal projection, a novel projection which is computationally efficient and has low distortion. We show that the areal projection can be utilized for developing an efficient method for low distortion quantization of unit normal vectors. This is helpful for compact storage of spherical data and has applications in computer graphics. We introduce the QuickArealHex algorithm, a fast algorithm for quantization of surface normal vectors with very low distortion. The third part of the dissertation deals with a CPU time analysis of TGS, an R-tree bulkloading algorithm. And finally, the fourth part of the dissertation analyzes the BV-tree, a data structure for storing multi-dimensional data on secondary storage. Contrary to the popular belief, we show that the BV-tree is only applicable to binary space partitioning of the underlying data space.
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    Sigma-Delta Quantization: Number Theoretic Aspects of Refining Quantization Error
    (2006-07-18) Tangboondouangjit, Aram; Benedetto, John J.; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    The linear reconstruction phase of analog-to-digital (A/D) conversion in signal processing is analyzed in quantizing finite frame expansions for R^d. The specific setting is a K-level first order Sigma-Delta quantization with step size delta. Based on basic analysis, the d-dimensional Euclidean 2-norm of quantization error of Sigma-Delta quantization with input of elements in R^d decays like O(1/N) as the frame size N approaches infinity; while the L-infinity norm of quantization error of Sigma-Delta quantization with input of bandlimited functions decays like O(T) as the sampling ratio T approaches zero. It has been, however, observed via numerical simulation that, with input of bandlimited functions, the mean square error norm of quantization error seems to decay like O(T^(3/2)) as T approaches zero. Since the frame size N can be taken to correspond to the reciprocal of the sampling ratio T, this belief suggests that the corresponding behavior of quantization error, namely O(1/N^(3/2)), holds in the setting of finite frame expansions in R^d as well. A number theoretic technique involving uniform distribution of sequences of real numbers and approximation of exponential sums is introduced to derive a better quantization error than O(1/N) as N tends to infinity. This estimate is signal dependent.
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    How Many Bits? Radiometric Resolution as a Factor in Obtaining Forestry Information with Remotely Sensed Measurments
    (2006-01-19) Franks, Shannon; Goward, Samuel; Geography; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In this study, Landsat 7 and IKONOS data were compared to determine if higher quantization is beneficial for forestry remote sensing. An industrial forestry site in central Virginia was chosen for analysis because of its large variation in standing biomass. Data were selected and processed so that the measurements were as comparable as possible to one another. The processing steps included spatial aggregation, pixel alignment, and calibration to planetary reflectance. Due to several aspects of study design and execution, the results are inconclusive. The registered data sets were found to differ by more than 1-2%, which is above the theoretical limits based on their radiometric resolutions. Lessons learned from this study are that to investigate radiometric resolutions, extreme care must be taken to understand the consequences of every data processing step and that all differences in the compared datasets cannot be overcome.
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    Sigma Delta Modulation and Correlation Criteria for the Construction of Finite Frames Arising in Communication Theory
    (2004-04-29) Kolesar, Joseph Dennis; Benedetto, John J; Mathematics
    In this dissertation we first consider a problem in analog to digital (A/D) conversion. We compute the power spectra of the error arising from an A/D conversion. We then design various higher dimensional analogs of A/D schemes, and compare these schemes to a standard error diffusion scheme in digital halftoning. Secondly, we study finite frames. We classify certain finite frames that are constructed as orbits of a group. These frames are seen to have subtle symmetry properties. We also study Grassmannian frames which are frames with minimal correlation. Grassmannian frames have an important intersection with spherical codes, erasure channel models, and communication theory. This is the main part of the dissertation, and we introduce new theory and algorithms to decrease the maximum frame correlation and hence construct specific examples of Grassmannian frames. A connection has been drawn between the two parts of this thesis, namely A/D conversion and finite frames. In particular, finite frames are used to expand vectors in $\RR^d$, and then different quantization schemes are applied to the coefficients of these expansions. The advantage is that all possible outcomes of quantization can be considered because of the finite dimensionality.