1,763 research outputs found
Fundamental Limits on Data Acquisition: Trade-offs Between Sample Complexity and Query Difficulty
No full textWe consider query-based data acquisition and the corresponding information recovery problem, where the goal is to recover k binary variables (information bits) from parity measurements of those variables. The queries and the corresponding parity measurements are designed using the encoding rule of Fountain codes. By using Fountain codes, we can design potentially limitless number of queries, and corresponding parity measurements, and guarantee that the original k information bits can be recovered with high probability from any sufficiently large set of measurements of size n. In the query design, the average number of information bits that is associated with one parity measurement is called query difficulty (d̅) and the minimum number of measurements required to recover the k information bits for a fixed d̅ is called sample complexity (n). We analyze the fundamental trade-offs between the query difficulty and the sample complexity, and show that the sample complexity of n = c max{k,(k log k)/d̅} for some constant c > 0 is necessary and sufficient to recover k information bits with high probability as k→∞
Hyperspectral image unmixing using a multiresolution sticky HDP
No full textThis paper is concerned with joint Bayesian endmember extraction and linear unmixing of hyperspectral images using a spatial prior on the abundance vectors.We propose a generative model for hyperspectral images in which the abundances are sampled from a Dirichlet distribution (DD) mixture model, whose parameters depend on a latent label process. The label process is then used to enforces a spatial prior which encourages adjacent pixels to have the same label. A Gibbs sampling framework is used to generate samples from the posterior distributions of the abundances and the parameters of the DD mixture model. The spatial prior that is used is a tree-structured sticky hierarchical Dirichlet process (SHDP) and, when used to determine the posterior endmember and abundance distributions, results in a new unmixing algorithm called spatially constrained unmixing (SCU). The directed Markov model facilitates the use of scale-recursive estimation algorithms, and is therefore more computationally efficient as compared to standard Markov random field (MRF) models. Furthermore, the proposed SCU algorithm estimates the number of regions in the image in an unsupervised fashion. The effectiveness of the proposed SCU algorithm is illustrated using synthetic and real data
The television work of Alfred Hitchcock
No full textThe thesis uses close textual analysis to study and evaluate the television work of Alfred Hitchcock. The corpus consists of the twenty shows personally directed by Hitchcock, including his appearances before and after those shows. In response to most previous writing, which tends to compare the programmes with Hitchcock’s films (often unfairly) the thesis emphasises them as products of television. Programmes are evaluated on the basis of their perceived success as television- if they harness conditions related to television production and integrate them with narrative themes or to create meaning. Hitchcock is considered to be the major creative force in each programme.
Chapter One provides a variety of important contexts including a brief history of US television of the 1950s, key literature on Hitchcock and analyses of contemporaneous programmes not directed by Hitchcock. The textual analysis chapters (2-8) consider aesthetic or thematic programme aspects. Chapter Two studies the various roles played by Hitchcock’s appearances as series host. Chapter Three considers the impact of censorship on programmes frequently dealing with murder, violence and insanity. Chapter Four analyses Hitchcock’s implementation of varieties of voice-over narration, a common device in short dramatic forms. Chapter Five studies Hitchcock’s use of point-of-view shots, particularly in relation to their role in the delivery of the narrative twist. Chapter Six considers the key Hitchcock theme of detachment from the world. Chapter Seven looks at moments from the programmes which demonstrate how aesthetic is influenced by television production conditions.
Hitchcock created a number of television masterpieces. His achievements in television are in many ways comparable in quality and consistency to his theatrical films. Even when considered in the context of other 1950s US anthology dramas, the Hitchcock-directed programmes are superior on many levels. Elements of his film style were highly suited to television production. Many of his greatest achievements embrace and harness television production conditions in their presentation strategies to create an integration of style and meaning
Unsupervised Bayesian linear unmixing of gene expression microarrays
No full textBackground: This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Results: Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. Conclusions: The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor
On EM algorithms and their proximal generalizations
No full textIn this paper, we analyze the celebrated EM algorithm from
the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (1998)] and called Kullback-proximal algorithms. The proximal framework allows us to prove new
results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space
Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem
No full text© 2017 IEEE. In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel, the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced, whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme, where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection
Three dimensional shape modeling: Segmentation, reconstruction and registration.
No full textAccounting for uncertainty in three-dimensional (3D) shapes is important in a large number of scientific and engineering areas, such as biometrics, biomedical imaging, and data mining. It is well known that 3D polar shaped objects can be represented by Fourier descriptors such as spherical harmonics and double Fourier series. However, the statistics of these spectral shape models have not been widely explored. This thesis studies several areas involved in 3D shape modeling, including random field models for statistical shape modeling, optimal shape filtering, parametric active contours for object segmentation and surface reconstruction. It also investigates multi-modal image registration with respect to tumor activity quantification. Spherical harmonic expansions over the unit sphere not only provide a low dimensional polarimetric parameterization of stochastic shape, but also correspond to the Karhunen-Loeve (K-L) expansion of any isotropic random field on the unit sphere. Spherical harmonic expansions permit estimation and detection tasks, such as optimal shape filtering, object registration, and shape classification, to be performed directly in the spectral domain with low complexities. An issue which we address is the effect of center estimation accuracy on the accuracy of polar shape models. A lower bound is derived for the variance of ellipsoid fitting center estimator. Simulation shows that the performance of a maximum likelihood center estimator can approach the bound in low noise situations. Due to the large number of voxels in 3D images, 3D parametric active contour techniques have very high computational complexity. A novel parametric active contour method with lower computational complexity is proposed in this thesis. A spectral method using double Fourier series as an orthogonal basis is applied to solving elliptic partial differential equations over the unit sphere, which control surface evolution. The complexity of the spectral method is O(N2 log N) for a grid size of N x N as compared to O(N3) for finite element methods and finite difference methods. A volumetric penalization term is introduced in the energy function of the active contour to prevent the contour from leaking through blurred boundaries. Multi-modal medical image registration is widely used to quantify tumor activity in radiation therapy patients. Rigid global registration sometimes cannot perfectly overlay the tumor volume of interest (VOI), e.g. segmented from a CT anatomical image, with the apparent position of a tumor in a SPELT functional image. We investigate a new local registration method which aligns the CT and SPELT tumor volumes by maximizing the SPELT intensity within the CT-segmented tumor VOI.PhDApplied SciencesBiomedical engineeringElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129922/2/3042112.pd
Signal processing for magnetic resonance force microscopy.
No full textMagnetic resonance force microscopy (MRFM) is an emergent technology that has the potential for three-dimensional, non-destructive, and in-situ imaging of biological molecules with atomic resolution. Experiments at IBM have shown that MRFM is capable of detecting and localizing individual electron spins associated with subsurface atomic defects in silicon dioxide. In principle, detection of single nuclear spins is possible as well. MRFM detects the spins by measuring the small spin-induced forces on a micromachined cantilever. Detection of a single electron spin was studied in additive white Gaussian noise (AWGN). Four models of the single spin-cantilever interaction were proposed. We investigated three of these models. A heuristic argument was used to formulate a detector for the continuous-time classical model. Approximate forms of the optimal likelihood ratio test (LRT) for the discrete-time (DT) random telegraph and DT random walk models were derived which hold under certain conditions. It was shown that, under low signal to noise ratio (SNR), the LRT for a DT finite state Markov process in AWGN reduces to the matched filter statistic with the one-step minimum mean-squared error predictor used in place of the known signal values. The next challenge for MRFM is to demonstrate the technology's applicability as an imaging modality with advantages over those already in existence. We therefore considered the problem of image reconstruction in the MRFM setting, which is reconstructing sparse images from noisy projections. The goal here is to perform sparse reconstruction with the tuning parameters selected in a data-driven fashion. The empirical Bayes framework was investigated, and several sparse image reconstruction methods were proposed that are more scalable and have lower computational complexity than sparse Bayesian learning (SBL). In a simulation study, the proposed methods demonstrate benefits over SBL, Landweber, and the projected Landweber method. Under low SNR, a MAP-based solution produced low l1 and l2 reconstruction error. We found that the maximum penalized likelihood estimator using a l1 norm penalty and with its regularization parameter estimated by minimizing Stein's unbiased risk estimate produced consistently good results across a wide range of SNRs.PhDApplied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125905/2/3224766.pd
Semi-blind sparse image reconstruction with application to MRFM
No full textWe propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high-dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data
Resource Constrained Adaptive Sensing.
No full textRESOURCE 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.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57621/2/rangaraj_1.pd
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