1,721,322 research outputs found
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
Reconstructing signaling pathways from high throughput data.
No full textMany bioinformatics problems can be tackled from a fresh angle offered by the network perspective. Taking into account the network constraints on gene interaction, we propose a series of logically-coherent approaches to reconstruct signaling pathways from high throughput expression profiling data. These approaches proceed in three consecutive steps: co-expression network construction with controlled biological and statistical significance, network constrained clustering, and reconstruction of the order of pathway components. The first step relies on detecting pairwise co-expression of genes. We attack the problem from both frequentist statistics and Bayesian statistics perspectives. We designed and implemented a frequentist two-stage co-expression detection algorithm that controls both statistical significance (False Discovery Rate, FDR) and biological significance (Minimum Acceptable Strength, MAS) of the discovered co-expressions. In order to regularize variances of the correlation estimation in small sample scenario, we also designed and implemented a Bayesian hierarchical model, in which correlation parameters are assumed to be exchangeable and sampled from a parental Gaussian distribution. Using simulated data and the galactose metabolism data, we demonstrated advantages of our approaches and compared the differences among them. The second problem considered is distance-based clustering that accounts for network constraints extracted from the Giant Connected Component (GCC) of the network discovered from the data. The clustering is performed using a hybrid distance matrix composed of direct distance between adjacent genes and shortest-path distance between non-adjacent genes in the network. The third problem considered is the reconstruction of the order of pathway components. We applied a first-order Markov model, originally developed and applied to a network tomography problem in telecommunication networks, to reconstruct three well-known signaling pathways from unordered pathway components. We suggest that the methods proposed here can also be applied to other high throughput data analysis problems.PhDBioinformaticsBiological SciencesBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125940/2/3224798.pd
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
System modeling, sampling, interpolation and iterative reconstruction for the 3D Compton SPECT camera.
No full textIn the past twenty five years, efforts have been made to develop Compton Single Photon Emission Computed Tomography (SPECT) cameras for medical imaging. The Compton camera consists of a pair of position sensitive detectors, a Compton scatter detector and a detector to absorb the scattered photons. The energy and position information from these detectors gives information about the energy, position, and incident direction of the incoming gamma-ray. This electronic collimation is superior to conventional mechanical collimation since it utilizes as many emitted photons as possible from all directions, improves the solid angle of detection and therefore provides improved detection efficiency and increased sensitivity. Better sensitivity will have a positive impact on image noise and resolution. Development of practical Compton SPECT faces many new challenges. First, Compton SPECT acquires the projection data directly in 3D and requires storage of three sets of coordinates, two spatial coordinates and the angular coordinates. Therefore Compton SPECT cameras have to deal with very large amount of data leading to difficulties in computation. Hence, simplification of Compton SPECT camera is necessary. Second, new reconstruction methods need to be developed for the Compton SPECT conical projection geometry. This dissertation presents a method for reducing storage and computation which is based on an analytical model that has the potential to permit tractable fully 3D reconstructions. A mathematical model is proposed for the camera which exploits hemispherical symmetries by using an adapted spatial sampling pattern in the object domain. For each projection angle, the sampling pattern is uniform over a set of equispaced nested hemispheres. By using this sampling pattern the system matrix is reduced to a product of an (approximately) block circulant matrix and a sparse interpolation matrix. This representation reduces the very high storage and computation requirement inherent to 3D reconstruction. We consider a simple method for designing the detector pair trajectory around the field of view using a sinogram sampling diagram to guarantee proper object sampling. As the exploitation of hemispherical symmetries requires interpolation, we develop a 3D volumetric interpolation between hemispherical and cartesian coordinates. Finally, we present a 3D image reconstruction method using the 2D Fourier transform for which there exists a fast algorithm because of the block circulant structure of the transition matrix. These methods are simply illustrated for the noiseless case with implementation of a fully 3D penalized least squares reconstruction algorithm.PhDApplied SciencesBiomedical engineeringElectrical engineeringNuclear engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132465/2/9963889.pd
Adaptive target detection in radar imaging.
No full textThis thesis addresses a target detection problem in radar imaging for which the covariance matrix of an unknown Gaussian clutter background has block diagonal structure. This block diagonal structure is the consequence of a target lying along a boundary between two statistically independent clutter regions. We consider three different assumptions on knowledge of the clutter covariance structure: both clutter types totally unknown, one of the clutter types known except for its variance, and one of the clutter types completely known. Here we design adaptive detection algorithms using both the generalized likelihood ratio (GLR) and the invariance principles. There has been considerable recent interest in applying invariant hypothesis testing as an alternative to the GLR test. This interest has been motivated by several attractive theoretical properties of invariant tests including: exact robustness to variation of nuisance parameters, possible finite-sample min-max optimality, and distributional robustness, i.e. insensitivity to changes in the underlying probability distribution over a particular class. Furthermore, in some important cases the invariant test gives a reasonable test while the GLR test has worse performance than the trivial coin flip decision rule. By exploiting the known covariance structure, a set of maximal invariants is obtained and compared to the GLR procedure. These maximal invariants are a compression of image data which retain target information while being invariant to clutter parameters. In our deep-hide target detection problem, however, there are regimes for which either of the GLR and the invariant tests can outperform the other. We explore the relative advantages of GLR and invariance procedures and their robustness to segmentation errors in the context of this radar imaging and target detection application.PhDApplied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123236/2/3000976.pd
Multiple antennas in wireless communications: Array signal processing and channel capacity.
No full textWe investigate two aspects of multiple-antenna wireless communication systems in this thesis: (1) deployment of an adaptive beamformer array at the receiver; and (2) space-time coding for arrays at the transmitter and the receiver. In the first part of the thesis, we establish sufficient conditions for the convergence of a popular least mean squares (LMS) algorithm known as the sequential Partial Update LMS Algorithm for adaptive beamforming. Partial update LMS (PU-LMS) algorithms are reduced complexity versions of the full update LMS that update a subset of filter coefficients at each iteration. We introduce a new improved algorithm, called Stochastic PU-LMS, which selects the subsets at random at each iteration. We show that the new algorithm converges for a wider class of signals than the existing PU-LMS algorithms. The second part of this thesis deals with the multiple-input multiple-output (MIMO) Shannon capacity of multiple antenna wireless communication systems under the average energy constraint on the input signal. Previous work on this problem has concentrated on capacity for Rayleigh fading channels. We investigate the more general case of Rician fading. We derive capacity expressions, optimum transmit signals as well as upper and lower bounds on capacity for three Rician fading models. In the first model the specular component is a dynamic isotropically distributed random process. In this case, the optimum transmit signal structure is the same as that for Rayleigh fading. In the second model the specular component is a static isotropically distributed random process unknown to the transmitter, but known to the receiver. In this case the transmitter has to design the transmit signal to guarantee a certain rate independent of the specular component. Here also, the optimum transmit signal structure, under the constant magnitude constraint, is the same as that for Rayleigh fading. In the third model the specular component is deterministic and known to both the transmitter and the receiver. In this case the optimum transmit signal and capacity both depend on the specular component. We show that for low signal to noise ratio (SNR) the specular component completely determines the signal structure whereas for high SNR the specular component has no effect. We also show that training is not effective at low SNR and give expressions for rate-optimal allocation of training versus communication.PhDApplied SciencesElectrical engineeringSystems scienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/127656/2/3029341.pd
Inference methods for message endpoint localization in networks.
No full textPeople often build or organize networks in order to establish lines of communication. The subjects might utilize a telephone or computer network, or perhaps even something much more low-tech where certain individuals are designated to deliver messages in person. When certain parties of interest are communicating, it is desirable to monitor these networks in order to discover their motives, identities, and locations. Presently, government and private agencies are investing heavily in the development of equipment for network surveillance and algorithms for gleaning useful information from collected data. This thesis develops several tools for inference in networks with a focus on determining the locations of the sender and receiver of an intercepted message. We begin by deriving a distance metric that allows comparisons between different network topologies. The metric quantifies the distance between networks by the total cost of edit operations (such as node or link insertion or deletion) necessary to make the two networks isomorphic. We derive this graph edit distance through a sort of embedding scheme, and show how to compute it with a binary linear program. Upper and lower bounds are computable in polynomial time through relaxation to an assignment problem and standard linear programming, respectively. We move next to the estimation of an intercepted message's source and destination in a network of unknown topology. Sensors placed on some links or nodes in the network are capable of indicating whenever a specific message passes their assigned elements with a limited degree of timing precision. The source and destination (endpoints) are localized using a possibly unordered sensor activation pattern along with some prior information on the unknown network topology. We first use a semidefinite programming driven Monte Carlo approach to build approximate endpoint posterior distributions. Maximum a posteriori endpoint estimates can then be read directly from these. Next we utilize a hierarchical Bayesian model and a recursive expectation-maximization algorithm to develop online techniques for endpoint localization. Finally, some preliminary derivations are given for the application of well-known Markov chain Monte Carlo algorithms to this problem.PhDApplied SciencesElectrical engineeringSystems scienceUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126185/2/3237987.pd
Robust fusion of MRI and ECT data, and acceleration of EM algorithm using proximal point approach.
No full textA robust multisensor fusion approach to use prior information from one sensor data to regularize an inverse problem based on another sensor data is presented. The robust approach is based on minimax rules. We apply this method to an application in medical imaging where anatomical boundary information from Magnetic Resonance Imaging (MRI) or X-ray Computed Tomography data is used to improve Emission Computed Tomography (ECT) image reconstruction. A parametric model is used to extract boundary information from MRI image. We derive asymptotic expressions for Cramer-Rao (CR) bound for extraction for 2-D and 3-D shapes and present shapes that are estimated with least uncertainty and most uncertainty. We also discuss how to find the optimum center to extract the shape with least uncertainty. We derive an asymptotic expression for the minimax objective to get a penalized likelihood objective with quadratic penalty. The penalty weights are smoothed proportional to the uncertainty in boundary estimate. We implement a method that approximates this asymptotic approach to combine 2-D MRI and ECT data. Robustness of estimate of radioactive tracer uptake in a simple region of interest is achieved using this method. Finally, we apply proximal point approach to accelerate the Expectation Maximization (EM) algorithm. The EM algorithm is used to maximize likelihood and has linear convergence rate. Hence acceleration of EM algorithm is essential. The method is applied for two separate problems namely, reconstruction of 1-D signal and 2-D image from their noisy projections.PhDApplied SciencesElectrical engineeringHealth and Environmental SciencesMedical imagingPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132661/2/9977239.pd
Quantization strategies for low-power communications.
No full textPower reduction in digital communication systems can be achieved in many ways. Reduction of the wordlengths used to represent data and control variables in the digital circuits comprising a communication system is an effective strategy, as register power consumption increases with wordlength. Another strategy is the reduction of the required data transmission rate, and hence speed of the digital circuits, by efficient source encoding. In this dissertation, applications of both of these power reduction strategies are investigated. The LMS adaptive filter, for which a myriad of applications exists in digital communication systems, is optimized for performance with a power consumption constraint. This optimization is achieved by an analysis of the effects of wordlength reduction on both performance---transient and steady-state---as well as power consumption. Analytical formulas for the residual steady-state mean square error (MSE) due to quantization versus wordlength of data and coefficient registers are used to determine the optimal allocation of bits to data versus coefficients under a power constraint. A condition on the wordlengths is derived under which the potentially hazardous transient slowdown phenomenon is avoided. The algorithm is then optimized for no slowdown and minimum MSE. Numerical studies are presented for the case of LMS channel equalization. Next, source encoding by vector quantization is studied for distributed hypothesis testing environments with simple binary hypotheses. It is shown that, in some cases, low-rate quantizers exist that cause no degradation in hypothesis testing performance. These cases are, however, uncommon. For the majority of cases, in which quantization necessarily degrades performance, optimal many-cell vector quantizers are derived that minimize the performance loss. These quantizers are optimized using objective functions based on the Kullback-Leibler statistical divergence, or discrimination, and large deviations theory. Motivated by Stein's lemma, the loss in discrimination between two sources due to quantization is minimized. Next, formulas for the losses in discrimination between the hypothesized sources and the so-called tilted source are determined. These formulas are used to design quantizers that maximize the area under an analog to the receiver operating characteristic (ROC) curve. The optimal quantizer is shown to have fine resolution in areas where the log-likelihood ratio gradient is large in magnitude. The techniques are extended to the design of quantizers optimal for mixed detection-estimation objectives.PhDApplied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125412/2/3016859.pd
Unicast Internet tomography.
No full textInference of network internal characteristics has become an increasingly important issue for communication network operation. Since it is impractical to directly monitor the network internal nodes, people use the end-to-end information collected by probe packets to estimate the statistics of interest. This new area of networking research is called network tomography . When specialized to the Internet it is called Internet tomography. Our work focuses on unicast probing methods, which are supported by much of today's Internet. We first deal with the estimation of internal link delay distributions from end-to-end delay measurements. Unlike the discrete delay models used in previous work, we focus on continuous distributions of non-zero queueing delays. We send individual unicast packets throughout the network and develop an estimator for link delay cumulant generating functions (CGF) based on an over-determined system of equations. We propose a bias corrected estimator for the CGF which eliminates the nonlinearity effect of the log function. When the network is modelled by a logical tree we use packet pair probes to collect end-to-end delay information. We propose a novel hybrid continuous/discrete finite mixture model for the link delay distributions. A penalized maximum-likelihood expectation-maximization (PML-EM) algorithm is developed to select the model and estimate its parameters. Since the complexity of the algorithm grows exponentially with the size of the network, we propose an accelerated algorithm to obtain a linear reduction in run-time. The second problem we address is network topology discovery using end-to-end measurements. Topology estimation can be formulated as a hierarchical clustering problem of the leaf nodes based on pair-wise correlations as similarity metrics. Unlike previous work which first assumes the network topology being a binary tree and then tries to generalize to a non-binary tree, we provide a framework which directly deals with general logical tree topologies. Based on our proposed finite mixture model for the set of similarity measurements we develop a penalized hierarchical topology likelihood that leads to a natural hierarchical clustering algorithm for the leaf nodes. The performance of our algorithms are evaluated by matlab and ns-2 simulations.PhDApplied SciencesElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/124935/2/3163930.pd
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