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Description
Effective modeling of high dimensional data is crucial in information processing and machine learning. Classical subspace methods have been very effective in such applications. However, over the past few decades, there has been considerable research towards the development of new modeling paradigms that go beyond subspace methods. This dissertation focuses on the study of sparse models and their interplay with modern machine learning techniques such as manifold, ensemble and graph-based methods, along with their applications in image analysis and recovery. By considering graph relations between data samples while learning sparse models, graph-embedded codes can be obtained for use in unsupervised, supervised and semi-supervised problems. Using experiments on standard datasets, it is demonstrated that the codes obtained from the proposed methods outperform several baseline algorithms. In order to facilitate sparse learning with large scale data, the paradigm of ensemble sparse coding is proposed, and different strategies for constructing weak base models are developed. Experiments with image recovery and clustering demonstrate that these ensemble models perform better when compared to conventional sparse coding frameworks. When examples from the data manifold are available, manifold constraints can be incorporated with sparse models and two approaches are proposed to combine sparse coding with manifold projection. The improved performance of the proposed techniques in comparison to sparse coding approaches is demonstrated using several image recovery experiments. In addition to these approaches, it might be required in some applications to combine multiple sparse models with different regularizations. In particular, combining an unconstrained sparse model with non-negative sparse coding is important in image analysis, and it poses several algorithmic and theoretical challenges. A convex and an efficient greedy algorithm for recovering combined representations are proposed. Theoretical guarantees on sparsity thresholds for exact recovery using these algorithms are derived and recovery performance is also demonstrated using simulations on synthetic data. Finally, the problem of non-linear compressive sensing, where the measurement process is carried out in feature space obtained using non-linear transformations, is considered. An optimized non-linear measurement system is proposed, and improvements in recovery performance are demonstrated in comparison to using random measurements as well as optimized linear measurements.
ContributorsNatesan Ramamurthy, Karthikeyan (Author) / Spanias, Andreas (Thesis advisor) / Tsakalis, Konstantinos (Committee member) / Karam, Lina (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2013
Description
Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain.
This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges.
Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.
This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges.
Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.
ContributorsScarnati, Theresa (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Gardner, Carl (Committee member) / Sanders, Toby (Committee member) / Arizona State University (Publisher)
Created2018
Description
Recently, electric and magnetic field sensing has come of interest to the military for a variety of applications, including imaging circuitry and detecting explosive devices. This thesis describes research at the ASU's Flexible Electronics and Display Center (FEDC) towards the development of a flexible electric and magnetic field imaging blanket. D-dot sensors, which detect changes in electric flux, were chosen for electric field sensing, and a single D-dot sensor in combination with a lock-in amplifier was used to detect individuals passing through an oscillating electric field. This was then developed into a 1 x 16 array of D-dot sensors used to image the field generated by two parallel wires. After the fabrication of a two-dimensional array, it was discovered that commercial field effect transistors did not have a high enough off-resistance to isolate the sensor form the column line. Three alternative solutions were proposed. The first was a one-dimensional array combined with a mechanical stepper to move the array across the E-field pattern. The second was a 1 x 16 strip detector combined with the techniques of computed tomography to reconstruct the image of the field. Such techniques include filtered back projection and algebraic iterative reconstruction (AIR). Lastly, an array of D-dot sensors was fabricated on a flexible substrate, enabled by the high off-resistance of the thin film transistors produced by the FEDC. The research on magnetic field imaging began with a feasibility study of three different types of magnetic field sensors: planar spiral inductors, Hall effect sensors, and giant magnetoresistance (GMR). An experimental array of these sensors was designed and fabricated, and the sensors were used to image the fringe fields of a Helmholtz coil. Furthermore, combining the inductors with the other two types of sensors resulted in three-dimensional sensors. From these measurements, it was determined that planar spiral inductors and Hall effect sensors are best suited for future imaging arrays.
ContributorsLarsen, Brett William (Author) / Allee, David (Thesis director) / Papandreou-Suppappola, Antonia (Committee member) / Barrett, The Honors College (Contributor) / Department of Physics (Contributor) / Electrical Engineering Program (Contributor)
Created2015-05
Description
A much anticipated outcome of the rapidly emerging field of personalized medicine is a significant increase in the standard of care afforded to patients. However, before the full potential of personalized medicine can be realized, key enabling technologies must be further developed. The purpose of this study was to use enabling technologies such as medical imaging, image reconstruction, and rapid prototyping to create a model of an implant for use in vocal fold repair surgery. Vocal fold repair surgery is performed for patients with great difficulty in phonation, breathing, and swallowing as a result of vocal fold damage caused by age, disease, cancer, scarring, or paralysis. This damage greatly hinders patients' social, personal, and professional lives due to difficulty in efficient communication. In this project, the image reconstruction of a subject's vocal fold in 3D is demonstrated utilizing NIH-funded advanced image processing software known as ITK-SNAP, which uniquely allows both semi-automatic and manual image segmentation. The hyoid bone, thyroid cartilage, arytenoid cartilage, and empty airway of the larynx were isolated using active contouring for use as anatomical benchmarks. Then, the vocal fold mold, including the vocal fold, a superior extension along the thyroid cartilage, and an inferior extension along the airway, was modeled with manual segmentation. The configured, isolated, and edited vocal fold model was converted into an STL file. This STL file can be imported to a 3D printer to fabricate a mold for reconstruction of a patient specific vocal fold biocompatible implant. This feasibility study serves as a basis to allow ENT surgeons at the Mayo Clinic to dramatically improve reparative surgery outcomes for patients. This work embodies the strategic importance of multidisciplinary teams working at the interface of technology and medicine to optimize patient outcomes.
ContributorsPatel, Anjana Ketan (Author) / Pizziconi, Vincent (Thesis director) / Lott, David (Committee member) / Department of Psychology (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
This work is concerned with how best to reconstruct images from limited angle tomographic measurements. An introduction to tomography and to limited angle tomography will be provided and a brief overview of the many fields to which this work may contribute is given.
The traditional tomographic image reconstruction approach involves Fourier domain representations. The classic Filtered Back Projection algorithm will be discussed and used for comparison throughout the work. Bayesian statistics and information entropy considerations will be described. The Maximum Entropy reconstruction method will be derived and its performance in limited angular measurement scenarios will be examined.
Many new approaches become available once the reconstruction problem is placed within an algebraic form of Ax=b in which the measurement geometry and instrument response are defined as the matrix A, the measured object as the column vector x, and the resulting measurements by b. It is straightforward to invert A. However, for the limited angle measurement scenarios of interest in this work, the inversion is highly underconstrained and has an infinite number of possible solutions x consistent with the measurements b in a high dimensional space.
The algebraic formulation leads to the need for high performing regularization approaches which add constraints based on prior information of what is being measured. These are constraints beyond the measurement matrix A added with the goal of selecting the best image from this vast uncertainty space. It is well established within this work that developing satisfactory regularization techniques is all but impossible except for the simplest pathological cases. There is a need to capture the "character" of the objects being measured.
The novel result of this effort will be in developing a reconstruction approach that will match whatever reconstruction approach has proven best for the types of objects being measured given full angular coverage. However, when confronted with limited angle tomographic situations or early in a series of measurements, the approach will rely on a prior understanding of the "character" of the objects measured. This understanding will be learned by a parallel Deep Neural Network from examples.
The traditional tomographic image reconstruction approach involves Fourier domain representations. The classic Filtered Back Projection algorithm will be discussed and used for comparison throughout the work. Bayesian statistics and information entropy considerations will be described. The Maximum Entropy reconstruction method will be derived and its performance in limited angular measurement scenarios will be examined.
Many new approaches become available once the reconstruction problem is placed within an algebraic form of Ax=b in which the measurement geometry and instrument response are defined as the matrix A, the measured object as the column vector x, and the resulting measurements by b. It is straightforward to invert A. However, for the limited angle measurement scenarios of interest in this work, the inversion is highly underconstrained and has an infinite number of possible solutions x consistent with the measurements b in a high dimensional space.
The algebraic formulation leads to the need for high performing regularization approaches which add constraints based on prior information of what is being measured. These are constraints beyond the measurement matrix A added with the goal of selecting the best image from this vast uncertainty space. It is well established within this work that developing satisfactory regularization techniques is all but impossible except for the simplest pathological cases. There is a need to capture the "character" of the objects being measured.
The novel result of this effort will be in developing a reconstruction approach that will match whatever reconstruction approach has proven best for the types of objects being measured given full angular coverage. However, when confronted with limited angle tomographic situations or early in a series of measurements, the approach will rely on a prior understanding of the "character" of the objects measured. This understanding will be learned by a parallel Deep Neural Network from examples.
ContributorsDallmann, Nicholas A. (Author) / Tsakalis, Konstantinos (Thesis advisor) / Hardgrove, Craig (Committee member) / Rodriguez, Armando (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2020