+publisher:"University of Colorado" +contributor:("Shannon M. Hughes")

University of Colorado

1. Tembarai Krishnamachari, Rajesh. A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback.

Degree: PhD, Electrical, Computer & Energy Engineering, 2011, University of Colorado

URL: https://scholar.colorado.edu/ecen_gradetds/38

► We study the performance of multiple-antenna systems under finite-rate feedback of some function of the current channel realization from a channel-aware receiver to the… (more)

▼ We study the performance of multiple-antenna systems under finite-rate feedback of some function of the current channel realization from a channel-aware receiver to the transmitter. Our analysis is based on a novel geometric paradigm whereby the feedback information is modeled as a source distributed over a Riemannian manifold. While the right singular vectors of the channel matrix and the subspace spanned by them are located on the traditional Stiefel and Grassmann surfaces, the optimal input covariance matrix is located on a new manifold of positive semi-definite matrices - specified by rank and trace constraints - called the Pn manifold. The geometry of these three manifolds is studied in detail; in particular, the precise series expansion for the volume of geodesic balls over the Grassmann and Stiefel manifolds is obtained. Using these geometric results, the distortion incurred in quantizing sources using either a sphere-packing or a random code over an arbitrary manifold is quantified. Perturbative expansions are used to evaluate the susceptibility of the ergodic information rate to the quality of feedback information, and thereby to obtain the tradeoff of the achievable rate with the number of feedback bits employed. For a given system strategy, the gap between the achievable rates in the infinite and finite-rate feedback cases is shown to be O(2^-\frac{2N_f{N}}) for Grassmann feedback and O(2^-\frac{N_f{N}}) for other cases, where N is the dimension of the manifold used for quantization and N_f is the number of bits used by the receiver per block for feedback. The geometric framework developed enables the results to hold for arbitrary distributions of the channel matrix and extends to all covariance computation strategies including, waterfilling in the short-term/long-term power constraint case, antenna selection and other rank-limited scenarios that could not be analyzed using previous probabilistic approaches. Advisors/Committee Members: Mahesh K. Varanasi, Youjian(Eugene) Liu, Shannon M. Hughes.

Subjects/Keywords: Finite-rate Feedback; Grassmann/Stiefel Manifold; Information Theory; MIMO; Riemannian Geometry; Wireless Communications; Electrical and Computer Engineering; Mathematics

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APA (6^th Edition):

Tembarai Krishnamachari, R. (2011). A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/38

Chicago Manual of Style (16^th Edition):

Tembarai Krishnamachari, Rajesh. “A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback.” 2011. Doctoral Dissertation, University of Colorado. Accessed March 06, 2021. https://scholar.colorado.edu/ecen_gradetds/38.

MLA Handbook (7^th Edition):

Tembarai Krishnamachari, Rajesh. “A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback.” 2011. Web. 06 Mar 2021.

Vancouver:

Tembarai Krishnamachari R. A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2021 Mar 06]. Available from: https://scholar.colorado.edu/ecen_gradetds/38.

Council of Science Editors:

Tembarai Krishnamachari R. A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback. [Doctoral Dissertation]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/ecen_gradetds/38

University of Colorado

2. Ramirez Jr., Juan. Learning from Manifold-Valued Data: An Application to Seismic Signal Processing.

Degree: MS, Electrical, Computer & Energy Engineering, 2012, University of Colorado

URL: https://scholar.colorado.edu/ecen_gradetds/44

► Over the past several years, advances in sensor technology has lead to increases in the demand for computerized methods for analyzing seismological signals. Central… (more)

Subjects/Keywords: Machine Learning; Manifold-Valued Data; Seismology; Supervised Learning; Electrical and Computer Engineering

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APA (6^th Edition):

Ramirez Jr., J. (2012). Learning from Manifold-Valued Data: An Application to Seismic Signal Processing. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/44

Chicago Manual of Style (16^th Edition):

Ramirez Jr., Juan. “Learning from Manifold-Valued Data: An Application to Seismic Signal Processing.” 2012. Masters Thesis, University of Colorado. Accessed March 06, 2021. https://scholar.colorado.edu/ecen_gradetds/44.

MLA Handbook (7^th Edition):

Ramirez Jr., Juan. “Learning from Manifold-Valued Data: An Application to Seismic Signal Processing.” 2012. Web. 06 Mar 2021.

Vancouver:

Ramirez Jr. J. Learning from Manifold-Valued Data: An Application to Seismic Signal Processing. [Internet] [Masters thesis]. University of Colorado; 2012. [cited 2021 Mar 06]. Available from: https://scholar.colorado.edu/ecen_gradetds/44.

Council of Science Editors:

Ramirez Jr. J. Learning from Manifold-Valued Data: An Application to Seismic Signal Processing. [Masters Thesis]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/ecen_gradetds/44

University of Colorado

3. Kambli, Ketan Pradeep. Manifold Learning for Organization of Text Documents.

Degree: MS, Electrical, Computer & Energy Engineering, 2011, University of Colorado

URL: https://scholar.colorado.edu/eeng_gradetds/18

► The quantity of information in the world is soaring. We are living in an information age with abundant sources that generate information. While this… (more)

▼ The quantity of information in the world is soaring. We are living in an information age with abundant sources that generate information. While this data has the potential to transform every aspect of our life, it is very difficult to analyze and make inference from this huge amount of data. One example of this data deluge is the massive amount of textual data being generated on a daily basis from sources such as newspapers, blogs, tweets and other social network posts, emails, research papers, product descriptions and reviews, online discussion forums, digital libraries, knowledge databases, etc. This thesis tackles the problem of finding the hidden structure behind these collections of text documents and of organizing them better so as to help better navigate this sea of textual data. Traditionally, the techniques used to classify the documents by topic include probabilistic methods such as the naive Bayes classifier, margin-based learning techniques such as support vector machines, and statistical manifold learning methods such as the Fisher information non-parametric embedding. We believe that the set of documents can be represented by points in a high-dimensional space that lie on or near a low-dimensional manifold. Hence, manifold learning or dimensionality reduction techniques can help to recover the underlying manifold and retrieve the inherent modes of variability in the set of documents. This will aid towards effective organization of these documents. Indeed, we find that many popular manifold learning methods perform well at organizing test datasets. We also propose a different view of the local similarity of documents and thereby introduce the Earth Mover's distance as a local distance metric to replace Euclidean distance metric for the distance between the documents. The manifold learning methods, modified to incorporate the Earth Mover's distance, do provide improvement in the results as expected. Finally, we show that the spectral clustering promises to be a useful technique for the purpose of text organization. Advisors/Committee Members: Shannon M. Hughes, Peter Mathys, Youjian Liu.

Subjects/Keywords: dimensionality reduction; earth mover's distance; manifold learning; text organization; textual data deluge; Artificial Intelligence and Robotics; Computer Sciences; Electrical and Computer Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kambli, K. P. (2011). Manifold Learning for Organization of Text Documents. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/eeng_gradetds/18

Chicago Manual of Style (16^th Edition):

Kambli, Ketan Pradeep. “Manifold Learning for Organization of Text Documents.” 2011. Masters Thesis, University of Colorado. Accessed March 06, 2021. https://scholar.colorado.edu/eeng_gradetds/18.

MLA Handbook (7^th Edition):

Kambli, Ketan Pradeep. “Manifold Learning for Organization of Text Documents.” 2011. Web. 06 Mar 2021.

Vancouver:

Kambli KP. Manifold Learning for Organization of Text Documents. [Internet] [Masters thesis]. University of Colorado; 2011. [cited 2021 Mar 06]. Available from: https://scholar.colorado.edu/eeng_gradetds/18.

Council of Science Editors:

Kambli KP. Manifold Learning for Organization of Text Documents. [Masters Thesis]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/eeng_gradetds/18

University of Colorado

4. Qi, Hanchao. Low-Dimensional Signal Models in Compressive Sensing.

Degree: PhD, Electrical, Computer & Energy Engineering, 2013, University of Colorado

URL: https://scholar.colorado.edu/ecen_gradetds/68

► In today's world, we often face an explosion of data that can be difficult to handle. Signal models help make this data tractable, and… (more)

▼ In today's world, we often face an explosion of data that can be difficult to handle. Signal models help make this data tractable, and thus play an important role in designing efficient algorithms for acquiring, storing, and analyzing signals. However, choosing the right model is critical. Poorly chosen models may fail to capture the underlying structure of signals, making it hard to achieve satisfactory results in signal processing tasks. Thus, the most accurate and concise signal models must be used. Many signals can be expressed as a linear combination of a few elements of some dictionary, and this is the motivation behind the emerging field of compressive sensing. Compressive sensing leverages this signal model to enable us to perform signal processing tasks without full knowledge of the data. However, this is only one possible model for signals, and many signals could in fact be more accurately and concisely described by other models. In particular, in this thesis, we will look at two such models, and show how these other two models can be used to allow signal reconstruction and analysis from partial knowledge of the data. First, we consider signals that belong to low-dimensional nonlinear manifolds, i.e. that can be represented as a continuous nonlinear function of few parameters. We show how to apply the kernel trick, popular in machine learning, to adapt compressive sensing to this type of sparsity. Our approach provides computationally-efficient, improved signal reconstruction from partial measurements when the signal is accurately described by such a manifold model. We then consider collections of signals that together have strong principal components, so that each individual signal may be modeled as a linear combination of these few shared principal components. We focus on the problem of finding the center and principal components of these high-dimensional signals using only their measurements. We show experimentally and theoretically that our approach will generally return the correct center and principal components for a large enough collection of signals. The recovered principal components also allow performance gains in other signal processing tasks. Advisors/Committee Members: Shannon M. Hughes, Youjian Liu, Francois Meyer, Lijun Chen, Alireza Doostan.

Subjects/Keywords: algorithms; compressive sensing; nonlinear manifolds; high-dimensional signals; Electrical and Computer Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Qi, H. (2013). Low-Dimensional Signal Models in Compressive Sensing. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/68

Chicago Manual of Style (16^th Edition):

Qi, Hanchao. “Low-Dimensional Signal Models in Compressive Sensing.” 2013. Doctoral Dissertation, University of Colorado. Accessed March 06, 2021. https://scholar.colorado.edu/ecen_gradetds/68.

MLA Handbook (7^th Edition):

Qi, Hanchao. “Low-Dimensional Signal Models in Compressive Sensing.” 2013. Web. 06 Mar 2021.

Vancouver:

Qi H. Low-Dimensional Signal Models in Compressive Sensing. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Mar 06]. Available from: https://scholar.colorado.edu/ecen_gradetds/68.

Council of Science Editors:

Qi H. Low-Dimensional Signal Models in Compressive Sensing. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/ecen_gradetds/68

University of Colorado

5. Matviychuk, Yevgen. Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing.

Degree: PhD, Electrical, Computer & Energy Engineering, 2016, University of Colorado

URL: https://scholar.colorado.edu/ecen_gradetds/124

► While the field of image processing has been around for some time, new applications across many diverse areas, such as medical imaging, remote sensing,… (more)

▼ While the field of image processing has been around for some time, new applications across many diverse areas, such as medical imaging, remote sensing, astrophysics, cellular imaging, computer vision, and many others, continue to demand more and more sophisticated image processing techniques. These areas inherently rely on the development of novel methods and algorithms for their success. Many important cases in these applications can be posed as problems of reversing the action of certain linear operators. Recently, patch-based methods for image reconstruction have been shown to work exceptionally well in addressing these inverse problems, establishing new state-of-the-art benchmarks for many of them, and even approaching estimated theoretical limits of performance. However, there is still space and need for improvement, particularly in highly specialized domains. The purpose of this thesis will be to improve upon these prior patch-based image processing methods by developing a computationally efficient way to model the underlying set of patches as arising from a low-dimensional manifold. In contrast to other works that have attempted to use a manifold model for patches, ours will rely on the machinery of kernel methods to efficiently approximate the solution. This will make our approach much more suitable for practical use than those of our predecessors. We will show experimental results paralleling or exceeding those of modern state-of-the-art image processing algorithms for several inverse problems. Additionally, near the end of the thesis, we will revisit the problem of learning a representation for the manifold from its samples and develop an improved approach for it. In contrast to prior methods for manifold learning, our kernel-based strategy will be robust to issues of learning from very few or noisy samples, and it will readily allow for interpolation along or projection onto the manifold. Advisors/Committee Members: Shannon M. Hughes, Youjian Liu, Lijun Chen, Jem Corcoran, Elizabeth Bradley.

Subjects/Keywords: Image processing; Inverse problems; Kernel methods; Machine learning; Manifold models; Computer Sciences; Electrical and Computer Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Matviychuk, Y. (2016). Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/124

Chicago Manual of Style (16^th Edition):

Matviychuk, Yevgen. “Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing.” 2016. Doctoral Dissertation, University of Colorado. Accessed March 06, 2021. https://scholar.colorado.edu/ecen_gradetds/124.

MLA Handbook (7^th Edition):

Matviychuk, Yevgen. “Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing.” 2016. Web. 06 Mar 2021.

Vancouver:

Matviychuk Y. Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Mar 06]. Available from: https://scholar.colorado.edu/ecen_gradetds/124.

Council of Science Editors:

Matviychuk Y. Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/ecen_gradetds/124

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