subject:(high dimensional signals)

University of Colorado

1. 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 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

Record Details Similar Records Cite « Share

❌

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 05, 2021. https://scholar.colorado.edu/ecen_gradetds/68.

MLA Handbook (7^th Edition):

Qi, Hanchao. “Low-Dimensional Signal Models in Compressive Sensing.” 2013. Web. 05 Mar 2021.

Vancouver:

Qi H. Low-Dimensional Signal Models in Compressive Sensing. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Mar 05]. 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

Universidade do Rio Grande do Sul

2. Gastal, Eduardo Simões Lopes. Efficient high-dimensional filtering for image and video processing.

Degree: 2015, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/118258

Filtering is arguably the single most important operation in image and video processing. In particular, high-dimensional filters are a fundamental building block for several applications, having recently received considerable attention from the research community. Unfortunately, naive implementations of such an important class of filters are too slow for many practical uses, specially in light of the ever increasing resolution of digitally captured images. This dissertation describes three novel approaches to efficiently perform high-dimensional filtering: the domain transform, the adaptive manifolds, and a mathematical formulation for recursive filtering of non-uniformly sampled signals. The domain transform defines an isometry between curves on the 2D image manifold in 5D and the real line. It preserves the geodesic distance between points on these curves, adaptively warping the input signal so that high-dimensional geodesic filtering can be efficiently performed in linear time. Its computational cost is not affected by the choice of the filter parameters; and the resulting filters are the first to work on color images at arbitrary scales in real time, without resorting to subsampling or quantization. The adaptive manifolds compute the filter’s response at a reduced set of sampling points, and use these for interpolation at all input pixels, so that high-dimensional Euclidean filtering can be efficiently performed in linear time. We show that for a proper choice of sampling points, the total cost of the filtering operation is linear both in the number of pixels and in the dimension of the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, providing a sound theoretical justification. Finally, we introduce a mathematical formulation for linear-time recursive filtering of non-uniformly sampled signals. This formulation enables, for the first time, geodesic edge-aware evaluation of arbitrary recursive infinite impulse response filters (not only low-pass), which allows practically unlimited control over the shape of the filtering kernel. By providing the ability to experiment with the design and composition of new digital filters, our method has the potential do enable a greater variety of image and video effects. The high-dimensional filters we propose provide the fastest performance (both on CPU and GPU) for a variety of real-world applications. Thus, our filters are a valuable tool for the image and video processing, computer graphics, computer vision, and computational photography communities.

Filtragem é uma das mais importantes operações em processamento de imagens e vídeos. Em particular, filtros de altas dimensões são ferramentas fundamentais para diversas aplicações, tendo recebido recentemente significativa atenção de pesquisadores da área. Infelizmente, implementações ingênuas desta importante classe de filtros são demasiadamente lentas para muitos usos práticos,…

Advisors/Committee Members: Oliveira Neto, Manuel Menezes de.

Subjects/Keywords: Computação gráfica; High-dimensional filtering; Domain transform; Processamento : Imagem; Adaptive manifolds; Non-uniformly sampled signals; Geodesic filtering; Euclidean filtering; Hybrid filtering

Record Details Similar Records Cite « Share

❌

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

APA (6^th Edition):

Gastal, E. S. L. (2015). Efficient high-dimensional filtering for image and video processing. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/118258

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gastal, Eduardo Simões Lopes. “Efficient high-dimensional filtering for image and video processing.” 2015. Thesis, Universidade do Rio Grande do Sul. Accessed March 05, 2021. http://hdl.handle.net/10183/118258.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gastal, Eduardo Simões Lopes. “Efficient high-dimensional filtering for image and video processing.” 2015. Web. 05 Mar 2021.

Vancouver:

Gastal ESL. Efficient high-dimensional filtering for image and video processing. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2015. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/10183/118258.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gastal ESL. Efficient high-dimensional filtering for image and video processing. [Thesis]. Universidade do Rio Grande do Sul; 2015. Available from: http://hdl.handle.net/10183/118258

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Florida

3. Baek, Hyunho. Signal and Power Integrity of High-Speed IC in Chip-Package System.

Degree: PhD, Electrical and Computer Engineering, 2013, University of Florida

URL: https://ufdc.ufl.edu/UFE0046137

Subjects/Keywords: Capacitors; Electric potential; Input output; Modeling; Noise measurement; Parametric models; Polynomials; Signals; Simulations; Three dimensional modeling; characterization; chip; high; ic; integrity; io; modeling; package; power; signal; speed; test

Record Details Similar Records Cite « Share

❌

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

APA (6^th Edition):

Baek, H. (2013). Signal and Power Integrity of High-Speed IC in Chip-Package System. (Doctoral Dissertation). University of Florida. Retrieved from https://ufdc.ufl.edu/UFE0046137

Chicago Manual of Style (16^th Edition):

Baek, Hyunho. “Signal and Power Integrity of High-Speed IC in Chip-Package System.” 2013. Doctoral Dissertation, University of Florida. Accessed March 05, 2021. https://ufdc.ufl.edu/UFE0046137.

MLA Handbook (7^th Edition):

Baek, Hyunho. “Signal and Power Integrity of High-Speed IC in Chip-Package System.” 2013. Web. 05 Mar 2021.

Vancouver:

Baek H. Signal and Power Integrity of High-Speed IC in Chip-Package System. [Internet] [Doctoral dissertation]. University of Florida; 2013. [cited 2021 Mar 05]. Available from: https://ufdc.ufl.edu/UFE0046137.

Council of Science Editors:

Baek H. Signal and Power Integrity of High-Speed IC in Chip-Package System. [Doctoral Dissertation]. University of Florida; 2013. Available from: https://ufdc.ufl.edu/UFE0046137

		in
And / Or
		in
And / Or
		in
And / Or
		in

Open Access Theses and Dissertations