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Multidimensional geometrical signal ...

Lu, Yue.

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Multidimensional geometrical signal representation: Constructions and applications.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Multidimensional geometrical signal representation: Constructions and applications./
Author:	Lu, Yue.
Description:	175 p.
Notes:	Adviser: Minh N. Do.
Contained By:	Dissertation Abstracts International68-11B.
Subject:	Engineering, Electronics and Electrical. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3290305
ISBN:	9780549340942

Multidimensional geometrical signal representation: Constructions and applications.
Lu, Yue.

Multidimensional geometrical signal representation: Constructions and applications. - 175 p.

Adviser: Minh N. Do.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.

The main theme of this dissertation is to develop a new set of theories and techniques in signal processing that can explore the intrinsic geometrical information in multidimensional data in a robust and efficient way. The primary technique we employ to approach this problem is multidimensional filter banks, due to their computational advantages, their design flexibilities, and their direct connection with the theory of basis (nonredundant) and frame (redundant) decomposition of multidimensional signals.

ISBN: 9780549340942Subjects--Topical Terms:

626636
Engineering, Electronics and Electrical.

Multidimensional geometrical signal representation: Constructions and applications.
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008 110524s2007 ||||||||||||||||| ||eng d
020 $a 9780549340942
035 $a (UMI)AAI3290305
035 $a AAI3290305
040 $a UMI $c UMI
100 1 $a Lu, Yue. $3 1271283
245 1 0 $a Multidimensional geometrical signal representation: Constructions and applications.
300 $a 175 p.
500 $a Adviser: Minh N. Do.
500 $a Source: Dissertation Abstracts International, Volume: 68-11, Section: B, page: 7550.
502 $a Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
520 $a The main theme of this dissertation is to develop a new set of theories and techniques in signal processing that can explore the intrinsic geometrical information in multidimensional data in a robust and efficient way. The primary technique we employ to approach this problem is multidimensional filter banks, due to their computational advantages, their design flexibilities, and their direct connection with the theory of basis (nonredundant) and frame (redundant) decomposition of multidimensional signals.
520 $a Separable multidimensional wavelet transforms have very limited directionality. Furthermore, different directions are mixed in certain wavelet subbands. To solve this problem, we propose a simple Directional Extension for Wavelets (DEW) that fixes this subband mixing problem and improves the directionality.
520 $a The contourlet transform was constructed as a directional multiresolution image representation that can efficiently capture and represent singularities along smooth object boundaries in natural images. We propose a new contourlet construction whose basis images are sharply localized in frequency and regular in space.
520 $a We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary N-dimensional (N ≥ 2) signals with a simple and efficient tree-structured construction. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like features in multidimensional volumetric data. An important building block of the NDFB is the hourglass filter banks. We propose a novel mapping-based design for the hourglass filter banks in arbitrary dimensions, featuring perfect reconstruction, finite impulse response filters, efficient implementation using lifting/ladder structures, and a near-tight frame construction.
520 $a We propose a computational procedure to find all alias-free quantized sampling lattices with minimum sampling density for a given frequency support. Central to this algorithm is a novel condition linking alias-free sampling with the Fourier transform of the indicator function defined on the frequency support. We also derive simple closed-form expressions of these Fourier transforms for a fairly general class of support regions consisting of arbitrary N-dimensional polytopes. With these closed-form expressions, the search for desired alias-free sampling lattices becomes a purely analytical and computational testing procedure.
590 $a School code: 0090.
650 4 $a Engineering, Electronics and Electrical. $3 626636
690 $a 0544
710 2 $a University of Illinois at Urbana-Champaign. $3 626646
773 0 $t Dissertation Abstracts International $g 68-11B.
790 $a 0090
790 1 0 $a Do, Minh N., $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3290305