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MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN

Abstract: 

This paper extends the theory of the one-dimensional oversampled linear-phase perfect reconstruction filter banks (OLPPRFBs) developed by Gan et al. to multidimensional (MD) cases and proposes MD nonseparable oversampled lapped transforms (NSOLTs). NSOLTs allow us to achieve an overcomplete analysis-synthesis system with nonseparable, symmetric, realvalued, overlapping, and compact-supported filters. The proposed systems are based on lattice structures and the redundancy is flexibly controlled by the number of channels and downsampling ratio. The proposed structure is shown to be capable of constructing Parseval tight frames in any number of dimensions. The number of design parameters are examined under the Parseval tight frame constraint. In order to design NSOLTs specified for sparse approximation of image or volume data, an example-based design procedure is introduced. The effectiveness of this method is verified by examining design samples and evaluating their sparse approximation performance using the iterative hard thresholding algorithm for a natural image and MRI volume data patch.

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Paper Details

Authors:
Kosuke Furuya, Naotaka Yuki
Submitted On:
18 September 2017 - 7:34pm
Short Link:
Type:
Poster
Event:
Presenter's Name:
Shogo Muramatsu
Paper Code:
MQ-PB.5
Document Year:
2017
Cite

Document Files

Icip2017PosterRev2.pdf

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[1] Kosuke Furuya, Naotaka Yuki, "MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN", IEEE SigPort, 2017. [Online]. Available: http://sigport.org/2218. Accessed: Sep. 20, 2019.
@article{2218-17,
url = {http://sigport.org/2218},
author = {Kosuke Furuya; Naotaka Yuki },
publisher = {IEEE SigPort},
title = {MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN},
year = {2017} }
TY - EJOUR
T1 - MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN
AU - Kosuke Furuya; Naotaka Yuki
PY - 2017
PB - IEEE SigPort
UR - http://sigport.org/2218
ER -
Kosuke Furuya, Naotaka Yuki. (2017). MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN. IEEE SigPort. http://sigport.org/2218
Kosuke Furuya, Naotaka Yuki, 2017. MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN. Available at: http://sigport.org/2218.
Kosuke Furuya, Naotaka Yuki. (2017). "MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN." Web.
1. Kosuke Furuya, Naotaka Yuki. MULTIDIMENSIONAL NONSEPARABLE OVERSAMPLED LAPPED TRANSFORMS: THEORY AND DESIGN [Internet]. IEEE SigPort; 2017. Available from : http://sigport.org/2218