Computation and optimization of frame bounds for the Laplacian pyramid

Author

Yu Pan ; Li Chai ; Yuxia Sheng

Author_Institution

Wuhan Univ. of Sci. & Technol., Wuhan, China

fYear

2013

fDate

25-27 May 2013

Firstpage

1423

Lastpage

1428

Abstract

The Laplacian pyramid (LP) plays an important role in multiresolution processing. It can be viewed as a special oversampled filter bank (OFB) frame that provides a redundant signal representation. This paper studies the computation and optimization of frame bounds for the LP frame. For any given N-level LP, an algorithm is developed to compute its polyphase matrix, based on which the linear matrix inequality (LMI) conditions are provided to compute the frame bounds. We show that the frame bound ratio can be decreased by adjusting the gain of each sub-channel without changing frequency selective property. The minimal ratio as well as the corresponding optimal gain factors has been obtained by solving some LMIs, which can be easily solved by existing handy software. Various numerical examples are given to show the effectiveness of the proposed methods.

Keywords

channel bank filters; linear matrix inequalities; optimisation; signal representation; signal resolution; signal sampling; LMI; LP frame; Laplacian pyramid; N-level LP; OFB; frame bound computation; frame bound optimization; frame bound ratio; frequency selective property; linear matrix inequality; multiresolution processing; optimal gain factor; oversampled filter bank; polyphase matrix; redundant signal representation; subchannel; Filter banks; Filtering algorithms; Finite impulse response filters; Laplace equations; Optimization; Reliability; Upper bound; FBs; Frame bound ratio; Laplacian pyramid; Polyphase;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Decision Conference (CCDC), 2013 25th Chinese

Conference_Location

Guiyang

Print_ISBN

978-1-4673-5533-9

Type

conf

DOI

10.1109/CCDC.2013.6561149

Filename

6561149