Efficient Computation of Frame Bounds Using LMI-Based Optimization

Author

Chai, Li ; Zhang, Jingxin ; Zhang, Cishen ; Mosca, Edoardo

Author_Institution

Sch. of Inf. Sci. & Eng., Wuhan Univ. of Sci. & Technol., Wuhan

Volume

56

Issue

7

fYear

2008

fDate

7/1/2008 12:00:00 AM

Firstpage

3029

Lastpage

3033

Abstract

This correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction (PR) filter banks (FBs). It first shows that computation of the optimal frame bounds for complex-valued oversampled PR FBs can be formulated as a convex optimization subject to complex-valued linear matrix inequality (LMI) constraints and solved by effective interior-point algorithms. It then deals with discrete-time Weyl-Heisenberg (WH) frames to compute bounds on the WH frames by real-valued LMI optimization. The WH frames are closely related to modulated FBs and have complex coefficients. Four examples are given to illustrate the generality and effectiveness of the proposed method.

Keywords

linear matrix inequalities; state-space methods; LMI-based optimization; discrete-time Weyl-Heisenberg frames; frame bounds; interior-point algorithms; linear matrix inequality; perfect reconstruction filter banks; Biomedical computing; Biomedical engineering; Chemical technology; Constraint optimization; Filter bank; Fourier series; Linear matrix inequalities; Magnetic resonance imaging; Optimization methods; Sampling methods; Convex optimization; frame bounds; linear matrix inequality; oversampled filter banks;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2006.914354

Filename

4545251