Computation of the Dual Frame: Forward and Backward Greville Formulas

Author

Gan, Lu ; Ling, Cong

Author_Institution

Dept. of Electr. Eng. & Electron., Liverpool Univ.

Volume

3

fYear

2007

fDate

15-20 April 2007

Abstract

We study the computation of the dual frame for oversampled filter banks (OFBs) by exploiting Greville´s formula, which was derived in 1960 to compute the pseudo inverse of a matrix when a new row is appended. In this paper, we first develop the backward Greville formula to handle the case of row deletion. Based on Greville´s formula, we then study the dual frame computation of the Laplacian pyramid. Through the backward Greville formula, we investigate OFBs for robust transmission over erasure channels. The necessary and sufficient conditions for OFBs robust to one erasure channel are derived. A post-filtering structure is also presented to implement the dual frame when the transform coefficients in one subband are completely lost.

Keywords

Laplace equations; channel bank filters; filtering theory; matrix inversion; Laplacian pyramid computation; backward Greville formula; dual frame computation; erasure channels; matrix inversion; oversampled filter banks; post-filtering structure; Closed-form solution; Educational institutions; Filter bank; Gallium nitride; Laplace equations; Polynomials; Resilience; Robustness; Sampling methods; Sufficient conditions; Error resilience; Frames; Greville formula; Laplacian pyramid; Oversampled filter banks;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on

Conference_Location

Honolulu, HI

ISSN

1520-6149

Print_ISBN

1-4244-0727-3

Electronic_ISBN

1520-6149

Type

conf

DOI

10.1109/ICASSP.2007.366817

Filename

4217847