By Topic

An efficient computational scheme for the two-dimensional overcomplete wavelet transform

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Ngai-Fong Law ; Dept. of Electron. & Inf. Eng., Hong Kong Polytech. Univ., China ; Wan-Chi Siu,

We have studied the computational complexity associated with the overcomplete wavelet transform for the commonly used spline wavelet family. By deriving general expressions for the computational complexity using the conventional filtering implementation, we show that the inverse transform is significantly more costly in computation than the forward transform. To reduce this computational complexity, we propose a new spatial implementation based on the exploitation of the correlation between the lowpass and the bandpass outputs that is inherent in the overcomplete representation. Both theoretical studies and experimental findings show that the proposed spatial implementation can greatly simplify the computations associated with the inverse transform. In particular, the complexity of the inverse transform using the proposed implementation can be reduced to slightly less than that of the forward transform using the conventional filtering implementation. We also demonstrate that the proposed scheme allows the use of an arbitrary boundary extension method while maintaining the ease of the inverse transform.

Published in:

Signal Processing, IEEE Transactions on  (Volume:50 ,  Issue: 11 )