Armlets and balanced multiwavelets

Jian-ao Lian

doi:10.1117/12.506295

13 November 2003 Armlets and balanced multiwavelets

Jian-ao Lian

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.506295
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

In the scalar-valued setting, it is well-known that the two-scale sequences {q_k} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p_k} of their corresponding orthogonal scaling functions, such as q_k = (-1)^kp_1-k. However, due to the non-commutativity of matrix multiplication, there is little such development in the multi-wavelet literature to express the two-scale matrix sequence {Q_k} of an orthogonal multi-wavelet in terms of the two-scale matrix sequence {P_k} of its corresponding multi-scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multi-wavelets of dimension r = 2. We will apply our results to constructing a family of the most recently introduced notion of armlet of order n and a family of the n-balanced orthogonal multi-wavelets.

Citation Download Citation

Jian-ao Lian "Armlets and balanced multiwavelets", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.506295

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available