Construction for a class of smooth tight frames in L2 (ℝ2)

Haihui Wang; Lizhong Peng

doi:10.1142/S0219691307001926

Construction for a class of smooth tight frames in L² (ℝ²)

Haihui Wang^*
, Lizhong Peng

^*Corresponding author for this work

School of Mathematical Sciences

Peking University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We generalize the inequality P(z) ² + P(-z) ² ≤ 1 (Ref. 1) to the inequality P(z₁, z₂) ² + P(-z₁, z₂) ² + P(z₁, -z₂) ² + P(-z₁, -z₂) ² ≤ 1 in L² (ℝ ²); and construct compactly supported tight frames with good symmetry and dilation matrix 2I under the condition that both the low-pass filter and high-pass filters are unknown.

Original language	English
Pages (from-to)	613-625
Number of pages	13
Journal	International Journal of Wavelets, Multiresolution and Information Processing
Volume	5
Issue number	4
DOIs	https://doi.org/10.1142/S0219691307001926
State	Published - Jul 2007

Keywords

Compact supported
Smoothness
Symmetry
Tight frame wavelet

Access to Document

10.1142/S0219691307001926

Cite this

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title = "Construction for a class of smooth tight frames in L2 (ℝ2)",

abstract = "We generalize the inequality P(z) 2 + P(-z) 2 ≤ 1 (Ref. 1) to the inequality P(z1, z2) 2 + P(-z1, z2) 2 + P(z1, -z2) 2 + P(-z1, -z2) 2 ≤ 1 in L2 (ℝ 2); and construct compactly supported tight frames with good symmetry and dilation matrix 2I under the condition that both the low-pass filter and high-pass filters are unknown.",

keywords = "Compact supported, Smoothness, Symmetry, Tight frame wavelet",

author = "Haihui Wang and Lizhong Peng",

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T1 - Construction for a class of smooth tight frames in L2 (ℝ2)

AU - Wang, Haihui

AU - Peng, Lizhong

PY - 2007/7

Y1 - 2007/7

N2 - We generalize the inequality P(z) 2 + P(-z) 2 ≤ 1 (Ref. 1) to the inequality P(z1, z2) 2 + P(-z1, z2) 2 + P(z1, -z2) 2 + P(-z1, -z2) 2 ≤ 1 in L2 (ℝ 2); and construct compactly supported tight frames with good symmetry and dilation matrix 2I under the condition that both the low-pass filter and high-pass filters are unknown.

AB - We generalize the inequality P(z) 2 + P(-z) 2 ≤ 1 (Ref. 1) to the inequality P(z1, z2) 2 + P(-z1, z2) 2 + P(z1, -z2) 2 + P(-z1, -z2) 2 ≤ 1 in L2 (ℝ 2); and construct compactly supported tight frames with good symmetry and dilation matrix 2I under the condition that both the low-pass filter and high-pass filters are unknown.

KW - Compact supported

KW - Smoothness

KW - Symmetry

KW - Tight frame wavelet

UR - https://www.scopus.com/pages/publications/34447318346

U2 - 10.1142/S0219691307001926

DO - 10.1142/S0219691307001926

M3 - 文章

AN - SCOPUS:34447318346

SN - 0219-6913

VL - 5

SP - 613

EP - 625

JO - International Journal of Wavelets, Multiresolution and Information Processing

JF - International Journal of Wavelets, Multiresolution and Information Processing

IS - 4