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

^*此作品的通讯作者

数学科学学院

Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	613-625
页数	13
期刊	International Journal of Wavelets, Multiresolution and Information Processing
卷	5
期	4
DOI	https://doi.org/10.1142/S0219691307001926
出版状态	已出版 - 7月 2007

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10.1142/S0219691307001926

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链接到 Scopus 的出版物

引用此

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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

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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

ER -