Dual-Tree Wavelet Transform and Applications

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基本資料

Project title

Code/計畫編號

NSC93-2115-M019-002

Translated Name/計畫中文名

對偶樹小波轉換及應用

Project Coordinator/計畫主持人

Mong-Shu Lee

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Computer Science and Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=1000590

Year

2004

Start date/計畫起

01-08-2004

Expected Completion/計畫迄

31-07-2005

Bugetid/研究經費

375千元

ResearchField/研究領域

數學

由於離散小波轉換( Discrete Wavelet Transform)具有快速運算、兼具時間域及頻率域的局部性及可提供我們生活中對訊號及影像的多層解析分解的功能，這些原因使它在過去十年已成功地運用在訊號處理領域。但離散小波轉換也遭遇到一些先天上的問題，使得它不能在訊號及影像處理上做更廣泛的應用。第一個缺點是此轉換對訊號的移轉性太敏敢，表示只要輸入訊號在時間軸上移轉，則其相對應的小波轉換係數就變得難以捉摸。而第二個缺點是小波轉換係數在影像內容方向的選擇上較差。為了同時克服這些缺點，我們在此計劃中設計一個對偶樹小波轉換(Dual-Tree Wavelet Transform)，而它在一些訊號問題處理上明顯勝過離散小波轉換。根據我們對此兩轉換同時輸入階梯函數的初步研究結果，我們將更進一步以統計的模式來分析此兩轉換在高頻子頻帶及影像邊緣的能量集中效能差異。 Over the last decade or so, discrete wavelet transform (DWT) have been successfully used in the signal processing field for a variety reasons: Wavelet transform is fast, local in the time and frequency domain, and wavelet transform provides multiresolution analysis of real –world signals and images. Unfortunately, the DWT also has some disadvantages that undermine its broader use to signal and image processing applications. First, it is shift sensitive because input-signal shifts generate unpredictable changes in DWT coefficients. Second, the DWT coefficients have poor directional selectivity. To overcome these shortcomings, a new implementation of Dual-Tree Wavelet Transform (DTWT) is presented in these projects. It has significant advantages over DWT in shift invariance and directionality for certain signal problems. Based on these investigations obtained when the input signal to both DWT and DTWT is a step function, we plan to analyze the energy packing efficiency properties statistically towards the high frequency subbands and edges in decomposed images on both transforms.

Keyword(s)

小波轉換
對偶樹
複數小波
能量集中效能
Wavelet transform
Dual tree
Complex wavelets
Energy packing efficiency

DSpace CRIS

Dual-Tree Wavelet Transform and Applications

基本資料

Description