提昇型離散小波轉換之研究及其在影像壓縮中之應用

Abstract

繼離散型餘弦轉換 (discrete cosine transform; DCT) 被廣泛應用於影像壓縮領域之後，離散型小波轉換 (discrete wavelet transform; DWT) 是目前學術界和工業界研究、發展的重點，並且已經被新一代的靜態影像壓縮標準 (如 JPEG2000) 和動態影像壓縮標準 (如 MPEG-4，H.264/AVC) 所採用。早期的離散型小波轉換其實現方式是基於迴旋計算 (convolution-based) 方式，而新一代的離散型小波轉換其實現方式是所謂提昇型(lifting-based) 。「提昇型離散小波轉換」 (lifting-based DWT)具有計算效率高、節省記憶空間、可執行整數至整數小波轉換、適合平行處理，以及在某些場合無邊界延伸的問題等優點。又因其使用上非常具有彈性，所以目前仍然是大家研究的重點。 本論文首先討論方向適應型離散小波轉換 (direction-adaptive DWT) ，然後提出應用於任意形狀物體影像的提昇式形狀適應型離散小波轉換 (lifting shape-adaptive DWT)，以及可以應用於任意形狀影像、且具方向適應性的形狀方向適應型離散小波轉換 (shape-direction-adaptive DWT；SDA-DWT)。由實驗結果得知本論文提出的新方法除了保有提昇型離散小波轉換的優點之外，因為具有形狀及方向上的適應性，故可以在有限的代價上獲得影像壓縮效能的顯著提昇。除此之外我們也討論結合提昇型離散小波轉換 (lifting-based DWT) 和向量量化 (vector quantization; VQ) 來改善影像壓縮效率的一些方法。

After the discrete cosine transform (DCT) was widely used in image compression, discrete wavelet transform (DWT) was the new dominated transform for research and industrial applications, and it has been adopted in the new still-image compression standards (e.g. JPEG2000) and video compression standards (e.g. MPEG-4 and H.264/AVC). In literature, the realization of DWT was convolution-based in early days, and for better computation efficiency, saving memory space, integer-to-integer transform, parallel processing, and boundary extension problem the lifting-based DWT was proposed later. Lifting-based DWT is still an important research topic, since it is more flexible than the convolution-based DWT to adopt new functionalities. In this dissertation, the lifting-based DWT was studied, and a lifting-based direction-adaptive DWT was discussed. Then, the lifting-based shape-adaptive DWT (LSA-DWT) and the lifting-based shape-direction-adaptive DWT, which was adaptive in shape and direction, were proposed. Because SDA-DWT has the adaptabilities of shape and direction, by paying affordable cost, we can achieve superior improvement in image compression. Beside lifting-based SA-DWT and SDA-DWT, the combination of lifting-based DWT and vector quantization (VQ) was discussed in the dissertation.