適用於簡單圖形與本質模態函數之先進壓縮技術

Advanced Compression Techniques for Simple Images and Intrinsic Mode Functions

陳盈柔(Ying-Jou Chen)

指導教授 ： 丁建均

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.02574

摘要

為了達到有效率的資料傳輸與節省儲存資源，資料壓縮技術扮演了不可或缺的角色。以數位影像的應用為例，當今最被廣泛使用的JPEG影像壓縮標準以及最新的JPEG2000靜態影像壓縮標準，皆是數位影像資料壓縮的實際應用。儘管現今之壓縮標準大多能提供不錯的壓縮成果，但隨著人們對資料品質以及傳輸效率的要求，更先進的資料壓縮演算法仍然是當今一個重要的研究領域。
　　本篇論文分別提出針對簡單圖形與本質模態函數的先進壓縮技術。在第一部分，我們設計了一個能夠提升簡單圖形壓縮效率的演算法，此壓縮技術能提供比JPEG與JPEG2000更佳之壓縮成效。第二部分，我們探討了針對本質模態函數的壓縮方法並提出一個有效率的壓縮方式。
　　在簡單圖形的壓縮技術方面，我們利用以分割圖形為基礎的壓縮方法，在此方法中，我們將對圖形的描述歸納成兩大類，分別為邊緣資訊的描述與內容資訊的描述。首先，簡單圖形將根據其影像之像素值被分割成若干個區域，每個區域內部之像素值將高度集中於少數幾個像素值中。接下來，我們將利用一個二次多項式的邊緣近似技術來記錄區域的分割方式，以上便是邊緣資訊的相關資料。在內部資訊的描述方面，我們將根據各區域內部像素值的分布型態對區域進行分類，再對各區域進行主要像素值投票的動作以產生一個近似影像。接下來，殘值影像將能由原簡單圖形與近似影像求得，針對殘值影像的編碼，我們提出一個利用鄰近像素值預測的模型與區域分類協助的編碼方式來提升對殘值影像的壓縮效率。模擬結果顯示，此壓縮技術相較於JPEG與JPEG2000壓縮標準及其他現存之壓縮演算法，能夠對簡單圖形達到較高之壓縮成效。
　　針對本質模態函數的壓縮方法，我們探討了本質模態函數所屬之分量數與各種壓縮方式之壓縮效率的關係，設計出一個能夠針對不同分量數的本質模態函數轉換壓縮方式的適應性演算法。假設本質模態函數的分量總數為N，若欲壓縮之本質模態函數的分量數不大於N/2，我們將採用轉換編碼的方式來進行壓縮；若此本質模態函數所屬之分量數大於N/2，我們提出了一個增強型極值編碼的方法對其進行壓縮。在增強型極值編碼的方法中，首先我們將對本質模態函數進行特徵點的擷取，再對所擷取之特徵點做預測編碼來降低資料間之相關性以提升壓縮效率。由實驗結果發現我們所提出之針對不同分量數的本質模態函數轉換壓縮方式的適應性演算法相較於使用單一編碼模式的壓縮方法確實能夠針對本質模態函數達到較好的壓縮成果。

關鍵字

影像編碼 ； 影像壓縮 ； 邊緣近似 ； JPEG ； JPEG2000 ； 預測編碼 ； 轉換編碼 ； 本質模態函數 ； 經驗模態分解

並列摘要

In this thesis, two compression techniques are proposed. First, we design an image coding scheme for simple images in order to enhance the compression efficiency of the state-of-the-art compression standards, namely Joint Photographic Expert Group (JPEG) and JPEG2000. Second, we study the compression method for the Intrinsic Mode Functions (IMF) and propose an effective coding approach for IMFs.
For simple image compression, a segmentation-based approach is developed. In this approach, the descriptors of the simple image are divided into two parts: the contour-related information and the content-related information. First, the simple image is partitioned into several parts where the pixel values are highly concentrated. A novel boundary description technique based on 2nd order polynomial approximation is adopted and the descriptions are stored as the contour-related information. Second, the content within each partition is classified by the proposed criterion following with a mechanism named majority voting to generate the approximated image. Then, the residual image could be derived by the original simple image and the approximated image. To encode the residue, we propose a context-based arithmetic coder based on the neighborhood information and the classification derived in the second step to improve the compression efficiency. The content-related information includes the classification for each partition, the approximated image, and the residue. Simulations show that the proposed compression technique outperforms JPEG, JPEG2000, and other existing methods for simple image compression.
For the compression of the IMF, we investigate the characteristics of the IMFs with different rankings and design an adaptive scheme that using different coding methods for the IMF with different rankings. If the total number of the IMFs is N, while dealing with the IMF with ranking number less or equal to N/2, the transform coding would be applied for compression. Otherwise, the newly devised approach named enhanced extreme coding would be used to record the IMF. In the enhanced extreme coding approach, the point selection is performed firstly following by the point encoding process. The point selection procedure is to find the significant points of the IMF while the point encoding process uses the concept of predictive coding to eliminate the correlations among the selected points. The proposed mode switching compression technique achieves better compression performance than the single mode compression scheme.

並列關鍵字

Image Coding ； Image Compression ； Boundary Approximation ； JPEG ； JPEG2000 ； Predictive Coding ； Transform Coding ； Intrinsic Mode Function ； Empirical Mode Decomposition

參考文獻

Compression Basics

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Transform Coding

[6] I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” Information Theory, IEEE Transactions on, vol. 36, no. 5, pp. 961-1005, 1990.