小波轉換與改良式編碼法在影像壓縮方面的應用

Abstract

影像壓縮的主要目的是要減少資料儲存量，而資料量之所以可以減少 ，則是利用了在影像本身中存在著累贅資料，所以簡單來說，要去除掉這 些累贅的影像資料即可達到影像壓縮的目的。通常的作法先是將圖像的頻 帶作分離，再各別依據視覺能夠察覺的程度做資料取捨，而這項程序可以 藉由分頻濾波器來完成。在設計這樣的濾波器時，本論文考慮使用離散小 波轉換，其主因是依據離散小波轉換的觀念而設計出的分頻濾波器，不僅 具有很好的頻帶分離效果，且分離出來的信號仍舊保留著影像空間上的資 訊。經由濾波器處理之後，其高頻部份裡的灰階統計圖可以被視作為廣義 高斯分佈，於是在減低資料量時，本論文採用了純量量化器，並且對最佳 量化器作探討；另一個高頻部份的處理方式，則是看其能量的多寡來作取 捨。至於低頻的部份，我們先使用數值捨入來達成豐富資料的保存目的， 再來採用差分脈衝調變編碼法作資料壓縮。編碼方面，當高頻部份經由量 化過後，通常不僅會呈現一長串連續的資料，而且其熵值也很低的，所以 本論文嘗試使用不同的編碼方式。這些方法計有荷夫曼編碼法，Run- Length編碼法，結合 RLC與HC編碼法以及我們研發出的改良式Run-Length 編碼法。最後本論文藉由兩張常用的影像壓縮測試圖，說明改良式Run- Length編碼法在壓縮方面的優越表現。 The main purpose of image compression is to reduce the amount of data for storage or transmission. An image, in general, possesses a large of insignificant data which is called the redundancy component. More precisely, we could remove the redundancy by many techniques of image coding at the cost of reducing little fidelities if lossy coding methods were introduced. One of the efficient methods in image compression is the so called subband coding. The image can be separated into different frequency bands after applying the technique of subband coding. Moreover, the individual subimages are further processed from the acceptance of the visual point. In this thesis, the discrete wavelet transforms were adopted since the transforms not only split the original image into different frequency components perfectly but retain the information in spatial domain. After applying the discrete wavelet transforms, the histograms of higher frequency components can be considered tobe Generalized Gaussian Distributions. Following that, we choose the scalar quantizers to process the transformed data. The optimal scalar quantizer is also discussed. By the way, we usually drop some insignificant subimages if their energy is small enough. In the part of the lowest frequency subimage, which possesses the largest energy in general, the information contained is important so that the coding method, differential pulse code modulation, is suggested to maintain the image loyalty and to reduce the entropy. After taking the previous processing, the data was appeared continuously and had low-value entropy. In this thesis, we intend to use some coding methods, whichinclude the Huffman coding, the Run-Length coding, combination of Run-Length and Huffman coding and the revised Run-Length coding, to compress the data losslessly for getting better compression ratios. Finally, we describe the great performance in reconstruction fidelities and compression ratios of the revised Run-Length coding by two testbed images, Lena and Mandrill.