改善格倫布編碼與 JPEG2000 之影像壓縮技術

Abstract

隨著網路以及多媒體的進步，人們對於影像以前影片的需求越來越高了。在過去，人們對於影像以及影片的需求僅止於清晰的圖片或是撥放順暢的影片即可。但隨著時代的進步，這些已經不能滿足人們的需求。許多高解析度、高品質的影像以及影片等規格紛紛出現，像是HD高規格的影片。因為如此，所以影像以及影片的容量也隨之增加。因為這些高規格的影像以及影片需要大量的儲存容量，所以許多不同的壓縮技術也隨之產生。最有名的影像壓縮技術應該非JPEG莫屬，它是Joint Photographic Experts Group的縮寫。JPEG是世界上最有名的影像壓縮標準，而且直到現在都還是廣為全世界所使用。 霍夫曼編碼是JPEG裡面所使用的熵編碼方法，而且也是世界上有名的熵編碼方法之一。然而當一個輸入資料呈現幾何分布的時候，霍夫曼編碼會無法處理這樣類型的資料。為了解決這類型的問題，格倫布編碼就隨之誕生了。格倫布編碼也是一種熵編碼方法，而且特別是對於輸入資料呈現幾何分布的時候，格倫布編碼特別的有效。而且相較於霍夫曼編碼需要紀錄編碼表才可以將資料解碼，格倫布編碼不需要紀錄編碼表就可以將資料解碼。但是格倫布編碼也有缺點，當輸入資料不呈現幾何分布的時候，格倫布編碼的效果就無法達到那麼好。另外，通常我們的輸入資料都是有正數跟負數的，但是格倫布編碼只適用於正數。也就是說，當輸入資料有負數或是呈現非幾何分布的時候，我們就不適合用格倫布編碼去處理。為了解決這個問題，我們提出了改良過後的格倫布編碼以及非對稱的幾何分布模型。改良過後的格倫布編碼以及非對稱的幾何分布模型可以使用在許多地方，而且它的效果也非常好。 此外，也是有許多不同的壓縮方法也非常有名，像是JPEG2000以及SPIHT等，也都比JPEG擁有更好的壓縮效率以及品質。在JPEG2000裡面，算術編碼是他的熵編碼方法，而且在JPEG2000使用的算術編碼中，它的機率分布表示固定的。因為如果要把每個機率分布表都記錄下來的話需要很多的儲存空間，所以JPEG2000是採用統一的機率分布表來處理每一筆資料，而且仍然有很好的壓縮效果。為了想辦法改善機率分布表的問題，我們提出了新的算術編碼方法，它不僅可以使用多個機率分布表，而且它整體的壓縮效果比JPEG2000更為優秀。 緩衝暫存空間在影像壓縮中也是個值得探討的問題。因為現在的隨身裝置，像是數位相機，智慧型手機等等的體積越來越小，所以在這些裝置上的儲存空間也越來越珍貴。在使用相同的緩衝暫存空間來達到更好的影像壓縮品質或許會是一個很好的研究方向。在此我們提出了一個新的方法，結合了離散餘弦轉換以及離散小波轉換。相較於傳統的JPEG標準，我們的方法跟他們在緩衝暫存空間的需求上相同，但卻有比他們更好的壓縮效果。

With the advancement of the Internet and the multimedia, the demand of people in image and video becomes higher and higher. In the past days, the requirements may be just a clear photo or a smooth video, but people did not satisfy with that. So the high quality image and video have been come out, such as high resolution pictures, high definition (HD) video, and full high definition (full HD) video. Because the size of multimedia data becomes higher, so people need to find some new ways to deal with the high data size of the multimedia. To solve the problem, there are some of the compression techniques. The most well-known image compression technique is Joint Photographic Experts Group 0[2][3], which is also called JPEG. JPEG is the most popular standard in image compression and still have been widely used in the worldwide nowadays. The Huffman coding is used in JPEG, and it is the most famous entropy coding method and widely used in many images and video coding standards. Nevertheless, Huffman coding cannot be used if the source is ideally geometrically distributed because the number of elements is infinite. But Golomb coding can do well when the source is ideally geometrically distributed. Golomb coding is a good entropy coding method when the data source is geometric distribution, and it does not need coding table, but Huffman coding does. Nonetheless when the input data is not geometric distribution, the Golomb coding may not be a good choice. Moreover, the input data may be positive and negative numbers, but the Golomb coding is only for positive numbers. To solve the problem, we proposed the modified Golomb coding with asymmetric two-sided geometric distributed data. It can be used in many ways, and can have better performance. In addition, there are still some famous image compression standards, such as JPEG2000, SPIHT, and …etc. Some of them have better performance in compression than that of JPEG. JPEG2000 [4][7][8] is another worldwide image compression standard, and can have better compression ratio and image quality than JPEG does. The arithmetic coding is used in the encoder of JPEG2000, and its probability table is fixed. Because record every probability table needs lots of storage space, it may be not efficient to record every probability table and the compression ratio may be worse. So the JPEG2000 standard used a fixed probability table to deal with everything, and still have good performance. To improve this part, we proposed a new kind of arithmetic coding, which can use arithmetic coding with different probability table, but still have better compression ratio than that of JPEG2000. The buffer size of the image compression standard is still another problem. Due to the size of mobile systems, such as digital cameras and cell phones, is becoming smaller today. The storage space of those systems may be more precious. Using the same buffer size to have the better image quality may be another good topic for image compression. To deal with this topic, we proposed a new method, which is combined discrete cosine transform and discrete wavelet transform. Compare to the JPEG standard, our method need the same buffer size as JPEG, but have better performance than that of JPEG.