本文为印度Rourkela国立技术研究所（作者：Swastik Das）的学士论文，共47页。

图像压缩解决了减少表示数字图像所需的数据量的问题。压缩是通过去除三个基本数据冗余中的一个或多个来实现的：（1）编码冗余，当使用小于最佳（即最小长度）的码字时出现；（2）由于图像像素之间的相关性而产生的像素间冗余；（3）由于数据导致的心理视觉冗余，被人类视觉系统忽略（即视觉上不重要的信息）。

哈夫曼码包含每个源符号（例如灰度值）的最小可能码符号数（例如位），但受源符号一次编码一个符号的约束。因此，将哈夫曼编码与离散余弦变换（DCT）减少图像冗余的技术相结合，在很大程度上有助于图像数据的压缩。

离散余弦变换（DCT）是变换编码的一个例子。当前的JPEG标准使用DCT作为基础。DC将最高能量重新定位到图像的左上角，较小的能量或信息被转移到其他区域。DCT可以快速计算，最适合于边缘光滑的图像，如人类拍摄的照片。与傅立叶变换不同，DCT系数都是实数。反离散余弦变换（IDCT）可以用来从图像的变换表示中提取图像。离散小波变换（DWT）在信号处理和图像压缩中得到了广泛的应用，小波编码由于其固有的多分辨率特性，特别适用于具有可扩展性和可容忍退化的应用。最近，JPEG委员会发布了基于DWT的新图像编码标准JPEG-2000。

Image Compression addresses the problem of reducing the amount of data required to represent the digital image. Compression is achieved by the removal of one or more of three basic data redundancies: (1) Coding redundancy, which is present when less than optimal (i.e. the smallest length) code words are used; (2) Interpixel redundancy, which results from correlations between the pixels of an image & (3) psycho visual redundancy which is due to data that is ignored by the human visual system (i.e. visually nonessential information). Huffman codes contain the smallest possible number of code symbols (e.g., bits) per source symbol (e.g., grey level value) subject to the constraint that the source symbols are coded one at a time. So, Huffman coding when combined with technique of reducing the image redundancies using Discrete Cosine Transform (DCT) helps in compressing the image data to a very good extent. The Discrete Cosine Transform (DCT) is an example of transform coding. The current JPEG standard uses the DCT as its basis. The DC relocates the highest energies to the upper left corner of the image. The lesser energy or information is relocated into other areas. The DCT is fast. It can be quickly calculated and is best for images with smooth edges like photos with human subjects. The DCT coefficients are all real numbers unlike the Fourier Transform. The Inverse Discrete Cosine Transform (IDCT) can be used to retrieve the image from its transform representation. The Discrete wavelet transform (DWT) has gained widespread acceptance in signal processing and image compression. Because of their inherent multi-resolution nature, wavelet-coding schemes are especially suitable for applications where scalability and tolerable degradation are important. Recently the JPEG committee has released its new image coding standard, JPEG-2000, which has been based upon DWT.

1 引言

2 图像压缩

3 基于离散余弦变换的图像压缩

4 基于离散小波变换的图像压缩

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