Abstract: The sparse representation based on over-complete dictionary is a new image representation theory. The redundancy of over-complete dictionary can make it effectively capture the geometrical characteristics of the images. SAR image compression is achieved based on over-complete dictionary sparse representation. Only the sparse decomposition coefficients and the index are needed to be stored in order to seize the image’s information. A learning method—K-SVD is adopted to design the dictionary. Because the training examples are all from the image itself, the dictionary should be more approximate to the image’s structure. The simulation implies the proposed method is useful for SAR image compression and it outperforms the DCT based Jpeg method and the wavelet based EZW and SPIHT method.

Key words: sparse representation, image compression, K-SVD algorithm, wavelet transform

摘要： 基于过完备字典的图像稀疏表示是一种新的图像表示理论，利用过完备字典的冗余性可以有效地捕捉图像的各种结构特征，从而实现图像的有效表示。采用基于过完备字典稀疏表示的方法实现SAR图像的压缩。为了得到表示图像所需要的信息，只需要存储稀疏分解的系数极其对应的坐标，实现压缩的目的。采用K-SVD算法实现过完备字典的构造。K-SVD算法是一种基于学习的算法，由于训练样本全部来自于图像本身，因此字典能够更好地逼近图像本身的结构，实现稀疏表示。仿真表明对于SAR图像的压缩，算法是有效的，并且优于基于DCT的Jpeg算法和基于小波变换的EZW和SPIHT算法。

关键词: 稀疏表示, 图像压缩, K-SVD算法, 小波变换