中文摘要：

JPEG和JPEG 2000标准在高压缩率条件下解压缩得到的图像会出现失真,利用冗余字典的稀疏表示可以在高压缩率下获得较高质量的解压缩图像,但单一的冗余字典表示不能充分反映图像结构。针对上述问题,提出一种利用分类冗余字典进行稀疏表示从而实现图像压缩的方法。利用KSVD方法训练平滑和细节2类冗余字典,根据字典原子与图像信号相关系数和表示误差的关系,通过改进的正交匹配追踪算法对图像进行稀疏表示,分别得到平滑表示系数和忽略较小取值的细节表示系数,将这些系数及其对应字典原子的索引值进行量化编码,完成图像压缩。实验结果表明,与JPEG、JPEG 2000以及基于单一冗余字典的方法相比,该方法在高压缩率条件下可以获得视觉效果更好的解压缩图像。

英文摘要：

When images are decompressed at high compression rate,the compression standard JPEG and JPEG 2000 will cause distortion. The use of redundant dictionary for sparse representation can obtain better quality of image decompression at high compression rates,but the single redundant dictionary cannot fully represent the structure of image.In view of the above problems,an image compression method based on sparse representation of classified redundant dictionary is proposed. It uses Kernel Singular Value Decomposition（ KSVD） algorithm to train smoothing and detailed redundant dictionaries respectively, and uses improved Orthogonal Matching Pursuit（ OMP） algorithm to represent images sparsely according to the relationship between the correlation coefficient of dictionary atoms and image signals and the representation error, so that smoothing representation coefficients and detailed representation coefficients without much lower values are respectively obtained. Finally,these coefficients and their corresponding indexes of dictionary atoms are quantified coded to compress images. Experimental results show that the proposed method can get decompressed images with better visual effect compared with JPEG, JPEG 2000 and the method based on single redundant dictionary at the high compression ratio.