运用压缩感知理论的图像稀疏表示与重建

doi:10.3969/j.issn.0255-8297.2014.05.002

应用科学学报 ›› 2014, Vol. 32 ›› Issue (5): 447-452.doi: 10.3969/j.issn.0255-8297.2014.05.002

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运用压缩感知理论的图像稀疏表示与重建

丰祥1,2，万旺根1,2

1. 上海大学通信与信息工程学院，上海200444
2. 上海大学智慧城市研究院，上海200444

收稿日期:2013-12-12 修回日期:2014-01-15 出版日期:2014-09-23 发布日期:2014-01-15
作者简介:丰祥，博士生，研究方向：计算机视觉与图形处理，E-mail: fengxiang0727@shu.edu.cn；万旺根，教授，博导，研究方向：计算机视觉与智能信息处理，E-mail: wanwg@staff.shu.edu.cn
基金资助:
国家自然科学基金（No.61373084）；国家“863”高技术研究发展计划基金（No.2013AA01A603）；上海市教育委员会科研创新
项目基金（No.14YZ011）资助

Sparse Representation and Reconstruction of Image Based on Compressed Sensing

FENG Xiang1,2, WAN Wang-gen1,2

1. School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China
2. Institute of Smart City, Shanghai University, Shanghai 200444, China

Received:2013-12-12 Revised:2014-01-15 Online:2014-09-23 Published:2014-01-15

摘要/Abstract

摘要： 讨论了压缩感知理论用于图像稀疏重建的基本流程. 采用正交匹配追踪重建算法和正交归一化的随机高斯测量矩阵，对离散余弦变换和离散小波变换两种稀疏表示算法进行分析比较，通过调节实验图像的分块大小和采样率大小、采样率和稀疏表示算法对重构效果和效率的影响. 在图像的稀疏表示方面，离散余弦变换整体上比离散小波变换性能更好. 为了在重构效果与效率之间取得平衡，需要合理选择分块大小和采样率.

关键词: 压缩感知, 稀疏表示, 图像重建, 匹配正交追踪

Abstract: Application of compressed sensing to sparse reconstruction of image is discussed. An orthogonal matching pursuit algorithm for reconstruction and Gaussian random matrix for measurement are used. We analyze and compare DCT and DWT both theoretically and experimentally. By adjusting the sub-block size and sampling rate of the experimental images, we make a comprehensive comparison of sub-block size,sampling rate and influences of the two algorithms on effectiveness and efficiency of sparse reconstruction in terms of runtime, reconstruction error and visual effects. In sparse image representation, DCT exhibits better overall performance than DWT. In order to achieve an optimal balance between reconstruction effectiveness and efficiency, a reasonable choice of sub-block size and sampling rate is required.

Key words: compressed sensing, sparse representation, image reconstruction, orthogonal matching pursuit

中图分类号:

TP391

丰祥1,2，万旺根1,2. 运用压缩感知理论的图像稀疏表示与重建[J]. 应用科学学报, 2014, 32(5): 447-452.

FENG Xiang1,2, WAN Wang-gen1,2. Sparse Representation and Reconstruction of Image Based on Compressed Sensing[J]. Journal of Applied Sciences, 2014, 32(5): 447-452.

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运用压缩感知理论的图像稀疏表示与重建

Sparse Representation and Reconstruction of Image Based on Compressed Sensing

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