|Table of Contents|

[1] Liao Fan, Yan Lu, Wu Jiasong, Han Xu, et al. Algorithm for reconstructing compressed sensing color imagingusing the quaternion total variation [J]. Journal of Southeast University (English Edition), 2015, 31 (1): 51-54. [doi:10.3969/j.issn.1003-7985.2015.01.009]
Copy

Algorithm for reconstructing compressed sensing color imagingusing the quaternion total variation()
基于四元数域总变差方法的压缩感知彩色图像重建算法
Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
31
Issue:
2015 1
Page:
51-54
Research Field:
Computer Science and Engineering
Publishing date:
2015-03-30

Info

Title:
Algorithm for reconstructing compressed sensing color imagingusing the quaternion total variation
基于四元数域总变差方法的压缩感知彩色图像重建算法
Author(s):
Liao Fan1;  Yan Lu1;  Wu Jiasong1;  2;  Han Xu1;  Shu Huazhong1;  2
1Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China
2Centre de Recherche en Information Médicale Sino-français(CRIBs), Southeast University, Nanjing 210096, China
廖帆1;  严路1;  伍家松1;  2;  韩旭1;  舒华忠1;  2
1东南大学影像科学与技术实验室, 南京210096; 2东南大学中法生物医学信息研究中心, 南京210096
Keywords:
total variation;  compressed sensing;  quaternion;  sparse reconstruction;  color image restoration
总变差;  压缩感知;  四元数;  稀疏重建;  彩色图像恢复
PACS:
TP391
DOI:
10.3969/j.issn.1003-7985.2015.01.009
Abstract:
A new method for reconstructing the compressed sensing color image by solving an optimization problem based on total variation in the quaternion field is proposed, which can effectively improve the reconstructing ability of the color image. First, the color image is converted from RGB(red, green, blue)space to CMYK(cyan, magenta, yellow, black)space, which is assigned to a quaternion matrix. Meanwhile, the quaternion matrix is converted into the information of the phase and amplitude by the Euler form of the quaternion. Secondly, the phase and amplitude of the quaternion matrix are used as the smoothness constraints for the compressed sensing(CS)problem to make the reconstructing results more accurate. Finally, an iterative method based on gradient is used to solve the CS problem. Experimental results show that by considering the information of the phase and amplitude, the proposed method can achieve better performance than the existing method that treats the three components of the color image as independent parts.
提出了一种基于四元数域总变差方法的彩色图像压缩感知重建算法, 该算法可有效提高彩色图像的重建能力.首先, 将彩色图像从RGB空间转换到CMYK空间, 并将CMYK空间的各个分量赋值给一个四元数矩阵.同时通过四元数的欧拉形式, 将四元数矩阵转换为幅度和相位的信息.然后, 为了完善重建的结果, 将四元数矩阵的幅度和相位作为压缩感知优化方程新的平滑约束项.最后, 用基于梯度的迭代算法来求解压缩感知优化方程.实验结果表明, 所提出的算法考虑了幅度和相位的信息, 比现有的将彩色图像的3个分量当作独立分量的算法效果好.

References:

[1] Candes E J, Tao T. Decoding by linear programming [J]. IEEE Transactions on Information Theory, 2005, 51(12): 4203-4215.
[2] Donoho D L. Compressed sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[3] Candès E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information [J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
[4] Baraniuk R. Compressive sensing [J]. IEEE Signal Processing Magazine, 2007, 24(4):118-121.
[5] Ell T A, Sangwine S J. Hypercomplex Fourier transforms of color images [J]. IEEE Transactions on Image Processing, 2007, 16(1): 22-35.
[6] Mairal J, Elad M, Sapiro G. Sparse representation for color image restoration [J]. IEEE Transactions on Image Processing, 2008, 17(1): 53-69.
[7] Majumdar A, Ward R K. Compressed sensing of color images [J]. Signal Processing, 2010, 90(12): 3122-3127.
[8] Yu S, Khwaja A S, Ma J. Compressed sensing of complex-valued data [J]. Signal Processing, 2012, 92(2): 357-362.
[9] Dai Q, Sha W. The physics of compressive sensing and the gradient-based recovery algorithms [EB/OL].(2009-06-08)[2014-04-14]. http://arxiv.org/abs/0906.1487.
[10] Poon C. On the role of total variation in compressed sensing-structure dependence [EB/OL].(2014-01-22)[2014-04-14]. http://arxiv.org/pdf/1407.5337.
[11] Oliveri G, Anselmi N, Massa A. Compressive sensing imaging of non-sparse 2D scatterers by a total-variation approach within the born approximation[J]. IEEE Transactions on Antennas and Propagation, 2014, 62(10): 5157-5170.

Memo

Memo:
Biographies: Liao Fan(1983—), male, graduate; Shu Huazhong(corresponding author), male, doctor, professor, shu.list@seu.edu.cn.
Foundation items: The National Basic Research Program of China(973 Program)(No.2011CB707904), the National Natural Science Foundation of China(No.61201344, 61271312, 61073138), the Specialized Research Fund for the Doctoral Program of Higher Education(No.20110092110023, 20120092120036), the Natural Science Foundation of Jiangsu Province(No.BK2012329).
Citation: Liao Fan, Yan Lu, Wu Jiasong, et al. Algorithm for reconstructing compressed sensing color imaging using the quaternion total variation[J].Journal of Southeast University(English Edition), 2015, 31(1):51-54.[doi:10.3969/j.issn.1003-7985.2015.01.009]
Last Update: 2015-03-20