摘要
Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated with the dictionary were presented. This paper shows the recoverability of block-sparse signals are associated with the block structure when a random dictionary is given. Several probability inequalities are obtained to show how the recoverability changes along with the block structure parameters, such as the number of nonzero blocks, the block length, the dimension of the measurements and the dimension of the block-sparse representation signal. Also, this paper concludes that if the block-sparse structure can be considered, the recoverability of the signals wil be improved. Numerical examples are given to il ustrate the availability of the presented theoretical results.
Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated with the dictionary were presented. This paper shows the recoverability of block-sparse signals are associated with the block structure when a random dictionary is given. Several probability inequalities are obtained to show how the recoverability changes along with the block structure parameters, such as the number of nonzero blocks, the block length, the dimension of the measurements and the dimension of the block-sparse representation signal. Also, this paper concludes that if the block-sparse structure can be considered, the recoverability of the signals wil be improved. Numerical examples are given to il ustrate the availability of the presented theoretical results.
基金
supported by the International Cooperation Project of Guangdong Natural Science Fund(2009B050700020)
the Natural Science Foundation of China-Guangdong Natural Science Foundation Union Project(U0835003)
作者简介
Corresponding author.Yuli Fu was born in 1959, He received his Ph.D. degree in control theory and engineering from the Huazhong University of Science and Technology, in 2000. From 2000 to 2002, he was a postdoctoral researcher in the School of Electronic and Information Engineering at the South China University of Technology. Now, he is a professor in the same university. His research interests are focused on adaptive signal processing and artificial intelligent. E-mail： fuyuli@scut.edu.cn,lian Zou was born in 1983. He received his Ph.D. degree in signal and information processing from the South China University of Technology in 2013. No,,v. he is an assistant professor in Yangtze University. His research interests are focused on adaptive signal processing and numerical optimization. E-mail： zoujianjz@gmail.comQiheng Zhang was born ill 1986. He received his B.S. degree in electrical engineering from the Information Engineering University, in 2008. He is currently working toward the Ph.D. degree in the School of Electronic and Information Engineering, South China University of Technology. His research interests include compressed sensing and image fusion. E-mail： qiheng.zhang@gmail.comHaifeng Li was born in 1984. He received his M.S. degree in the School of Mathematics and Information Science, Henan Normal University, in 2011. He is currently purst, ing his Ph.D. degree in the School of Electronic and Information Engineering, South China University of Technology. His research interests include compressed sensing and convex programming. E-mail： lihaifengxx@126.com
