On Modified l_1-Minimization Problems in Compressed Sensing

2013 ◽  
Author(s):  
Man Bahadur Basnet
Keyword(s):  
Compressed Sensing ◽  
Minimization Problems

scholarly journals Nonmonotone Adaptive Barzilai-Borwein Gradient Algorithm for Compressed Sensing

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yuanying Qiu ◽  
Jianlei Yan ◽  
Fanyong Xu
Keyword(s):  
Global Convergence ◽  
Compressed Sensing ◽  
Convergence Result ◽  
Gradient Algorithm ◽  
Search Direction ◽  
Quadratic Model ◽  
Minimization Problems ◽  
Norm Minimization ◽  
Descent Property ◽  
Favorable Structure

We study a nonmonotone adaptive Barzilai-Borwein gradient algorithm forl1-norm minimization problems arising from compressed sensing. At each iteration, the generated search direction enjoys descent property and can be easily derived by minimizing a local approximal quadratic model and simultaneously taking the favorable structure of thel1-norm. Under some suitable conditions, its global convergence result could be established. Numerical results illustrate that the proposed method is promising and competitive with the existing algorithms NBBL1 and TwIST.

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