Efficient minimization for dictionary based sparse representation and signal recovery

This paper provides an efficient minimization algorithm for dictionary based sparse representation and its application in some signal recovery problems. Dictionary has shown great potential in effectively representing various kinds of signals sparsely. However the computational cost associated with dictionary based sparse representation can be tremendous, especially when the representation problem is coupled with the complex encoding processes of the signals. The proposed algorithm tackles this problem by alternating direction minimizations with the use of Barzilai-Borwein's optimal step size selection technique to significantly improve the convergence speed. Numerical experiments demonstrate the high efficiency of the proposed algorithm over traditional optimization methods. © 2011 ACM.