A New Momentum Gradient Projection Methods For Sparse Signal Reconstruction

Compressed sensing(CS)is a new sampling theory.It has a wide range of applications in atmosphere,wireless communication,geology and other fields.CS samples the sparse signal with the bandwidth less than that of Nyquist sampling law,and reconstructs original signal with very high probability.Sparse signal reconstruction is the core content of compressed sensing theory,and refers to the reconstructed algorithms for recovering the original signal from the sparse signal.Two methods are proposed by using the convex combination of the neg-ative gradient direction and the momentum term as the search direction.The first method adopts backtracking line search.Under mild condition-s,the method is proved to be globally convergent.The second method takes the exact line search step,and dynamically select the momentum parameters,which speeds up the convergence of the algorithm.Numerical experiments show that with existing methods of solving large-scale regular-ized least squares problem,two new algorithms both in time and in signal reconstruction quality are competitive.