Abstract: By designing a new approximation of Hessian matrix, we obtained a new quadratic approximate model of function in the current iteration point, and used this model and delay strategy to obtain a new stepsize. Combined with the new stepsize, we proposed a modified iteratively approximated gradient projection algorithm for solving the problem of sparse signal reconstruction in compressed sensing, and gave the proof of convergence. Experimental result shows that the proposed algorithm can not only restore the nonzero elements in the original signal, but also reconstruct the signal effectively. Compared with the classical algorithm, the proposed algorithm has higher reconstruction efficiency.

Key words: compressed sensing (CS), Hessian matrix, stepsize, sparse reconstruction