Alternating direction exterior point continuation method (ADEPCM) is proposed to solve the

l

1-regularization problem

which is the classic problem of signal compression and reconstruction for compressed sensing (CS).The first step of ADEPCM is to express the

l

1-regularization problem of the sparse coefficient in the transform domain as an equivalent constrained optimization problem by using variable splitting (VS) technology.Then

by introducing the penalty function

the two variables are alternatively minimized by Gauss-Seidel method

and the penalty

variable is updated by a continuation scheme

and then the sparse coefficient in the transform domain is reconstructed.Finally

the original signal is reconstructed by the orthogonal inverse transform.And the experimental simulations demonstrate that the ADEPCM algorithm yields a slightly higher peak signal to noise ratio (PSNR) reconstructed image as well as a much faster convergence rate as compared to some existing reconstruction algorithms.